Solve Break-Even Question: C=5.5\sqrt{}x+10,000, R=3.29x

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Homework Help Overview

The problem involves finding the break-even point between cost and revenue functions defined as C=5.5√x+10,000 and R=3.29x. The original poster expresses uncertainty about how to approach the problem, particularly in relation to factoring and the use of a calculator.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss setting C equal to R to form a quadratic equation. There are questions about the applicability of the quadratic formula given the presence of a square root in the equation. Some suggest squaring both sides to eliminate the square root, while others propose a substitution method to simplify the problem.

Discussion Status

The discussion includes various approaches to solving the equation, with participants providing different methods and clarifications. Some guidance has been offered regarding the substitution method, which may help the original poster in understanding how to proceed without a calculator.

Contextual Notes

The original poster indicates a lack of familiarity with calculus and expresses concern about whether they are in the correct forum for their question. There is also mention of a potential reliance on a graphing calculator, which is not applicable in this case.

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Homework Statement


C=5.5\sqrt{}x+10,000
R=3.29x
C=R

Homework Equations





The Attempt at a Solution


I really don't have an attempt. Accountant tryin to learn calculus from his old book. I don't know where to start or I guess i should say i don't know how to factor. The book usually shows an emblem of a graphing calculator when you should use one and this problem doesn't have the emblem. so how do I solve without calculator? Thanks. Been a part of many forums, but never a math forum. Am i posting in the correct area?
 
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Have you tried setting C=R then forming a quadratic and finally using the quadratic formula.
 
I have. However, there is an X to the 1/2. Will the quadratic still work? Sorry if this is really easy. Just gettin back ino it.
 
You can square it to get rid of the squareroot. :-)
 
set C=R then square both side, expand.
congratulations you got yourself a quadratic equation.
 
bigwill5112 said:

Homework Statement


C=5.5\sqrt{}x+10,000
R=3.29x
C=R

Homework Equations





The Attempt at a Solution


I really don't have an attempt. Accountant tryin to learn calculus from his old book. I don't know where to start or I guess i should say i don't know how to factor. The book usually shows an emblem of a graphing calculator when you should use one and this problem doesn't have the emblem. so how do I solve without calculator? Thanks. Been a part of many forums, but never a math forum. Am i posting in the correct area?

You don't have to square a thing to solve this.
<br /> \begin{align*}<br /> 3.29x &amp; = 5.5 \sqrt{\,x} + 10000 \\<br /> 3.29x - 5.5 \sqrt{\, x} - 10000 &amp; = 0<br /> \end{align*}<br />

Let u = \sqrt x and substitute - you get a quadratic to solve, then you can back-substitute to find x
 
statdad said:
You don't have to square a thing to solve this.
<br /> \begin{align*}<br /> 3.29x &amp; = 5.5 \sqrt{\,x} + 10000 \\<br /> 3.29x - 5.5 \sqrt{\, x} - 10000 &amp; = 0<br /> \end{align*}<br />

Let u = \sqrt x and substitute - you get a quadratic to solve, then you can back-substitute to find x

Ahaa. THANKS! I appreciate everyone's help.
 

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