Nicole owns a small textile company that produces shirts. on a particular day, nicole has one worker come into the shop to make shirts. she must pay the worker $29 per hour and also pay $2.50 per shirt for material costs. the worker created an average of 5 shirts per hour and nicole's total expenses for labor and materials were $290.50. write a system of equations that could be used to determine the number of hours the worker worked and the number of shirts the worker made. define the variables that you use to write the system.

Step-by-step explanation:

Let x be the number of working hours

She must pay the worker $29 per hour

So, Cost of labor for x hours = 29 x

The worker created an average of 5 shirts per hour

So, no. of shirts produced in x hours = 5x

Cost of 1 shirt = 2.50

Cost of 5x shirts = 2.50(5x)

Total expenses for labor and materials =

We are given that  Nicole's total expenses for labor and materials were $290.50

So,  

Hence a system of equations that could be used to determine the number of hours the worker worked and the number of shirts the worker made is

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.