3-120 (a) More Solving By Rewriting Sean was trying to solve for x in the equation
0.4(x - 2) = 3.4 -0.2x. He said to his teammate,
April, “Decimals! I wish that we only had equations with
whole numbers!" Suddenly, April blurted out, "Wait,
Sean! I think there is another way. Can't you first
rewrite this equation so it has no decimals? Then it will
be faster and easier to solve!"
What is April talking about? Explain what she means.
Then rewrite the equation so that it has no decimals.

2x3 – 6x2 – 14x + 24 square centimeters

if i'm wrong i'm sorry : )

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.

98%

step-by-step explanation:

b. 2 and 4

step-by-step explanation: