- Point c is 6 inches from plane M. To the nearest integer, what is the area, in square inches, of the portion of M that contains all points that are not more than 12 inches from c? a)33 b)113 c)339 d)452 e)565 2)If p,s, and t are distinct positive primes, what is the least perfect cube that is divisible by p^2 s^5 t^7 a)p^3 s^3 t^3 b)p^3 s^6 t^9 c)p^9 s^9 t^9 d)p^6 s^15 t^21 e)p^8 s^125 t^343 3) If f(x) = 3sin(pie(x))+cos(2pie(x)) a)2 b)3 c)4 d)2pie e)3pie
- please justify your answer so I can understand the concept
- The region formed is a circle with radius 6√3 in (draw the plane and point c, and determine the set of points exactly 12 inches from c - then you can determine the region). Its area is π(6√3 in)^2 ≈ 339 in^2, C.
- You want the exponents on p, s, t to be multiples of 3 (so that it is a perfect cube) and as small as possible (since you want the *smallest* perfect cube). p^3 s^6 t^9 does this, so B is correct.
- Incomplete. Also, use pi or π instead of pie.
@MITer94
I answered question 2 as b but the answer key states that the answer is d.
@MITer94
I actually didn’t understand question one. Is point c above plane m or is it beside it? I am not able to imagine it
@gameplayer for 1., the orientation of c with respect to M doesn’t matter - c could be on either side of M.
For example, if I took a sheet of paper to represent the plane (although the sheet would have to be infinitely large), then c could be any point that is exactly 6 inches from that sheet of paper. c could be on either side of the sheet.
For 2., B is correct.
@MITer94
Oh okay. I got the idea 
thanks for your help