Sara is serving wings and burgers at her party. Wings cost $6.00 per serving and burgers are $3.00 each. Sara knows that at least 4 of her friends want wings. Sara must spend less than $45.00. Sara graphs a system of inequalities to determine how many servings of each kind of food she could serve to stay within her budget.

According to the dark blue area on the graph, which coordinate pair satisfies the system for the number of wing servings and burgers that Sara can serve?
A) (5, 4)
B) (2, 5)
C) (8, 3)
D) (6, 5)

A) (5,4)

Step-by-step explanation:

Just take a look at the intersection in the dark blue area. The only point that fits in that area is A) (5,4). And this makes sense, but let's check it anyways:

5 wing + 4 burger < 45

5(6) + 4(3) < 45

42 < 45. If she bought one more burger, she would be at $45, and the problem asked us to be under $45, so this is our answer.

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.