Algebra 2 Trigonometry Regents

FRANKFORT, N.Y. (WKTV) - The Senior Vice-President of Texas Instruments paid a visit to Frankfort-Schuyler High School on Tuesday in order to see first hand how their new advanced calculators are being used.

Texas Instruments calculators were often the most important tool to students in 11th and 12th grade mathematics. However, as technology has changed, the company has created newer, more advanced devices.

Mrs. Audrey Cucci's math class at Frankfort-Schuyler is just one of thousands of districts across the state who use the new devices.!

"It's a special-purpose, handheld device that is aimed specifically at helping students learn math and science," said Melendy Lovett, Senior Vice-President of Texas Instruments.

Cucci's class is preparing for the upcoming regents exams. From calculus, to algebra, to trigonometry, the 11th graders are interactive with their learning thanks to a new device - the TI Nspire calculator.

Cucci said she just started using the Nspire calculators this year, and that the students are already comfortable with the new devices because they are so used to new technology. She says their adaptive abilities to the ever-changing technology has shown in their work.

"I have found from not using them last year to using them this year...I have seen a great boost in grades," Cucci said. "My kids are probably, on average, ten points higher than my kids this year."

"What she does and how she incorporates the new technology really enhances the ! classroom," said Dana Morse, the New York State Education Tech! nology C onsultant for Texas Instruments. "And I thought it would be great to show people from Dallas how the technology is being used to reach out to the students and raise the level of the curriculum."

Algebra 2 Trigonometry Regents

old geometry regents exams

Related Rates Exam Review

SUMMARY

• Exam Review Intro
• Related Rates: Area, Perimeter, and Diagonal of a Rectangle
• Related Rates: Shadows Including Similar Triangles
• Related Rates: Distance and Velocity and Spongebob!

Exam Review Intro

We do our exam review in three ways:

1. Doing mini-exams pre-test style
2. Doing questions in class related to rusty topics
3. Doing old exam free-response questions and study how each question evolved throughout the years and do 3 questions a night

Today's class we decided to do #2, reviewing related rates.


Related Rates: Area, Perimeter, and Diagonal of a Rectangle



The length (L), the width (W), and the rates of which the lengths (dL/dt) and widths (dW/dt) are changing.

By convention, we're going to designate an increasing rate as a positive rate and a decreasing rate as a negative rate.

a) We know the formula for the area of a rectangle as A = L * W, where A is area, L is length, and W is width. Since we're looking for the rates of change (That's the definition of a derivative!) we differentiate the formula, with respect to time.

Since L * W is a product, we use The Product Rule to differentiate.

Since area, length, and width are all with respect to time--meaning that area, length, and width are functions of time--we must use The Chain Rule to differentiate.

Answer: dA/dt = 32 cm/s^2; increasing

b) ! We know the formula for the perimeter of a rectangle as P = 2L + 2W. Differentiate the formula using The Chain Rule, since P, L, and W are with respect to time--a function within a function! Then plug and chug.

Answer: dP/dt = -2 cm/s; decreasing

c) We know that the diagonal (D), the length (L), and the width (W) are related in The Pythagorean Theorem: the square of two sides (in this case, L and W) equals the square of the hypotenuse (D), so D^2 = L^2 + W^2. Differentiate the formula using The Power Rule and The Chain Rule.

< /a>
Answer: dD/dt = -33 cm/13 s; decreasing


Related Rates: Shadows Including Similar Triangles



We know the height of the lamppost (L = 16), the height of the man (M = 6), the rate at which the man walks toward the streetlight (db/dt = -5), and the length of the man's shadow from the base of the lamppost (b = 10).

Since the man is walking toward the lamppost, b! y convention, the rate is negative.

b) Using similar triangles, we can see that the ratio of L to M equals the ratio of s to b+s. We simplify our proportions and differentiate to determine the rates of change (That's the definition of a derivative!). To differentiate, we use The Product Rule and The Chain Rule--Refer to Related Rates: Area, Perimeter, and Diagonal of a Rectangle for reference. We plug in the numbers to obtain ds/dt.

Answer: -3 ft/sec

a) Note this question is underlined in blue. The exam would never ask you to do part B because you need to do part B anyways to answer part A. The rate of the tip of the man's shadow is dP/dt. To obtain dP/dt, we differentiate P = b + s.

Answer: -8 ft/sec


Related Rates: Distance and Velocity and Spongebob!

HOMEWORK!



HOUSEKEEPING

• Next scribe is bench.
• Wiki constructive modification due Sunday midnight.
• Developing Expert Voices projects due soon.
• AP calculus exam is in two weeks.
• Three AP calculus exam free-response per night.
• Homework: Olympic Spongebob!
• We will be reviewing applications of derivatives (related rates and optimization), applications of integrals (density and volume), and techniques of antidifferentiating (integration by! parts).
  

related rates problems and solutions

How to Solve Problems of Ratio and Proportions

Ratio and Proportions


The problems and ratio and proportions can be on the basis of unitary methods. For example if A can do a piece of work in 12 days. B is 20% more efficient than A. Find the number of days it takes B to do the same piece of work. It means If A is 100, B is 120. Then we do the calculations like this. We want to find out the number of days. So the days which are given are taken in the numerator. So we write

12

Then one quantity is 100 and 120. Now if A is 100 and B is 120, what will be the impact on the quantity we want to find out i.e. number of days. Definitely B will take less days. So we take 100 in the numerator and 120 in the denominator. And write

12 x (100/120) and calculate the required value.

Taking one more example, if 30 men working 7 hours a day can do a piece of work in 18 days, in how many days will 21 men working 8 hours a day do the same piece of work. Again we think like this: the quantity(days) that we want to find out, we take the corresponding quantity(18 days) in the numerator. Thus:

18

Now we find the impact of individual element on the number of days. Taking men, first there were 30men, now there are 21, So number of men have decreased so number of days will be more so we take greater quantity (30) in the numerator and 21 in the denominator as:

18 x (30/21)

Taking hours a day, first there were 7 hours per day, now there are 8 hours per day. So number of days to do a particular work will become less as the number of hours per day are increasing. So we take 7 ( less qty) in the numerator and the other in the denominator as:

18 x (30/21) x (7/8) Solving we can get the answer.

The questions can be asked about specific ratios e.g. Divide 581 into three parts such that 4 times the first may be equal to 5 times the second and 7 times the third.

In such cases the ratio will be ¼ : 1/5:1/7, Then divide the amount in this ratio.

In any two-d figure if the corresponding sides are in the ratio a: b, then there areas in the ratio a^2 :b^2. Eg. Sides of a hexagon becomes three times. Find the ratio of the areas of the new and the old hexagons. The ratio will be 9:1

The questions are also asked of Mixtures eg. A mixture contains milk and water in the ratio 8:3. On adding 3 liters of water, the ratio of milk to water becomes 2: 1. Find the quantity of milk and water in the mixture.

Here we proceed like this:

M : W

8:3 <-- Initial ratio

2:1<-- After adding three liters of water.

