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

In summary, the conversation revolved around finding the upper and lower bounds of a quadratic equation by setting two functions equal to each other and solving for x. One person got a root of 6 and assumed the lower bound was 2. Another person suggested using the quadratic formula to find the other root. The conversation then shifted to a different question about finding the value of a parameter q in order to get an area of 25 between two given functions. The method for solving this question involves setting the two functions equal to each other and finding the intersecting points, but the coefficient q is currently unknown.
  • #1
olicoh
24
0
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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  • #2
How did you get the upper and lower bounds?
You should have set your two functions equal to each other and solve for x.
 
  • #3
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
 
  • #4
setting your equations equal we have,
[tex]\sqrt{x - 2}[/tex] = 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.
 
  • #5
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
 

1. What is the concept of "area between two curves"?

The area between two curves refers to the region enclosed by two curves on a graph. It is the area between the two curves and the x-axis.

2. How do you calculate the area between two curves?

To calculate the area between two curves, you need to find the points of intersection between the two curves. Then, you can use the definite integral to find the area between these points. The integral of the upper curve minus the integral of the lower curve will give you the area between the two curves.

3. What if the curves intersect multiple times?

If the curves intersect multiple times, you will need to break up the region into smaller sections and calculate the area for each section separately. Then, you can add up all the individual areas to find the total area between the two curves.

4. Can the area between two curves be negative?

Yes, the area between two curves can be negative if the upper curve is below the lower curve at certain points. This means that the lower curve is actually enclosing a larger area than the upper curve in that particular region.

5. What are some real-life applications of finding the area between two curves?

One real-life application is in economics, where the area between the supply and demand curves represents the equilibrium quantity and price in a market. It is also used in engineering to calculate volumes of irregular shapes, and in physics to calculate work done by a variable force.

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