A baseball diamond is a square with sides 90 ft long. A batter is at bat, with runners at first and second base. At the moment the ball is hit, the runner at first base runs to
second base at 25 ft/s. Simultaneously, the runner on second base runs to third base
at 15 ft/s. How fast is the distance between these two runners changing 2 s after the
ball is hit?

The runner on first has distance from second of  90 -25t, where t is the time in seconds since he left 1st base.

The runner on second has a distance from second of  15t, where t is the time in seconds since he left 2nd base

Then the Pythagorean theorem tells us the distance between the runners is :

d = √((90 -25t)² +(15t)²)

The rate of change of distance between the runners is the derivative of this with respect to time.

dd/dt = 2(90-25t)(-25)+2(15t)(15) / (2sqrt(90-25t)^2 + 15t^2)

Replace t with 2 and solve to get: -31

The distance between runners is decreasing at 31 ft/s two second after they leave the bases.

2

step-by-2step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204