Now since there is no change in the milk , we make the ratio of both the quantities equal by multiplying the second ratio by 4. Then it looks like:

M: W

8:3 <-- Initial Ratio

8:4 <-- After adding 3 liters of water

-----

0: 1 <-- Difference in ratios.

-----

Thus increase in qty of water in ratio =1 ~ 3 liter actually, so Initial qty of milk must be (3/1) x 8= 24 liters and water (3/1) x 3 = 9 liters

This method is very powerful and can be used in such situations under varying exam conditions.

Or the questions can be asked like this: How many rupees, fifty paise coins and twenty-five paise coins of which the numbers are proportional to 2 ½, 3 and 4 are together worth Rs. 210. Here the ratio is 2 ½:3:4 = 5:6:8 Their proportional value= 5 x 1: 6/2: 8/4= 5:3:2, Now Divide 210 Rs. In this ratio we have value of rupees= 5/10 x 210= 105 Rs. So there are 105 coins of one rupee, Similarly value of 50 paise coins will be 3/10 x 210= 63 Rs. So there are 126 coins of 50 paise and so on.

Or it can be find the numbers which when added to the terms of the ratio 11:23 makes it equal to the ratio 4:7. Here we find a number that we add to the terms so that it becomes a multiple of 4 and then check. Adding 1 to 11 and 23 makes it equal to 12/24 but the ratio is not 1:2 . Then we add 5 to 11:23 and find that the numbers become 16:28 or the ratio becomes 4:7 so the number that should be added is 5.

Most of the questions in ratio and proportions can be solved by this method.

You can evaluate yourself taking this test.

solve proportions

Week of May 24-28, 2010

Monday, May 24 - all assignments are due on Tuesday
Hon. Geom. - Review Ch. 10. 6 - 10.7 **Study for short test - tomorrow

Hon. Alg. 8 - Solving systems by elimination using multiplication. p.391 #9-14, 17-22

Hon. Alg. II - Review for final exam

PSSA Math 7 - Writing proportions for word problems. Worksheet. Continue to work on corrections


Tuesday, May 25 - all assignments are due on Wednesday
Hon. Geom. - Had a test. **Study for final exam on June 1
Hon. Alg. 8 - Reviewed for final. **Study for final exam - pd. 2 on June 1, pd. 4 on June 3

Hon. Alg. II - Reviewed for final. **Study for final exam - pd. 5 on June 4, pd. 6 on June 2

PSSA Math 7 - Cumulative review. Worksheet. Continue to work on corrections


Wednesday, May 26 - all assignments are due on Thursday
Hon. Geom. - Reviewed last test, reviewed for final. **Final - June 1

Hon. Alg. 8 - Reviewed for final. Worksheet. **Final - pd. 2 on June 1, pd. 4 on June 3

Hon. Alg. II - Reviewed for final. *! *Final - pd. 5 on June 4, pd. 6 on June 2

PSSA Math 7 - Worked on corrections. Continue to work on corrections


Thursday, May 27 - all assignments are due on Friday
Hon. Geom. - Study for final exam on June 1

Hon. Alg. 8 - Review worksheet. **Final - pd. 2 on June 1, pd. 4 on June 3

Hon. Alg. II - Study for final exam. **Final - pd. 5 on June 4, pd. 6 on June 2

PSSA Math 7 - Worked on corrections. Continue to work on corrections.


Friday, May 28
Hon. Geom. - Study for final on Tuesday

Hon. Alg. 8 - Final - pd. 2 on June 1; pd. 4 on June 3

Hon. Alg. II - Final - pd. 5 on June 4; pd. 6 on June 2

PSSA Math 7 - Worked on corrections. Continue to work on corrections

simplifying rational expressions worksheet

Complexity Everywhere

I know that whenever I write about TCS politics on this blog, it ends up bad. For instance, I get a comment such as the following one (left by an anonymous to my last post):

What makes it tough for some of the papers you cite is the view that shaving off log factors is often viewed as much less interesting than larger improvements.

This, of course, makes my latin blood run even hotter, and I cannot help writing follow-up posts (this is the first). If only I could keep my promise of not writing about politics, my life would be so much simpler. (If only I could learn from history... I got to observe my father become a leading figure in Romanian Dermatology a decade before he could get a faculty position — mainly due to his latin blood. He got a faculty position well into his 50s, essentially going straight to department chair after the previous chair retired.)

So, let's talk about shaving off log factors (a long overdue topic on! this blog). As one of my friends once said:

All this talk about shaving off log factors from complexity people, who aren't even capable of shaving on a log factor into those circuit lower bounds...

There is something very deep in this quote. Complexity theorists have gone way too long without making progress on proving hardness, their raison d'être. During this time, drawing targets around the few accidental arrows that hit walls became the accepted methodology. For instance, this led to an obsession about the polynomial / non-polynomial difference, where at least we had an accepted conjecture and some techniques for proving something.

Complexity theory is not about polynomial versus non-polynomial running times. Complexity theory is about looking at computational problems and classifying then "structurally" by their hardness. There are beautiful structures in data structures:

• dictionaries take constant time, ra! ndomized. (But if we could prove that deterministically, dynam! ic dicti onaries need superconstant time per operation, it would be a very powerful message about the power of randomness — one that computer scientists could understand better than "any randomized algorithm in time n^c can be simulated deterministically in time n^10c if E requires exponential size circuits.")
  
  
• predecessor search requires log-log time. The lower bound uses direct sum arguments for round elimination in communication complexity, a very "complexity topic." A large class of problems are equivalent to predecessor search, by reductions.
  
  
• the hardness of many problems is related to the structure of a binary hierarchy. These have bound of Θ(lg n) or Θ(lg n / lglg n) depending on interesting information-theoretic issues (roughly, can you sketch a subproblem with low entropy?). There are many nonobvious reductions bet! ween such problems.
  
  
• we have a less sharp understanding of problems above the logarithmic barrier, but knowledge is slowly developing. For instance, I have a conjecture about 3-player number-on-forehead games that would imply n^Ω(1) for a large class of problems (reductions, again!). [This was in my Dagstuhl 2008 talk; I guess I should write it down at some point.]
  
  
• the last class of problems are the "really hard" ones: high-dimensional problems for which there is a sharp transition between "exponential space and really fast query time" and "linear space and really slow query time." Whether or not there are reductions among these is a question that has preoccupied people for quite a while (you need some gap amplification, a la PCP). Right now, we can only prove optimal bounds for decision trees (via communication complexity), and some weak connections to NP (if SAT requires strongly exponential time, partial match requires we! akly exponential space).
  

Ok, perhaps you simply! do not care about data structures. That would be short-sighted (faster data structures imply faster algorithms; so you cannot hope for lower bounds for algorithms before proving lower bounds for data structures) — but it is a mistake that I can tolerate.

Let's look at algorithms:

• Some problems take linear time (often in very non-obvious ways).
  
  
• Sorting seems to take super-linear time, and some problems seem to be as fast as sorting. My favorite example: undirected shortest paths takes linear time, but for directed graphs it seems you need sorting. Why?
  
