A waiter served 12 customers at lunch. Then he worked the dinner shift and served 5 new customers per hour. Write an equation that represents the number of customers the waiter served over lunch and dinner. Identify the x and y variables and explain the meaning of the slope and y-intercept.

The question is asking to find an equation of how many customers the waiter served.

Given: 12 customers at lunch; 5 per hour for dinner

Find: number of customers served at lunch AND dinner

We use variables for this, x and y. A general equation is usually y=ax+b, where y is the solution, x is the variable, and a and b are numbers.

Knowing this information, since it is already given that 12 customers were served, the equation turns into y=ax+12

Additionally, since we don't know how many hours she worked, we can use that as a variable. y=5x+12

x=how many hours the waiter worked at dinner

y=overall hours the waiter worked at both lunch and dinner

slope=5, means customers are going up 5 every hour

y-intercept=12, the given/starting point on the y-axis

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.

1. perpendicular

2. parallel

3. perpendicular