<p>For any cube, if the volume is V cubic inches and the surface area is A square inches.
Then V is directly proportional to which of the following?
A^2
A
A^3
A^3/2
A^2/3
I got this one wrong in May and I really don't know how to answer it.</p>
<p>For All x, let the function f be defined by f(x)= a(x-h)^2 +k. If a and k are constants which of the following cannot be true?
f(10)=1
f(0)=-5
f(0)=5
f(1)=-h
f(-1)=h</p>
<p>the answer to this one is B, but why can't D be an answer? :S </p>
<p>Please guys I need an explanation to both of them.. thank you!</p>
<p>Cube one:</p>
<p>Solve for the volume and surface area in terms of the side length, let’s call it s.</p>
<p>V=s^3 -> s=V^(1/3)
A=6s^2 -> s=(1/6)A^(1/2)</p>
<p>Set them equal, so V^(1/3)=(1/6)(A^(1/2)). Multiply the exponents of V and A by 3 so we get V. Now, V=(1/6)(A^(3/2)) Therefore V is directly proportional to A^(3/2) and we are done. -> D</p>
<p>Second Question:</p>
<p>I remember this question. you left out that a and k are positive constants, so h can be negative, but f(0)=a(-h)^2+k = ah^2 + k and since k is squared, it will either be positive or 0. If it is positive, the product ah^2 will be positive and because k is positive, f(0) must equal a positive number. If h is 0, then f(0)= k and since k is positive, f(0) must equal a positive number, k. So B, f(0)=-5 cannot be true because f(0) must be a positive number. -> B</p>
<p>thanks there! that was very helpful! :)</p>