  
• FFT seems to require Θ(n lg n) time. I cannot over-emphasize how powerful an interdisciplinary message it would be, if we could prove this. There are related problems: if you can beat the permutation bound in external memory, you can solve FFT in o(n lg n). The permutation bound in external memory is, to me, the most promissing attack to circu! it lower bounds.
  
  
• some problems circle around the Θ(n sqrt(n)) bound, for reasons unclear. Examples: flow, shortest paths with negative lengths, min convolution with a mask. But we do have some reductions (bipartite matching is as hard as flow, bidirectionally).
  
  
• some problems circle around the n² bound. Here we do have the beginning of a classification: 3SUM-hard problems. But there are many more things that we cannot classify: edit distance and many other dynamic programs, min convolution (signal processing people thought hard about it), etc.
  
  
• some problems have an n*sort(n) upper bound, and are shown to be X+Y-hard. Though the time distinction between n² and n*sort(n) is tiny, the X+Y question is as tantalizing as they get.
  
  
• some problems can be solved in n^ω by fast matrix multiplication, while others seem to be stuck at n³ (all pairs sh! ortest paths, given-weight triangle). But interestingly, this ! class is related to the n² problems: if 3SUM needs quadratic time, given-weight triangle requires cubic time; and if min-convolution requires quadratic time, APSP requires cubic time.
  
  
• what can we say about all those dynamic programs that run in time n⁵ or something like that? To this party, TCS comes empty-handed.
  
  
• how about problems in super-polynomial sub-exponential running time? Ignoring this regime is why the misguided "polynomial / non-polynomial" distinction is often confused with the very meaningful "exponential hardness." There is much recent work here in fixed-parameter tractability. One can show, for instance, that k-clique requires n^Ω(k) time, or that some problems require 2^{Ω(tree-width)} time.
  
  And what can we say about k-SUM and all the k-SUM-hard problems (computational geometry in k dimensions)? This is an important illustration of the "curse of dimensionality" in ! geometry. I can show that if 3SAT takes exponential time, k-SUM takes n^Ω(k) time.
  
  Finally, what can we say about PTAS running times? In my paper with Piotr and Alex, we showed that some geometric problems requires n^{Ω~(1/ε^2)} running time. This has a powerful structural message: the best thing to do is to exhaustive search after a Johnson-Lindenstrauss projection.
  
  
• inside exponential running time, there is the little-known work of [Impagliazzo-Paturi] showing, for instance, that sparse-3SAT is as hard as general 3SAT. Much more can be done here.
  

Lest we forget, I should add that we have no idea what the hard distributions might look like for these problems... Average case complexity cannot even talk about superpolynomial running times (a la hidden clique, noisy parity etc). 

This is what complexity theory is about. Sometimes, it needs to unde! rstand log factors in the running time. Sometimes, it needs to! underst and log factors in the exponent. Whereever there is some fascinating structure related to computational hardness, there is computational complexity.

While we construct exotic objects based on additive combinatorics and analyze the bias of polynomials, we should not forget that we are engaging in a temporary exercise of drawing a target around an arrow — a great exploration strategy, as long as it doesn't make us forget where we wanted to shoot the arrow in the first place.

And while complexity theory is too impotent right now to say anything about log factors, it should not spend its time poking fun at more potent disciplines.

polynomial simplifier

Gchem Lecture 5: Nuclear Structure

Protons and neutrons in a nucleus are held together by the strong nuclear force. It's the strongest of the four fundamental forces because it must overcome the electrical repulsion between the protons.

Unstable nuclei are said to be radioactive, and they undergo a transformation to make them more stable--they do this by altering the number and ratio of protons and neutrons. This is called radioactive decay. There's 3 types: alpha, beta, and gamma. The nucleus that undergoes radioactive decay is called the parent, and the resulting (more stable nucleus) is called the daughter.

Alpha: When a large nucleus wants to become more stable by reducing the number of protons and electrons it emits an alpha particle--it contain! s 2 protons and 2 neutrons. This reduces the parent's atomic number by 2 and the mass number by 4.

Beta: there are 3 types: Beta (-), Beta (+), and electron capture. Each type involves the transmutation of a neutron into a proton (and vice versa) through the action of the weak nuclear force; beta particles are less massive than alpha particles and therefore less dangerous

Beta (-): Unstable nucleus contains too many neutrons--> it converts a neutron into a proton and an electron (Beta (-) particle that is ejected; the resulting atomic number is increased by 1 but the mass number remains the same. This is the most common type of beta decay so when the MCAT mentions it, it means this.

Beta (+): Unstable nucleus contains too few neutrons--> it converts a proton into a neutron and a positron (ejected). The positron is like ! an electron, only positive. The resulting atomic mass is 1 le! ss than the parent but the mass number remains the same.

Electron Capture: unstable nucleus capture an electron from the closest electron shell (n=1) and uses it to convert a proton into a neutron--> causes the atomic number to be reduced by 1 while the mass number remains the same

Gamma Decay: is simply an expulsion of energy; a nucleus in an excited energy state (which is usually the case after a nucleus has undergone alpha or any type of beta decay) can "relax" to its ground state by emitting energy in the form of one or more photons. These photons are called gamma photons. They have neither mass nor charge. Their ejection from a radioactive atom changes neither the atomic number nor the mass number of the nucleus (i.e. does not change the identity of the nucleus like alpha or beta decay).

Quick note on nuclear binding energy: every nucleus that contains protons and neutrons has this. It is the energy that was released when the individuals nucleons were bound together by the strong force to form the nucleus. It's also equal to the energy that would be required to break up the intact nucleus into its individual nucleons. In short, the greater the binding energy per nucleon, the more stable the nucleus.

Mass defect: when nucleons bind together to form a nucleus, some mass is converted to energy, so the mass of the combined nucleus is less than the sum of the masses of all its nucleons individually. The difference, deltaM, is the mass defect and will always be positive.
DeltaM=total mass of separate nucleons - mass of nucleus

polar aprotic solvents list

Slope calculator

In this blog we are going to learn about mathematics concept slope.
Slope: -It is the measure of a line which is inclined in relation to the horizontal.
Slope of any line in geometry means the ratio of vertical to the horizontal distance between any points on it.
Meaning of Slope of a line tangent to the graph in differential calculus is given by the particular functions derivatives & represents the rate of modify of the function with respect of modify in the independent variable.
In a graph of a position function, the slope of the tangent signifies an objects instantaneous velocity.
Point Slope Forms: -
Point Slope is the technique of representing or plotting an equation on a graph paper on an x-y axis. It is used to take a graph & find the equation in a specific contour.
The equation for Point Slope Form is given below: -
Y-y1=m(x-x1)
Here is the example of how we can find the slope.

Example:

Find the slope from the given equation, y = 2x + 4

Solution:

Here, the equation is given in slope intercept form,

y = mx + c

Where, m = slope

y = 2x + 4

m = 2.

The answer is 2.

