Question

1. Write the equation of a circle in standard form whose center is at (3,-2) and has a radius of 11:

2. Find the average rate of change of a linear function y = f(x) = 2x - 1 if input x is changing
from x=1 to x=3:

Answer 1

1. The standard form equation of a circle with center (h,k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Plugging in the given values, we get:
(x - 3)^2 + (y + 2)^2 = 11^2
(x - 3)^2 + (y + 2)^2 = 121

So the equation of the circle is:
(x - 3)^2 + (y + 2)^2 = 121

2. The average rate of change of a linear function y = f(x) = mx + b over an interval [x1, x2] is given by:
average rate of change = (f(x2) - f(x1)) / (x2 - x1)
Plugging in the given values, we get:
average rate of change = (2 * 3 - 1 - (2 * 1 - 1)) / (3 - 1)
average rate of change = (5 - 1) / (3 - 1)
average rate of change = 4 / 2
average rate of change = 2

So the average rate of change of the function y = 2x - 1 over the interval [1, 3] is 2