I’m having a little trouble understanding the explanation for #3 on the Working in Three Dimensions…

Hello Mike,
Basically, I’m having a little trouble understanding the explanation for #3 on the Working in Three Dimensions section on page 284. I got a little lost after the part where you explained how d was the height (this makes sense to me). Like, how do we “recognize that the ab term in the surface area expression must represent both the top and the bottom of the prism”? I think it’s somewhere from the equation but I don’t know where. I would greatly appreciate your help here Mike. Thanks!

Hello! For question #8 on page 111…

Hello! For question #8 on page 111 in the Exponents and Exponential Functions section, where did the 2^2 come from? The answer was 82.41*2^2= 329.6. Thank you ^_^.

COLLEGE BOARD Test 9 Math Section 3 #13

COLLEGE BOARD Test 9 Math Section 3 #13

Could you suggest a shortcut or fast way to solve this? All the answers are written in vertex form, so we can quickly eliminate two of them, as the coordinates of the vertex, as indicated by the graph provided, must be (3,1). That leaves choices A and C. Is there a quick way to solve from there without plugging in values from the graph?

Hello Mike, For problem 2 on page 284…

Hello Mike,
For problem 2 on page 284 (relating to “Working in Three Dimensions”), I had difficulty answering the question, because I don’t know what the inner radius of a sphere and how that differs from the outer radius of a sphere. Since I’m not able to find anything on the Internet that talks about this, could you please explain the difference to me?
And could you then tie it back to how the entire inner/outer radius thing is relevant to the question at hand (#2 on page 284)?