Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 42. How old is each sister? (a) Write an equation that represents the situation. Explain any variable used.
(b) Solve the equation from Part (a). Show your work. State your solution as a complete sentence.

a: K = 2s

K + s = 42

b: 2s + s = 42

K = 28

s = 14

Step-by-step explanation:

1. Come up with equations based on the information given.

K = Kim

s = sister

Kim is twice of her sister -> K = 2s

When you add Kim's age to her sister's age, you get 42 -> K + s = 42

2. Substitue for K to find out the value of s

K = 2s

2s + s = 42

3. Solve for s

s = 42/3

s= 14

4. Solve for K

K = 2s

K = 2*14

K = 28

answer: idk

step-by-step explanation:

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.