Gabriel owns a small textile company that produces shirts. On a particular day, Gabriel has one worker come into the shop to make shirts. He must pay the worker $14 per hour and also pay $3 per shirt for material costs. The worker created an average of 3 shirts per hour and Gabriel's total expenses for labor and materials were $230. 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:

>First lets break down the problem...

Worker Pay : $14 per hour

Material Costs : $3 per shirt

Average 3 shirts per hour is made

Total expenses : $230

>Now create variables

Worker pay : 14h (h is hours)

Material Costs: 3s ( s is shirts)

Shirts made : 3sh (sh is shirts per hour)

> Plug-in variables to make an equation

14h + 3s = 230

>Solve if needed ( Use the Substitution Property)

yess

step-by-step explanation:

idk whyy this is happening, i cant even read my notification bc i keep getting errors

~coco

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.