This is just an example on find slope.Next time we will see slope calculator.Before knowing slope calculator,going through slope worksheet you should know about slope.
Also you should know the concept of ogive,as its a equally important concept in math.

point slope calculator

Math online tutoring

i used to be a Math whiz when i was young. seriously, i was an excellent student in Math. i often competed in inter-school quiz bees as our school's representative. my parents were very pleased because they didn't need to hire a tutor for me. most students my age then had difficulty understanding the lessons in Math, and i do recall having to teach my classmates in their assignments. it was harder for students back then to actually get the help they need in comprehending the lessons.

good thing K-12 students can now get online tutoring so their lives will be a lot better when dealing with the much-dreaded subject. 5th grade Math has become easier, and so is 4th grade Math. 5th grade Math may be tougher than it looks, but with the proper online tutoring tool, students can excel in this subject, too. before they know it, adding fractions will just be a piece of cake.

online tutoring is not only great for 4th and 5th graders, but also for K-12 students who take up Algebra 2. yes, a lot of people may find Algebra 2 difficult but good thing help is now available to those who find it challenging. i know formula for volume and graphing linear equations can seem daunting, but there is hope now that online tutoring is within one's fingertips.

online tutor math

Chemistry Regents Exam Survival Guide

Before high school students in the Rivertowns hit the beach, barbeques, summer camps and pools, they'll have one more hurdle to face: Regents exams.

It can be hard for students to focus on studying history, English, social studies, and math, especially when attending consecutive testing periods and tempted to drop the books in lieu of some summer fun.

But with plenty of sleep, a good breakfast, and some perspective, teenagers in Hastings, Dobbs Ferry, and Irvington have a pretty good chance of not only acing their tests, but making it to the official last day o! f school without taking on unnecessary stress.

Patch recently spoke with Dr. Adam Stein of the Rivertowns Center for Attention Psychology in Irvington. A practicing psychologist since 2001, Dr. Stein specializes in working with kids and families.

Here are a few of his suggestions to local teens on how to survive Regents week:

*
Keep it All in Perspective

Try not to sweat it; exams will be over before you know it!

Dr. Stein suggests that students, try "not get overwhelmed by the big picture. Focus on whatever the task at hand is."

And don't forget, being overwhelmed "uses up a lot of energy."

*
Take Care of Yourself

While it may seem important to be focused and calm during a difficult chemistry exam, Dr. Stein says it's even more integral for teens to maintain "really good self care outside of the exam." This includes getting enough sleep, exercising, eating ! plenty of high-protein foods, and drinking water.

"! You'll b e able to regulate yourself more effectively during test time if you're practicing optimum self care," Stein noted.

Inside the testing room, he suggests bringing a snack and a bottle of water if it's allowed.

*

Chemistry Regents Exam Survival Guide

old geometry regents exams

Send Your R-Trees Packing

So long ago now I was looking at R-Trees and how scary the ones created by GiST indexing in PostGIS looked. I had actually already written a packing algorithm at the time - which I called Median-Split packing, which made some pretty nice looking indexes. Here is a picture of the index of the same data I was using before (the roads of British Columbia) when packed using Median-Split:


And here ! is a zoomed-in look at the densest area, the Greater Vancouver Area - approximately one third of all the road segments in the province are within this area which is on the order of 1/100th of the area of the province.


I have yet to do empirical tests to determine if the packed index works any better, but from a purely aesthetic point of view I'm happy with my packing algorithm. It works in O( n*log(n) ) time, using an algorithm similar to qui! ck-sort. I am confident there will be a measurable improvement! in perf ormance in terms of the number of page-accesses required for the packed index vs. the regularly constructed index, however the real question is, once caching and what-not is factored in, can you see a significant difference in query time in the database.

Lots of other people have thought about packing R-Tree indexes before, STR-Pack and Hilbert-Sort do perform similar operations in similar time, but I feel strongly that Median-Split does a better job than they do, particularly for region queries, which are common for map rendering (as opposed to point queries). I don't yet have any proof of this but it just "feels good". To my knowledge no-one else has published an algorithm that works the way Median-Split does - I may look into publishing it.

Shoehorning an index packing mechanism into PostgreSQL is a daunting task, so before I ! go down that road I'm going to do some simulations to determine if I'm right about the performance in terms of page-accesses.

median split

March, my birthday, and I'm still here!

Hi Readers! I am still here responding to people's requests for homework help, I just don't post the answers on my blog as much anymore. But rest assured, I am still here answering your emails.

Also, to celebrate my birthday this week, I invite you to partake in this fun online gaming experience called "Auditorium"!

http://www.playauditorium.com/

I enjoyed it so much that I played it all the way through on my first sitting!

math help for free

The turning of the histogram

I have been off for some time now, and I thought that it would be high time to post something on gnuplot. I have chosen an easy subject, but one that could turn out to be useful. At least, I have seen people searching for a solution to this problem with the histograms. If you needed it in the past, you have probably realised that gnuplot can make only vertical histograms. But sometimes, this is not the best way to represent data, and a horizontal version would be much better. For one thing, the horizontal one might take up much less space. If you want to learn how to produce the figure below, keep reading!

Making the graphs will require some work, but everything is quite straightforward. What we should note, however, is that we will still produce an upright image that we have to rotate later. If you set the terminal to postscript, you will probably use the figure in LaTeX, where you simply have to tell the compiler to rotate the figure by 90 degrees. If you set the terminal to a raster format, or print the screen, you can rotate the image in many applications, but if you want to adhere to the command line, you can, at least, under Linux, use the convert command as

convert -rotate 90 figure_in.png figure_out.png

The figure above was p! roduced based on the following data file

1989 0.1
1990 0.2
1991 0.2
1992 0.05
1993 0.15
1994 0.3
1995 0.1

(We have seen these data many times, you should know it by heart by now!) After this interlude, let us see the code! I will discuss it afterwards.

reset
set key at graph 0.24, 0.85 horizontal samplen 0.1
set style data histogram
set style histogram cluster gap 1
set style fill solid border -1
set boxwidth 0.8
set xtic rotate by 90 scale 0
unset ytics
set y2tics rotate b!  y 90
set yrange [0:0.35]; set xrange [-0.5:6.5]
set y2label 'Output' offset -2.5
set xlabel ' '
set size 0.6, 1
set label 1 'Year' at graph 0.5, -0.1 centre rotate by 180
set label 2 'Nowhere' at graph 0.09, 0.85 left rotate by 90
set label 3 'Everywhere' at graph 0.2, 0.85 left rotate by 90
p 'pie.dat' u 2 title ' ', '' u ($2/2.0+rand(0)/10.0) title ' ', '' u 0:(0):xticlabel(1) w l title ''

The first line after the reset is required, because we have to make our key ourselves. We simply specify the coordinates and that that we want to have a horizontal key (i.e., one in which the keys are placed to the right of the previous one), with a length of 0.1. If you want smaller or larger space between the keys, you can modify this, by adding the spacing flag to the set command. You can see the exact syntax by issuing ?key in the gnuplot prompt.
In the next four lines, we set up our histogram. The content of these lines ! might depend on what exactly we intend to plot. For more on th! is, chec k out the gnuplot demo page! We then rotate the xtics by 90 degrees. We do this, because the whole image will be rotated, and by rotating the xtics, we make sure that those will be horizontal at the end. For the very same reason, we also unset the ytics, and set the y2tics. We also set the y2label and xlabel. This latter one is empty, but we still need the space for it, so we set it to ' '. Beware the white space!

