Find the solution set for the equation, given the replacement set.

y = –5x + 8; {(6, –11), (4, –12), (5, –9), (3, –14)}
a.
{(6, –11)}
c.
{(4, –12)}
b.
{(3, –14)}
d.
{(5, –9)}

c. {(4, -12)}

Step-by-step explanation:

It is convenient to rearrange the equation to standard form:

5x +y = 8

Then check the offered points.

(6, -11): 5·6 -11 = 19 ≠ 8

(4, -12): 5·4 -12 = 8 . . . . . . this is in the solution set

(5, -9): 5·5 -9 = 16 ≠ 8

(3, -14): 5·3 -14 = 1 ≠ 8

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.