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