The next important step is the setting of the aspect ratio of our figure, which will be 0.6:1. Having done that, we introduce 3 labels: one for the xlabel, and two for the key. The placement of these labels is somewhat arbitrary, and depends on the particular terminal that you use. But only these three numbers and the coordinates of the key need any tweaking, really. At the very end, we plot our data. I plotted the second column twice, with an added random numbers, so that we can have ! two columns at each data point. Note that we plot the first column, too, but pass it to the xlabel command. By doing that, we can automate the labelling of the xtics, using the first column in our data file. Also note the specification of the titles: in the first two cases, the single quotes include a white space, while in the third one, there is nothing.

histograms examples

Rocky Run

Rocky Run was one of my favorite places. It was a place to have a beer with friends, a place to chat, and a place to eat a simple (but satisfying) meal. I am certainly not the first to blog about this (Columbia Talk, Howard County Maryland Blog). I first walked into Rock Run in 1996, and I kept coming back. Here are a few reasons why:

Quirky:

When you walked into Rocky Run, you knew this was not a national chain. It never took itself too seriously, and this was reflected in the dé! cor. One of the few restaurants in Columbia that had its own brewery, there was a quirkyness about the place. The enormous hot sauce collection, the Elvis booth, the Beatles room, the Buffett room. The peanuts on the floor in the bar (great when fashionable, even better that they stuck with it when it fell out of fashion). The foreign language tapes on continuous loop in the bathrooms. The Rocky Cocktails (I confess, I had a Jamaican Bobsled just last week!) The endless trivia games.

The Food

Since it opened, Rocky Run’s menu has always been full of offerings. Standouts in my mind where the chicken wings, which always seemed larger than the wings served at other restaurants in town. Crab Pretzels on Fridays during lent. The salads (the cobb salad was a personal favorite), of course the burgers, and the impossibly large “loaded” baked potatoes. The Cuban pannini was a late, but welcomed ! arrival on the menu.

If people asked me about the f! ood at R ocky Run, I would always respond “It’s the best comfort food in Columbia.” I think that said it all.

The Staff

Over the years, I have gotten to know many of the people behind the bar and waiting tables. It all started with Alex, who on that first day I walked into the bar, shook my hand, introduced himself and asked me what I would like to drink. I quickly came to know him and many others. The always bubbly Liz, Adam, who insisted on being called Fish. Mary Ellen, who was in training to become an EMT before she trashed her knee. The always nice Amy. Ruthie, who had issues, still managed to have a good time and smile.

During the late 1990’s Heidi and Sean tended bar on Friday nights, and they always managed to serve an impossibly large crowd. At that time, Margarita Maggies was still open, but not doing well, and people would park in the Maggies lot to go to Rocky Run. He! idi and Sean performed their craft well. They were fast, charming, and seemed to enjoy themselves.

As time passed, some interesting bartenders made their way through. Art was always fun with his libertarian views and his dislike of public displays of affection. Jeff was a master of many subjects. Henri, was just an all-around good guy; smart, witty, and a die-hard Wizards/Bullets fan.

There were a few that found love at Rocky Run. Caleb and Christy are still together and Tommy and Jenny were an item.

But, over the years, three stand out. Jason, who started as a busboy, became a waiter, host, bartender, bar manager, store manager, and I’m sure is still doing well. Jason, I have seen you grow so much over the last twelve years. I am honored to call you friend, and wish you well. Christy (as mentioned above), you have been part of my nights out for so long that I will miss you. Dave, you are a great man and I am sure good things! will happen for you.

I know that I have missed so ! many (oh , I remember another, Wendy!) who wore the bright orange “Rocky Rookie” shirts on their first day, I will miss you too, as well as everyone in the kitchen.

The Smartest Patrons Ever Known

I am serious about this point. Since the day it opened, Rocky Run always ran the NTN/Buzztime trivia games; Half hour trivia contests that linked thousands of restaurants across the United States. Rocky Run attracted a clientele that was adept at these games (and for a long time, I was one of them) and often times Rocky Run would be ranked in the top 20 in the nation. Occasionally, a person would arrive at Rocky Run just based on seeing the restaurant on the trivia boards at other restaurants. During the late 1990’s, Rocky Run and Nottingham’s were engaged in a battle of trivia supremacy. Trivia players were courted. Scores were displayed; cell phone calls were exchanged after games.

What ! gave this rivalry depth was that at Nottingham’s, it was known that the trivia players typically shared answers. At Rocky Run, the unwritten rule was that you played your game. Shouting out answers was considered bad form. That is not to say that the trivia players were stoic and silent. After playing for a while, players got to know each other. Most were witty, some were outright funny, and all liked passing time together.

So Moron, Phlegm, Farkle, Redgirl, Karl, and all the many people who got the trivia bug, I will find a place to play, and I hope to see you on the board too. I will miss you all.

Beyond the trivia, the folks at the bar were generally well versed in the topics of the day. You could always have a good conversation about national or local news. Just smart, wonderful people.

Where do we go from here?

I was at Rocky Run just last Friday. A friend of mine had just! accepted an offer for a new job, and we went out to celebrate! . We ha d dinner, discussed the job, what’s new in our families (my son wears a Size 1 shoe, and he starts kindergarten this month), sports, and the local politics scene. We had arrived at 6 o’clock, and the bar was busy. When we left at 9:30, the place was nearly empty. Christy, Dave and Jason were there. We said hello and things seemed all right.

I guess all we have are memories now. I can still see Joe and Ellis sitting at the end of the bar. Bobby holding court at one of the short tables. Don and Deanna discussing their latest travel plans. Bill and the trivia faithful playing trivia and chatting up each other. Jason and Terry stopping by for dinner. Some stranger saying out loud “Oh, I LOVE this song,” and me saying to myself “I love this song too.”

Yesterday I stopped by to take the picture to accompany this post. The owner came out and said hello. We talked for a short while and then I just had to ask: What! happened? He told me that business had really dropped off drastically in the last four months. I thanked him and inquired how the staff were doing. He had told me that more than a few had already found jobs. I was relieved to hear that. I just smiled and thanked him again. He smiled back and thanked me, then quietly went inside. I took a minute and sat on the bench outside. As I sat there, four cars pulled up, and each asked the same question: What happened? I told each what I had heard, and they all, hesitantly, walked back to their cars, muttering “This is awful…This was my favorite place…”

I don’t know where or when my friends and I will get together for happy hour, but when we do, we will loudly toast the memory of a place that enriched our lives (better said, provided an atmosphere that allowed us to enrich each others lives).

