4 Math Questions

Test Preparation SAT Preparation
1

<p>Thanks in advance for reading my long post!</p>

<p>Initial Velocity</p>

<p>From Barron's 2400:</p>

<p>A rock is shot up from a cannon with an initial velocity of 112 feet per second and moves according to the equation s=112t-16t^2, where s is the distance, in feet, from the ground, and t is time, in seconds. What is the maximum height reached by the stone?
A. 16 feet
B. 96 feet
C. 112 feet
D. 196 feet
E. 672 feet</p>

<p>I plugged it into my Ti-84+ and the highest value I get is x=4, y=192, and I also changed the window to alllow Ymax to be 200 like the book suggests, and it is needed almost 200, so I can solve the problem, but I want an alternative method. And I also want to know if there is a way that I can enter the X values and get the Y value back. I seem to remember the calculator being able to do that, but right now, I can only scroll up or down and it just shows me continuous integers of X and their respective Ys (ex. X=1, 2, 3, 4, etc). Is there a setting that needs to be turned on or something? I also tried using 2nd Calc and calculating the maximum, but the answer changed every time I calculated it. Am I doing something wrong?</p>

<p>The chapter in Barron's has an alternative method of using the formula of the Axis of Symmetry, x=-b/2a, but that seems to be such an obscure formula that I doubt that is the way the CB wants you to solve the problem, and seeing that a calculator is not <em>necessary</em> and I'm sure the CB doesn't want a student to spend twenty minutes making a graph...there has to be another way, right?</p>

<p>Easy Sum of Integers Problem</p>

<p>What is the sum of all even integers from 90 to 300?</p>

<p>I tried using the Sum of Arithmetic Sequences formula. The way I have it right now is...</p>

<p>Sum=(90+300)2/2. That is obviously incorrect as the twos would cancel and the answer would be way too small. Is the formula not correct, or is it not applicable to this type of problem? It seems like this question would be pretty easy to solve algebraically...</p>

<p>An Indirect Variance Problem</p>

<p>If x and y vary indirectly and x=10 and y=15, what is the value of x when y=20.</p>

<p>The way I'm doing it now is kinda just my guess on how to do the problem. Obviously since y increased, x decreases. I have xy=150. Then 150/20=7.5...is that correct? It would be much appreciated if someone could clear up the whole direct and indirect variance for me!</p>

<p>Finally...a probability problem</p>

<p>How many positive odd integers less than 1,000 can be formed using the digits 1, 2, 3, 4, and 8.</p>

<p>Obviously repeats are possible, and the ones digit place must be either 1 or 3. So I have 4<em>3</em>2=24. Is that correct?</p>

2

<p>Initial Velocity: </p>

<p>You're only using integers. What if the answer is a decimal (it's 3.5 by the way). If you're using the calculator's max function, make sure you get the upper and lower bounds right. You could press 2nd F4 (calc) Value to put in an x-value and return a y-value.
Two methods to get the answer:
1. Take the derivative, set it equal to zero. This assumes you know basic calc. If not, then 2. Because of symmetry, the max height is reached at the midpoint of the two zeros. Setting 112t-16t^2=0, you obtain t=0 and t=7, so the max is at t=3.5. You can get this from playing with the quadratic formula, averaging the two zeros to get -b/(2a), which is still 3.5 in this case. Plugging this in gives 196 ft.</p>

3

<p>Easy Sum of Integers Problem </p>

<p>You have the formula wrong. It should be: </p>

<p>(firstnumber + lastnumber) * (#ofnumbers) / 2 </p>

<p>which becomes: (90+300) * (211) / 2 = 41145 </p>

<p>The 211 comes from: 300-90+1 since you want to know how many numbers you are adding up. It's inclusive, hence the +1 at the end.</p>

4

<p>An Indirect Variance Problem</p>

<p>You are absolutely correct in your logic. </p>

<p>For indirect variance, the product is constant. xy=k. An increase in x corresponds to a decrease in y.
For direct variance, the quotient is constant. x/y=k. An increase in x is accompanied by an increase in y. </p>

<p>The answer is confirmed to be 15/2=7.5</p>

5

<p>Wow, thanks for the prompt response!
Any thoughts on the last probability question?
And what do you mean by, "You could press 2nd Math Value to put in an x-value and return a y-value.". I have a Ti-84+ and when I go to 2nd-Table and press 2nd-Math, i get the "test and logic" screen with 1. = 2. not =, etc.</p>

6

<p>a probability problem</p>

<p>How many positive odd integers less than 1,000 can be formed using the digits 1, 2, 3, 4, and 8.</p>

<p>The last digit must be a 1 or a 3. There are 3 digits. </p>

<p>"Obviously repeats are possible, and the ones digit place must be either 1 or 3. So I have 4<em>3</em>2=24. Is that correct?" </p>

<p>If digits can be repeated, look at how many possibilities there are for each. There are three digits (must be less than 1,000). It doesn't matter what order, so let's go backwards. For the last digit there are 2 possibilities (the two odds). For the second digit, there are 5 possibilities (it could be any of them). For the first, there are 5 (could be any again). </p>

<p>5<em>5</em>2 = 50</p>

7

<p>Sorry about the confusion with the calculator buttons. I meant 2nd calc value (and I fixed the above post). </p>

<p>Also, if you want, you can do this alternative:
2nd F2 (tblset)
change indepnt to "ask"
then go to 2nd F5 (table)
enter in your x-value, it will return the y-value</p>

8

<p>aha! I knew that I had used it before on my calc. Thanks a bunch!</p>

9

<p>Wet wet, i believe you did the question regarding the sum of even integers from 90-300 wrong. Your equation implies that there are 211 numbers. The question asks for the sum of EVEN integers, thus it is less than 211. It only works for numbers that go by ones, but in this case, its going by 2s.</p>

10

<p>Oops. I did the sum of all the integers. Sorry. </p>

<p>
[quote]
It only works for numbers that go by ones, but in this case, its going by 2s.

[/quote]
</p>

<p>No. Despite the apparent error, the *technique *is correct. </p>

<p>(firstnumber + lastnumber) * (#ofnumbers) / 2 </p>

<p>(90+300) * (106) / 2 = 20670 </p>

<p>The 106 comes from (300-90)/2 + 1
where the /2 comes from the fact that we look at only even
and the +1 is because it is inclusive. </p>

<p>Thanks for pointing that out though. I got sidetracked/lazy in a hurry to answer all four lol.</p>