Acat and a dog have a race. the cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. which of them will win the race?

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

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.