What is the range of the function g(x) = |x – 12| – 2? a). {y | y > –2} b). {y | y > –2} c). {y | y > 12} d). {y | y > 12}

Step-by-step explanation:

The function is given by

It is an absolute value function which has a v- shaped graph.

The vertex form of an absolute function is given by y = a|x-h| +k, where (h,k) is the vertex.

Comparing the given equation with this, we have

h = 12

k = -2

Hence, the vertex would be (12,-2).

Now, the range of the function is the set of y values for which the function is defined.

This function has vertex of (12,-2). hence, it would not be take any values which are less than -2. Please see the attache graph.

Hence, the range would be the all y values greater than or equal to -2.

Hence, range is given by

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.

stethere all not eveanp-by-step explanation: