Answer the 5 questions listed below show your work
1) divide the following and simplify, if necessary.
6 1/3 -: 5/6
your options are:
a) 36/5
b) 95/18
c) 38/5
d) 12/5
2) 3-7^2 + 3 * 4^2
a) -34
b) 2
c) 304
d) 64
3) find the following when a = -2, b = 3, c = -1/3
(7b - 2)/(-a) +1
a) -21/2
b) 17/2
c) 4/2
d) 21/2
4) find the following when a = -1, b = 5, c = -2/3.
(7b-10)/a -1
a) 11
b) -26
c) -13
d) 28
5) use the formulas for a cylinder:
r = 5
h = 7
v = ?
a) 12pi
b) 175pi
c) 24pi
d) 18pi

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.