Adriel is x years old and her younger sister is y years old. the sum of thei ages is 7. the difference of 3 times adriels age and her sisters age is 9. the related sum of the linear equation is x+y=7 3x-y=9. solve the linear equations. then find adriels age and her sisters age

set one of the equations to equal x or y

(substitution method)

x=7-y plug this into the other equation

3(7-y)-y=9 distribute

21-3y-y=9 --> 21-4y=9

get y alone

-4y=9-21--> -4y=-12 divide by -4 to solve

y=3 sisters age

plug this in to one of the equations to get Adriel's age

x+3=7

x=7-3

x=4 Adriel's age

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.

i think it might be a but you might want a second opinion