Agraphic designer is drawing a pattern of four concentric circles on the coordinate plane. the center of the circles is located at (-4, 3). the smallest circle has a radius of 3 units. if the radius of each circle is 4 units greater than the largest circle within it, then the equation of the fourth circle is

Hi!

The equation of a circle is (x – h)² + (y – k)² = r², with (h, k) being the center, r being the radius, and x + y being left as just x and y.

If the smallest circle has a radius of 3 units, then the next one is 7 units (4 units greater), and then the second largest 11 units, and then the largest 15. That means, for r in our equation, we're going to put in 15.

So we get:

(x – h)² + (y – k)² = 15², or

(x – h)² + (y – k)² = 225

The center of our circle is at (-4, 3). That means h = -4 and k = 3 in our equation. So let's substitute that in.

(x – (-4))² + (y – 3)² = 225

(x + 4)² + (y - 3)² = 225 is our final equation.

Hope this helped!

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.