intelli said:Find c>0 such that the area of the region enclosed by the parabolas y= x^2-c^2 and
y = c^2-x^2 is 110
what is value of c
i got 3.49 and it is wrong i don't understand how to do this problem any help would be greatly appreciated
berkeman said:How did you get 3.49? Show us your work please.
berkeman said:How did you get 3.49? Show us your work please.
Dick said:I get 3.45... as well. But that's not the same as 3.49. Maybe they want you to express it exactly using a cube root?
intelli said:no i tried that it doesn't work
Dick said:It looks fine to me.
berkeman said:I agree. Ask the prof, and please post the final answer back here. Thanks.
Dick said:I think he is figuring out which curve is on top of the region (y=c^2-x^2) and which is on the bottom (y=x^2-c^2) and then the x boundaries +c and -c. He think subtracts the lower curve y from the upper curve y and integrates over the whole region at once (rather than doing the first quadrant and multiplying by 4, like you did). But if you do his final integral, you get (8/3)*c^3. Just as you did.
The "shaded region" refers to the part of a figure or shape that is shaded in a diagram. Finding the area of this shaded region involves determining the total amount of space that is covered by the shaded portion of the figure.
The formula for finding the area of a shaded region will vary depending on the shape of the figure. For example, the area of a shaded circle can be found using the formula A = πr^2, where r is the radius of the circle. The area of a shaded rectangle can be found using the formula A = length x width. It is important to identify the shape of the shaded region and use the appropriate formula to calculate its area.
One common mistake is forgetting to include the units in the final answer. It is important to always include the correct units (such as cm^2 or m^2) when reporting the area of a shaded region. Another mistake is using the wrong formula for the given shape. It is important to double check the formula being used and make sure it is appropriate for the shape being calculated. Lastly, not taking into account the scale of the diagram can also lead to incorrect answers.
One way to check your answer is by using a different method to calculate the area. For example, if you used the formula for a rectangle to calculate the area of a shaded triangle, you can double check your answer by using the formula A = 1/2 base x height. Another way to check is by using the scale of the diagram. You can estimate the area of the shaded region using the scale and compare it to your calculated answer.
No, the area of a shaded region cannot be negative. Area is a measure of space and cannot be less than 0. If you get a negative value when finding the area of a shaded region, it may indicate that an error was made in the calculations or that the shape being calculated is not possible.