What are the intercepts of the line

y intercept (0,-32)

x intercept (3.2,0)

Step-by-step explanation:

To find the y intercept set x = 0 and solve for y

y = 10x -32

y = 0-32

y = -32

(0,-32)

To find the x intercept set y = 0 and solve for x

y = 10x -32

0 = 10x -32

Add 32 to each side

32 = 10x

Divide by 10

32/10 = x

(3.2,0)

Step-by-step explanation:

The y-intercept happens where x is 0, and the x-intercept if where y is 0. You can use this knowledge to find the intercepts.

This equation is written in slope-intercept form:

where b is the y-intercept, so the y-intercept is -32.

To find the x intercept, insert 0 as the value of y:

Solve for x. Add 32 to both sides:

Divide both sides by 10:

The x-intercept is at or .

Find the points:

Finito.

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.