3x - 5y = -35
12x+y=-6

x =y =

Step-by-step explanation:

in order to solve this system of equation  let us say

3x - 5y = -35equation 1

12x+y=-6equation 2

from equation 2

12x+y=-6equation 2

y =  -6 - 12x equation 3

substitute for y = -6 -12x into equation 1

3x - 5y = -35equation 1

3x -5( -6 - 12x) = -35

3x + 30 + 60x = -35

63x + 30  = -35

collect like terms

63x= -35 -30

63x = - 65

divide both sides by 63

63h/63 = -65/ 63

x = -1.03

put x = 1. 03 into equation 3

y =  -6 - 12x equation 3

y = -6 - 12( -1.03)

y = -6 + 12.38

y = 6.38

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.