Question

The region bounded by the parabolas y² = 5x and y² = 10x − 5

is rotated about the x-axis. The two curves intersect at x = ?

Answer 1

The two parabolas intersect at x = 1.

Step-by-step explanation:

To find the value of x at which the two curves intersect, we need to set the two equations equal to each other and solve for x.

Setting y² = 5x equal to y² = 10x - 5, we get 5x = 10x - 5.

Combining like terms, we get 5 = 5x.

Dividing both sides by 5, we find that x = 1.

Therefore, the two curves intersect at x = 1.