Carlos and Lily want to know the combined amount of money they made last week. They both made $12 per hour, but Carlos also made a $35 bonus. Carlos says the
combined amount is 12C + 35 + 121, where is the number of hours he worked,
and L is the number of hours Lily worked. Lily says the combined amount is
12(C + L) + 35. Who is right? Explain.

Lily: 12(C + L) + 35

Step-by-step explanation:

Variables:  C (Carlos) and L (Lily)

They both get: $12 for the hours they worked

We do not know how long they worked

We do know Carlos got an extra $35.

What does it mean?

12(C + L)+35

12 times the profit of Carlos and Lily. Plus the bonus of Carlos

x = 23.78

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.