I hope we can find a place that will have that same feel; that will give us a Seco! nd Chance.

course compass answers

hurry up and get here

is it Spring yet? this Winter is killing me. i'm not even in a wintery place and i'm ready for it to be over. i need some renewal, some rebirth. i feel like Springsteen....i wanna change my clothes, my hair, my face. a strange thing to feel restless whilst wandering. maybe i'm just home-sick. but when i get home, i want to purge. i need to shed the old stuff and exfoliate my life a bit. it's time to let the new stuff really OUT.

a change is coming. or will come, after i start working smarter towards it. a big personal one for me, actually. i'm making a break for it! . i've been wandering through the soundscape of the music world for several years now....floating along, making recordings, trying to improve my skills....but with no real plan. and it's time to step up with a plan.

the past few weeks i've been slowly coming to realizations that others have been easy to see. but i was inside and couldn't see it. simple things that i could say and do to help improve my status as an indie. spreading the word, the new music, everything.

but i say "i'm no business person. i don't know how to do this!" but that's a ridiculous statement. it doesn't matter that i didn't know how to do any of the stuff i now know how to do, before i learned how to do it. i simply did it. and now i know how to do stuff. and this time is no different. it's just time to be the person with the vision. and to write this vision down in words on a piece of paper. and to truly develop a real, long-term plan with definite goals, rather than just wander! ing along, hoping to be seen by a person with more money, powe! r, and c onnections than myself.

and finally, a distinction. Kristin Putchinski can no longer be on stage with ellen cherry. it sounds weird, but ellen cherry has to start standing on her own.

congreve cube

Flow Chemistry to help the Pharmaceutical Industry

We have recently started a new research project in collaboration with Mimi Hii from the Department of Chemistry (Enabling Oxidation Reactions on a Large Scale: Combining Electrochemistry with Flow). The project involves partners from Pfizer Global R & D.

In a nutshell, the project is about creating in situ reactants (oxidants and reductants) using electrochemical methods to react with pharmaceutical intermediates in a flow system (that is continuous production rather than batch operation). We hope that this will lead to much improved selectivities and yields with much reduced waste formation for many important chem! ical transformations.

We are currently filing a patent application on our ideas with Imperial Innovations.

chemistry help

Process Goals and Fun with Graphs!

It is timely that I came across this nice post today about goals, because I had been thinking yesterday about listing out some goals on my wall that are not topic-specific, so that I can refer to them throughout the year as I work with my kids on different assignments intended to address one of those life (or processing) skills.

Examples for Geometry:

• Visualization of parts vs. whole (Isolating info from one part of a diagram; combining info across multiple layers / perspectives.)


• Mechanical precision (Measuring and constructing lengths within 1 mm error and angles within 1 degree error; building solid models that won't fall apart.)


• Comprehension of diagrammed instructions (ie. for building anything)


• Attention to details in written instructions


• Judgment of reasonableness (of any physical or vi! sual quantity)


• Effective written and oral communication


• Perseverence and resourcefulness


• Team work

Examples for Precalculus:

• Interpretation of data (Understanding trends / real-world significance / impact.)


• Fluidity with technology (Using graphing calcs fluently and flexibly.)


• Flexibility / creativity of problem-solving approaches


• Risk-taking and reasoning about the unfamiliar


• Precision and clear step-by-step organization of thought process / math work


• Increased self-management of progress, frustration level


• Effective written and oral communication


• Perseverence and resourcefulness


• Team work

Maybe it's just me being cheesy, but I think both the students and I might benefit from my posting these goals on the wall -- especially if I do actually highlight different skills throughout t! he year, as is appropriate to a given lesson, so that the kids! would f eel like they're not just learning content for content's sake and we are working towards a bigger picture.

My lists of goals are pretty generic (not really even math-specific, for the most part... Most are just good habits of mind...), but they are reminders of what is most important to me. Naturally, between the freshmen (Geometry) and the juniors (Precalculus), there is quite a bit of a "life experiences" gap. So, my goals for the two groups are pretty different as well. My juniors don't need as much for me to hold their hands on following directions, but they might need a nudge to be more creative and/or persevering. Versus the freshmen, whose first task of this year is to learn to consistently read and follow instructions. :) They each are at a different developmental stage with their meta-learning.

We have an opportunity each day to impact kids, mathemagically or otherwise.

-----------------

By the way, I found some nice gra! phs for my graph-reading lesson that is coming up. They're neat, even though they are not terribly complex in a mathematical sense. (The textbook's got a couple of nice complex graphs to use for rigorous classwork exercises, so I feel like I could afford to spend the rest of the period looking at interesting -- albeit simpler -- graphs with the kids.) They have to do with the mobile market, digital textbooks, and digital music. I plan to have fairly open-ended discussions about trends in those graphs, who might be interested in reading them, and what their implications might be for those people. And then maybe end with why these kids should finish college.* It could end up being a total flop of a lesson hook, but I am curious to see what these juniors can bring to! the table.

If I have time, I am also thinking abou! t adopti ng a middle-school post-it bar graph activity to composite bar graphs and scatter plots. I would give every boy a yellow post-it and every girl a pink post-it, and we would start a bar graph template on the board -- for example, models or brands of cell phones. They would go put their post-its on the board, in the appropriate column, and we would re-arrange the post-its to stack the pink post-its on top of the yellow post-its, in order to create a composite bar graph showing how many boys, girls, and total # of students have each type of phone. You can also do this exercise with scatterplots (for example, height vs. foot length) and see at a glance 1. what the overall trend is within the class, and 2. what the gender-specific trend is within the class. Using only colored post-its! And requiring maybe only about 10 minutes, discussion included. ...I'll try to squeeze it into my Precalc lessons this week and tell you lurkers how it goes.

*From what I hear, many Salv! adorean private-school kids end up dropping out of college in the States, because they either lack the academic skills or -- more commonly -- can't deal with the fact that they no longer have a live-in maid and a designated chauffeur. This waste of an opportunity is terribly sad, considering that their parents can afford them to obtain a U.S. college education, while the majority of people in this country are living in poverty and many are starving. :(

But, can you really blame the kids for this injustice?? They are a product of the system (of huge disparity in wealth). sigh.

bar graph template for kids

Easy and elegant Brussels sprouts recipes

Brussels sprouts are not known as everyone’s favorite vegetable. This is because most people do not prepare Brussels sprouts properly, often under seasoning and over cooking them. The recipes below can start you down the road to being a Brussels sprouts lover.

First grown in 16th century Belgium, Brussels sprouts are cousins of the cabbage, another misunderstood vegetable. Both blend well with stronger ingredients like, garlic, onions, cheeses and! spices. When choosing Brussels sprouts look for small bright green spouts with compact leaves.

Click here to read more and get the recipes.

balanced equation calculator

Work Problem 5

The following was a question a anonymous visitor asked: Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?



Work problem 5 solution here

algebra free help

Organic Food Is A Scam

Don't believe me? Check out this study published in Reuters, today.

