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The positive number c for which the curve

y=c² −x²
divides the area under the curve y=9604−x²
from 0 to 98 into two equal areas is c=_______

1 Answer

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Final answer:

The problem involves finding the value of c where the curve y=c²-x² divides the area under the curve y=9604-x² equally from 0 to 98. This is found by equating and solving the integrals of both curves from 0 to 98. The calculation requires knowledge of integral calculus.

Step-by-step explanation:

The student is asking for the value of c where the curve y=c² - x² equally divides the area under the curve y=9604 - x² from 0 to 98.

To find this value, we must set up an integral for each area and solve for c such that the areas are equal. We integrate from 0 to 98 for both curves, but as the formula for y changes depending on c, we will be solving for the integral of (9604 - x²) and (c² - x²) separately. The goal is to find the value of c where the integral of the first curve from 0 to 98 minus twice the integral of the second curve from 0 to 98 equals zero (since we are told the areas are equal).

Using the integral properties for y = a - x², we calculate the areas and find the point where they match. This involves evaluating definite integrals and setting up an equality and then solving for c

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