<p>These questions are from Test #5 of the first edition of the BB.
Section 3:
Grid-in problem
(Hard) 18. h(t) = c - (d-4t)^2
At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after (t) seconds was given by the function (h) above, in which (c) and (d) are positive constants. If the ball reached its maximum height of 106 feet at time t = 2.5, what was the height, in feet, of the ball at time t = 1?</p>
<p>I got the answer but it was through a lot of typing in the calculator. I had enough time to solve it (answer is 70 btw) but I don't like the way I found the answer.</p>
<p>Section 7:
(Hard) 19. If k, n, x, and y are positive numbers satisfying x^(-4/3) = k^-2 and y^(4/3) = n^2, what is (xy)^(-2/3) in terms of n and k?
A. 1/(nk)
B. (n/k)
C. (k/n)
D. nk
E. 1
Answer: A
No idea how to solve this one</p>
<p>(Hard) 20. The figures above show the graphs of the function (f) and (g). THe function (f) is defined by f(x) = x^3 - 4x. The function g is defined by g(x) = f(x+h) + k, where (h) and (k) are constants. What is the value of hk?
A. -6
B. -3
C. -2
D. 3
E. 6
Answer: E
There is no way for me to put the graphs but they are both degree of 3 functions. The first function (f) one passes through the origin. The second function (g) is shifted two down and three right from the function (f). The problem gave us defined points in the function so I just counted those numbers. </p>
<p>First one. I’m going to give a fairly quick solution. If you need more details let me know:</p>
<p>The two conditions give the following equations:
c-d^2=6
c-(d-10)^2=106</p>
<p>The quickest way to find d is by using the derivative, but since you’re not expected to know any calculus, the quickest algebraic method is to subtract the equations above to get (d-10)^2-d^2=-100. FOILing gives d^2-20d+100-d^2 =-100, or -20d=-200. Dividing by -20 gives d = 10. Plug d=10 into the first equation to get c=106.</p>
<p>For the second one, recall that to get rid of an exponent you raise to the reciprocal power. Also remember that when you raise a power to a power you multiply the powers:</p>
<p>For the second one you could set find numbers that fit the equations. I used X=1,K=1,Y=27,N=9. From there you would see that (xy)^(-2/3)=0.1111 X is 1, and Y is 27, so basically you are taking the cube root of 27, which is 3, and raising it to the negative 2. Thus, you get 0.1 repeating. To find the right answer I just plugged in my numbers, and luckily the first one was the right answer.</p>
<p>If you can’t find the answer for the last one, just know that it relates to graph transformations. In this problem, k represents the vertical shift (the change in the y axis) and h represents the horizontal shift (the change in the x axis). Since the new function is two down, k = -2. Since the new function is three to the right, h = -3. It’s confusing that it’s -3 instead of 3 since, after all, any addition to the right is positive, but just remember that any changes to the x axis are the opposite of what you think would happen. So if it’s three to the right, it’s x-3. Similarly, if it’s 2 to the left, it’s x+2.</p>
<p>Small (but important) correction to E89’s solution. Whenever you pick numbers you MUST check EVERY answer choice. Just because (A) comes out correct it DOES NOT mean that (A) is the answer. More than 1 answer choice can come out correct.</p>
<p>Usually, the strategy of picking numbers can only be used to eliminate answer choices - it CANNOT be used to get the answer. If you choose numbers that aren’t too simple, then you can often eliminate 4 of the choices leaving you with the correct answer. But you will not know this for sure unless you check all 5 answer choices.</p>
<p>I know, usually I would keep going, but I saw the answer before I even started the problem, so there really was no point. However, you are right, you should always try all of the answer choices when picking numbers. Sorry about that.</p>