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# Real Life Situation

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You work for the BeeSwaks Candle Company and have been asked to update two of the company’s earliest candle designs, the Brick and the Egyptian. The original Brick was a cube 8 cm on a side. The original Egyptian was a pyramid 21 cm tall with a square base 10 cm on a side.

Improvements in the manufacturing process have made it possible to change the design of these candles for a fresh new look and improved profit. You have been asked to work within the following guidelines:

Name

The Brick                                                                       The Egyptian

Shape

rectangular prism                                                              right square pyramid

Base

dimensions can vary, but it must be a square          same dimensions as base of the Brick

Height

1 cm less than the side length of the base                                                21 cm

You need to prepare for your meeting with the BeeSwaks executives by writing and graphing functions so that you can compare the volumes and resulting production costs of each candle. The BeeSwaks executives want to see detailed support for the calculations done by their production staff, so you should come armed with labeled graphs and worked-out equations to support them.

Use your equations from Lesson 1 for the Brick candle and the Egyptian candle to create a graph of two polynomial functions so that you can compare volumes for different values of x. Compare the volumes.

Here is my equation for the Brick candle x^3 - x^2 and for the Egyptian candle v=7x^2

Use the graph from Question 1 to identify where the volumes are equal. Confirm this value by writing and solving an equation that describes the difference between the volumes of the candle types.

The same wax will be used to make each candle, and it costs  of 1¢ 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.

Nov 10, 2018

#1
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Your equations for the volumes are both correct.

I assume you can use this site or Desmos or something to make the graphs.

From the graph you'll see the two volume functions intersect at the point (8,448)

Let's show this algebraically.

\(x^2(x-1) - 7x^2=0\\ \forall x \neq 0\\ x-1-7 = 0\\ x-8=0\\ x=8\)

The wax cost funtion is just the volume functions times \$0.01, provided x is given in cm.

Brick is cheaper to make than Egypt up to a base width of 8cm.  At that size both candles cost \$4.48.

Larger than that the Egypt becomes cheaper to make.

Nov 10, 2018
#2
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For question 1 , I see how you showed it algebraically when they intersect, but how would I comprare the volumes with that information since it asks to compare the volumes of X ? Would the difference be where they intersect  ?

jjennylove  Nov 10, 2018
#3
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I as well posted the last part thats connected to these question if there anyway you could give a look at it. I would really aprrectiate and if you could explain how and the equations used,i would really like to make notes of this for future reference! Thank you again jjennylove  Nov 10, 2018
#4
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I don't understand what you are asking here.  The differerence between the volumes is given by

\(V_{brick}-V_{egypt} = x^2(x-1) - 7x^2 = x^2(x-8)\)

You can graph that instead of graphing each volume if you like and look for the

x intercept rather than where the two volumes intersect.

Rom  Nov 10, 2018
#5
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Im sorry I read your response wrong, that would be the equation .That makes sense . Thank for your help .

jjennylove  Nov 10, 2018
edited by jjennylove  Nov 10, 2018
edited by jjennylove  Nov 10, 2018
edited by jjennylove  Nov 10, 2018
edited by jjennylove  Nov 10, 2018