Determine the domain of the function f(x) = 2x - 4 when the range is {0, 12, 20}.

a. {2, 8, 12}

b. {0, 12, 20}

c. {4, 16, 24}

d. none of these

A.

Step-by-step explanation:

The range of a function is the possible values of y = f(x). We have that the range is {0,12,20}. Then, to find the domain we equalize the function to each range value and find the possible values of x (domain).

In the case os 0 we have:

0 = 2x-4

4 = 2x

x = 4/2 = 2.

In the case of 12 we have:

12 = 2x-4

12+4 = 2x

16 = 2x

x = 16/2 = 8.

In the case of 20 we have:

20 = 2x-4

20+4 = 2x

24 = 2x

x = 24/2 =12.

The, the domain of the function with that range is {2,8,12}. Then the answer is A.

d≈7.07in

step-by-step explanation:

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.