Acircle is centered at the point (-7, -1) and passes through the point (8, 7).
the radius of the circle is . the point (-15, lies on this circle.

Part 1) The radius of the circle is 17 units

Part 2) The point (-15,14) and (-15,-16) lies on this circle

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance from a circle's center to any point on the circle is called the radius of the circle

the formula to calculate the distance between two points is equal to

Find the distance (radius) between the points (-7,-1) and (8,7)

substitute in the formula

step 2

Find the equation of the circle in center radius form

where

(h,k) is the center of the circle

r is the radius of the circle

we have

substitute

Remember that

If the point (-15,y) lie on the circle, then the ordered pair must satisfy the equation of the circle

substitute the value of x=-15 in the equation

solve for y

take square root both sides

therefore

The point (-15,14) and (-15,-16) lies on this circle

see the attached figure to better understand the problem

23

step-by-step explanation:

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: