Mathematics, 27.07.2019 19:30 csarge2972

3. the same wax will be used to make each candle, and it costs 3/4 of a penny per cubic centimeter. write polynomial functions to show the cost of the wax that is used for making each candle for different values of x. graph the functions. discuss the costs. x2 (x-1) = x3 – x2 and v = 1/3 x2+7x

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For the brick candle, the volume is given by

$Volume=x^2(x-1) \\ \\ =x^3-x^2$

For the Egyptian candle, the volume is given by

$Volume= \frac{1}{3} x^2(21) \\ \\ =7x^2$

Given that the candle wax costs 3/4 of a penny per cubic centimeter, the cost of the wax that is used for making each candle for different values of x is given by:

For the brick candle:

$0.75(x^3-x^2)=0.75x^3-0.75x^2\, pennies$

For the Egyptian candle:

$0.75(7x^2)=5.25x^2\, pennies$

Answer from: jaquezdaking4919

1) $Cost_{BC}=0.75(x^{3}-x^{2})$

2) $Cost_{EC}= 5.25x^{2}$

3) Graph below

Initially, the cost of producing Egyptian Candles is higher than producing Brick ones. Until t = 8 than the cost of both equalizes. For t > 8 the Brick Candles turn to be more expensive to produce, and the Egyptian ones cheaper.

Step-by-step explanation:

Retrieving missing Information for the sake of clarity:

You work for the BeeSwaks Candle Company and have already updated the Brick and the Egyptian candles . The volume of the the brick is measured by the equation x^3-x^2 . The volume of the Egyptian candle was marked by the equation $7x^{2}$

So Volume functions:

Brick Candle: $x^{3}-x^{2}$

Egyptian candle: $7x^{2}$

The same wax will be used to make each candle, and it costs 3/4 of 1¢ (1 penny) per cubic centimeter. Write polynomial functions to show the cost of the wax that is used for making each candle for different values of x. Graph the functions. Discuss the costs.

Cost functions

Cost = 3/4Volume

1) Brick Candle: Multiply by 3/4 the Volume of brick candle volume function:

$Cost_{BC}=\frac{3}{4}(x^{3}-x^{2})\Rightarrow Cost_{BC}=0.75(x^{3}-x^{2})$

2) Egyptian Candle: Multiply by 3/4 the Volume of Egyptian Candle function:

$Cost_{EC}=\frac{3}{4}7x^{2}\Rightarrow Cost_{EC}=\frac{21}{4}x^{2}\Rightarrow Cost_{EC}= 5.25x^{2}$

3) Check it out the Graph of each Cost functions below:

Analyzing the graph below and setting the table functions, initially. the cost of producing Egyptian Candles is higher than producing Brick Candles. Until t = 8 than the cost of both equalizes. For t > 8 the Brick Candles turn to be more expensive to produce, and the Egyptian ones cheaper to produce.