What is the real value of q for an area of 25 between two given functions?

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Homework Help Overview

The discussion revolves around finding the real value of the parameter q for the area enclosed between two functions, H(x) = x² and P(x) = 4 - x² - qx, to equal 25. Participants are exploring the implications of the functions' intersection points and the role of the parameter q in determining the area.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss setting the two functions equal to find intersection points and question the determination of upper and lower bounds. There is mention of applying the quadratic formula to solve for x and the implications of the parameter q on the area calculation.

Discussion Status

The discussion is active, with participants sharing their attempts to find bounds and questioning assumptions about the values of q. Some guidance has been offered regarding solving for intersection points, but there is no explicit consensus on the correct approach or values yet.

Contextual Notes

Participants note the challenge of determining the area without knowing the coefficient q, which is a variable in the function P. There is also a reference to the need for quadratic equations arising from the intersection of the two functions.

olicoh
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The problem and attempt at solution is attached in the word document. I think I have it right but I'm not sure about the upper and lower bound.
 

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How did you get the upper and lower bounds?
You should have set your two functions equal to each other and solve for x.
 
magicarpet512 said:
How did you get the upper and lower bounds?
You should have set your two functions equal to each other and solve for x.
I did. I got 6... I didn't get any other number so I assumed the lower bound was 2
 
setting your equations equal we have,
\sqrt{x - 2} = 8 - x
Solving for x should give us a quadratic equation to work with, which will have two roots.
Just apply the quadratic formula. You have one of the roots already, and it is not an upper bound.
 
Could someone help me with this question:
given two functions: H(x) and P(x),
H(x)=x^(2) and P(x) = 4-x^(2 )- q*x.
Note, the function P also has a parameter, q which is a real number.


Find the real value(s) of the parameter q such that the area of the region enclosed between these two functions is equal to 25.

I know that I have to H(x)=P(x) to get the intersecting points , but how could I get an answer if I don't have the coefficient q
 

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