(This is the part where I criticize people who don't know what the hell they're talking about while only pretending to know what the hell I'm talking about. Note my complete lack of nutritional credentials and absence of any sited sources for my many claims. Good thing this is just some jaggoff shooting his mouth on a crappy blog and not an academic publishing.)

There is no nutritional advantage in paying significantly more money for the exact same food. Fruits, vegetable! s, meats, dairy. All of the thousands of food products under those categories also offer organic alternatives that cost a lot more. It is branding, pure and simple. By charging more, they create the illusion of superior quality. And like other similar products, the actual advantages of paying more is negligible at best.

Buying organic food is not evidence that you are more intelligent or more informed than the average consumer. It illustrates that you are gullible. Fertilizer, pesticides, growth hormones and whatever else farmers use to produce a high yield crop do not harm people one bit. And the absence of these things do not provide any nutritional advantage at all. But people don't spend more money on a commodity, that is universally available for much less money, unless they think they are smarter than the fools who buy conventionally grown food.

"Sure, I could pay a buck a pound for those giant, flavorful, red bell peppers. Or I could pa! y a buck seventy five a pound for the much smaller, wilty look! ing pepp ers next to them with the green 'organic' label. Evil corporate farms are poisoning our children with their chemicals and pesticides to make more money. Oprah said that growth hormones fed to dairy cows result in earlier puberty in children,type 2 diabetes and autism. So I'm going to pay more for less, because I know the truth. Everyone else is stupid but me."

Now, there are other reasons people buy organic food besides egotistical placebos. Some will claim organic food tastes better. I would suggest that by paying more, people convince themselves of any difference in quality. But organic food is usually grown closer to the place it is sold, so it reasons that will more likely be more fresh. That's fair. But you can still buy local, and therefore fresher and cheaper, produce in season. It doesn't need to be organic to be fresh.

There is a case to be made that synthetic fertilizer production results in a destructive cost on the environment. M! ost of those fertilizers are mined from quarries and result in significant damage to the natural state of the earth in that particular location. Many people choose to not indirectly support this practice by paying more money for food grown with compost. If that kind of symbolism is important to you, fine. But you should also avoid using anything made with concrete, asphalt or gravel, (you know, every building and road in existence) since those things are also products of planet raping quarries.

Eating organic food, driving a Prius, wiping your butt with recycled toilet paper. Whatever superficial lifestyle choice you make to convince yourself that you are not a environmentally destructive consumer, it all boils down to a snobbish transference of guilt. You're not making any kind of actual difference. You're just convincing yourself of an imagined personal superiority.

Perhaps you want to support small, family owned farms. I'm all for this. I fr! equent Salt Lake's Farmer's market. Currently I have a dozen ! ears of Utah corn in my fridge I bought from a roadside vendor. It may be organic. I really don't know. That's not why I buy it. I buy it because it's fresh, local, delicious and cheap.

The family farm in this country is something that is quickly dying out. Over the past couple of decades production methods have become more efficient and food prices have dropped. This is good for consumers and good for large scale farms that can afford the capital. But it costs more and more to stay in the game and more often than not, family farms can't afford to do it. So do you know what most of these small farms do to stay afloat? The maximize their production. Traditional fertilizers are cheap as hell when compared to compost. And considering the yield that results from them, it's far more lucrative to go the traditional route as opposed to organic. Most organic food is produced by the giant corporate farms who employ migrant labor at slave wages because it's the only way i! t can be produced on a large scale for a profit.

You want to support the small farmer? Buy the fertilized, hormone infused cheap stuff.

In the spirit of the Reuter's article, here is a clip from Penn and Teller's show, "Bullshit". Now, I usually don't take my political thought from "Illusionists!". But I do think this clip is pretty funny.

academic advantage scam

C Program to find four digit perfect square in which the number represented by the first two digits and last two digits are also perfect square | code | output

C Program to find four digit perfect square in which the number represented by the first two digits and last two digits are also perfect square

#include<stdio.h>
#include<math.h>

int main()
{
int i,left,right,a,d1,d2,d3,d4,x,y,num;

printf("Following numbers are the desired numbers:\n");
for(i=1000;i<=9999;i++)
{
//Find square root of i
a=sqrt(i);

//Test whether i is perfect square or not
if(i==a*a)
{
//Find all four digits
num=i;

d4=num%10;
num=num/10;

d3=num%10;
num=num/10;

d2=num%10;
num=num/10;

d1=num%10;
num=num/10;

//store first two digits
left=d1*10+d2;

//store last two digits
right=d3*10+d4;

//Check if these are perfect numbers or not
x=sqrt(left);
y=sqrt(right);

//print the number if all the conditions are satisfied
if(left==x*x&&right==y*y)
printf("%d \n",i);
}
}
}

Finding square of a number

Ratios and cherry almond cookies

How to do ratios

Equivalent fractions - a visual model of splitting the pieces further

With learning fractions, there is always the problem of "so many rules to remember". I offer this visual method of splitting the pieces further, and using the arrow notation as a remedy; hopefully this would help fix the method in students' minds.

Equivalent Fractions video at YouTube

Making equivalent fractions is like splitting all the pieces further into a certain number of new pieces. For example, if I split all the pieces in 3/5 into three new pieces, there will be 9 ! pieces. And, instead of 5th parts, they will be 15th parts. If you have an image and you split even the "white pieces" into three new ones, you'll see those 15 parts. So, 3/5 = 9/15.

The arrow notation shown in the video has one arrow between the numerators and another between the denominators. It also has a little "x3" written next to it. This is to signify into how many pieces we split the existing pieces.

This notation can help students not confuse equivalent fractions with fraction multiplication. The two fractions are equivalent or the "same amount of pizza"; one is not three times the other.

Please also see this free sample worksheet: Equivalent Fractions worksheet. This worksheet shows the same notation and the same idea as the video. It is a sample from my book Math Mammoth Fractions 1.
Please let me know what you think of this notation. I haven! 't see i t anywhere else, but maybe it does exist somewhere. Do you think it confuses or helps students?

How to do equivalent fractions

AP Exam Practice Quiz 1 and Intro to the Intermediate Value Theorem of Integrals

Introducing the first of a series of AP exam practice quizzes, the intermediate value theorem of integrals, the day when the AP Calculus 2008: Without Bound blog is unblocked at Daniel McIntyre Collegiate Institute, the series of YouTube videos in tandem with Flickr pics, and kristina's powerpoint presentations!

AP EXAM PRACTICE QUIZ 1


Let h b! e a function defined for all x does not equal 0 such that h(4) = -3 and the derivative of h is given by h'(x) = (x^2-2)/x for all x does not equal 0.


a) Find all values of x for which the graph of h has a horizontal tangent, and determine whether h has a local maximum, a local minimum, or neither at each of these values.

To determine if there are local extrema at the critical numbers, we must first determine the critical numbers. Remember that there are critical numbers when a function has an asymptote or is undefined. h' = 0 when x = sqrt(2) and -sqrt(2). h' is undefined at x = 0 since 0 isn't in the domain (as stated in the question). So critical numbers are x = sqrt(2), -sqrt(2), and 0.

