Which point lies on the circle represented by the equation (x + 5)2 + (-9)2 = 82?
A. (0,8)
B. (13,-9)
c. (-5,1)
D. (3,17)

None of the given points lies on the circle.

Step-by-step explanation:

The circle is represented by the following formula:

(x - xc)² + (y - yc)² = r²

Where (xc,yc) are the coordinates of the center and r is the radius of the circle. In the case we have:

(x+5)² + (y-9)² = 82

If a point belongs to this circumference, then the results of applying the points to the equation should be valid. To test all the points we are going to apply each to the equation as shown below:

A.

(0 + 5)² + (8-9)² = 82

5² + (-1)² = 82

25 + 1 = 82

26 = 82 (invalid)

The point does not lies on the circle.

B.

(13 + 5)² + (-9-9)² = 82

(18)² + (-18)² = 82

324 + 324 = 82

648 = 82 (invalid)

The point does not lies on the circle.

C.

(-5 + 5)² + (1 - 9)² = 82

0² + (-8)² = 82

64 = 82 (invalid)

The point does not lies on the circle.

D.

(3 + 5)² + (17-9)² = 82

8² + 8² = 82

64 + 64 = 82

128 = 82 (invalid)

The point does not lies on the circle.

507

Step-by-step explanation:

The function which represents the altitude of blimp is:

Here, x is the time in minutes

The function representing the time in minutes is:

Here, x is the height in thousands of feet of the blimp.

We need to calculate f(g(4)). g(4) gives the time in minutes when the height is 4000 feet. So, f(g(4)) will give the altitude of the blimp when its height is 4000 feet.

Substituting x = 4 in equation of g(x), we get:

So,

Therefore, the value of f(g(4)) is 507