We use the first derivative test on h' to see where h' is positive or negative. Why? Because when h' is positive, h is increasing; when h' is negative, h' is decreasing. So a change in sign in h' would indicate a slope of ze! ro at that point and that's where there are local extrema. Acc! ording t o the line analysis, we see that to the left of -sqrt(2), h' is negative; between -sqrt(2) and 0, h' is positive; between 0 and sqrt(2), h' is negative; and to the right of sqrt(2), h' is positive. Wherever h' changes sign from negative to positive, h has a local minimum; wherever h' changes sign from positive to negative, h has a local maximum. By the first derivative test (line analysis), there are local minimums at x = -sqrt(2) and x = sqrt(2). We don't look at 0 because it's not part of the domain of the function.


b) On what intervals, if any, is the graph of h concave up?

Rememberize these rules (from chapter 5 of your textbook):

If the second derivative is positive, the first derivative is increasing, and the parent function is concave up.

If the second derivative is negative, the first derivative is decreasing, and the parent function is concave down.

So wherever h" is positive, h is concave up.

We determine h" by differentiating h using the quotient rule.

We see that h" is positive, so h is concave up everywhere.


c) Write an equation for the line tangent to the graph of h at x = 4.

Pull out the point-slope formula: y-y1=m(x-x1)

The question gave us the x-coordinate: x = 4.
The question! gave us the y-coordinate: y= -3.
m is the slope at x = 4! , so plu g x = 4 into h' which spits out 7/2.

Plug those numbers into the equation. BING! BANG! BOOM! We're done part c.

y+3=(7/2)(x-4)


d) Does the line tangent to the graph of h at x = 4 lie above or below the graph of h for x > 4?

If we draw a line tangent to the graph at x = 4, the line is below the graph at x > 4, because h is concave up everywhere.


INTERMEDIATE VALUE THEOREM OF INTEGRALS

Similar to the intermediate ! (or mean) value theorem of derivatives (that in a closed interval between a and b there exists a point on a continuous function which equals the average value), there exists a point on a continuous function which equals the average integral of the function.


We have b = 3. We have a = 0. We have f(x) = 1-2x. Plug the numbers into the equation. BING! BANG! BOOM! We get the average integral. But why does it work?

< img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 361px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6Ie59VozP8pzClvD-TrJVJ9YLFtipLGiVrMUaRqs5opyNMypBfXhljt0Ruj3KsFZKPB_v3OrMrwsSrp8w1eEnGJ1-8kfN7E8UnEuMddTXmzkuwapIe5XTYPijtEfL2UfeqSOmiKJBlu3b/s400/6.bmp" alt="" id="BLOGGER_PHOTO_ID_5310238211959744338" border="0" />In this graph, pivot the yellow area found between c and b to the white area found between c and a. Notice that they fit together like a jigsaw puzzle to yield one big yellow rectangle. We can imagine that one big rectangle having the same area as the area under the graph, which we can see as the average value of the function.

HOUSEKEEPING

• Next scribe is benofschool.
• I'll be away on Monday to write the grade 12 English pilot exam.
• Don't forget to check Graeme's comment on Rence's post as it will prepare you for the exam!
  
• Don't forget to give Jamie your $1.25 donations so she can make her Betty Crocker style cheesec! ake!
• Pi Approximation Day is coming! Are we organizing the annual Coin Hunt for Pi Approximation Day too?

write equation of a line

Problem 444: Tangent circles, Secant line, Chords, Angles, Congruence

Geometry Problem
Click the figure below to see the complete problem 444 about Internally tangent circles, Secant line, Chords, Angles, Congruence.


See also:
Complete Problem 444

Level: High School, SAT Prep, College geom! etry

tangent circles

Problem 489: Parallelogram, Triangle, Quadrilateral, Area

Geometry Problem
Click the figure below to see the complete problem 489 about Parallelogram, Triangle, Quadrilateral, Area.


See also:
Complete Problem 489

Level: High School, SAT Prep, College geometry

area of a quadrilateral problems

Circle Geometry Area, Surface, Volume Skills -- Cross-Products

Mr Smith
Middle School E-Learning
Http://Site3e.Com/

circle area formula

Solidworks Arc Dimension

This is a very quick demo on how to add an arc length dimension into a sketch or drawing. I always forget how to do it.

Arc Length and Arc Length Formula

8.3 Homework & New TI84 Operating System!

The assignment for 8.3 is:

pg. 568 - 3-5, 7, 11, 14, 15, 20, 23

In other news, TI has released a new OS for the 84 family of calculators. Sorry 83 owners, this wont work for you! You will need TI Connect and a USB connection to your calculator in order to get the OS onto your calculator. Make sure you have fresh batteries in your calculator as this can take a great deal of time and power.

Follow the instructions below to install the OS:

1. Download TI Connect and install it on your computer. Make sure to have an icon on your desktop.


2. Download the new OS. Make sure to save it somewhere where you can find it.


3. After installing TI Connect, you'll need a TI Connectivity Cable to make the p! hysical connection from computer to calculator. The TI Connectivity Cable is a Standard A to Mini-B USB Cable for the TI-84 Plus, TI-84 Plus Silver Edition.


4. Once you have your calculator plugged into your computer, drag the OS you downloaded in step two onto the TI Connect icon on your desktop. This will initiate the transfer. Select your calculator from the list that pops up and then wait patiently as the transfer begins. Do not interrupt the transfer or turn off power for any reason. It can wreck your calculator. You will be notified when the transfer is complete.

Enjoy your new operating system!

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Free Calculus Online Tutor

We may accept help from anyone who would like to really help us.Like that there is a great service providers who provides the tutor for school and college students for all the subjects. This may be very useful especially for getting Calculus help. Calculus is a big step up from Algebra and TutorVista's expert Free calculus help will guide you in understanding the subject.

Make sure to visit Tutorvista.com to study deeper on calculus, statistics, precalculus, and other subjects dealing with numbers. Tutorvista.com allows you to get Calculus help from the best Calculus tutor that will guide you in understanding and examining the subject carefully. Since Calculus requires a thorough understanding of concepts, real, online tutoring like TutorVista’s is highly needed. You can get ! for absolutely Free calculus help here as well as other subjects. The best advantage with their Calculus help is that you can connect with a Calculus tutor using your home PC and get personalized attention. Also you don’t have to waste time in travel since you study Calculus from the comfort of home from best online calculus tutor. Tutorvista.com also offers Precalculus help online to solve precalculus limits problems, avail review on precalculus, and work on basic concepts. They have highly qualified tutors who have years of experience in Precalculus tutoring students across grades.

Try their free calculus help demo and interact with our expert calculus tutor. Studies show that online Calculus tutoring is as effective as traditional/conventional methods, and it is completely student driven.If you are encountering problem in Statistics, Tutorvis! ta.com also provides Statistics help by professional tutors to help you raise your grade in class. Visit Tutorvista.com for further information.

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