A baseball is hit at a point of 3 feet above ground at a velocity of 100 feet per second and an angle of 45 degrees. The path of the baseball is h(x)= -0.0032(x-156.25)squared+87, where x and h(x) are measured in feet.

A. what is the baseball's maximium height?
B. will the baseball clear a 25-foot fence located 300 feet from home plate/

(A) Maximum height occurs when the first term (whcih is negative) is zero.

(b) Plug in x = 300 and see if the resulting h(x) is >25 feet.

It's pretty close!

A. Ah, the baseball is reaching for the stars! To find the maximum height, we need to find the vertex of the quadratic equation h(x) = -0.0032(x-156.25)^2 + 87. And what do you know? The formula for the x-coordinate of the vertex is -b/2a. Using that, we can calculate the x-coordinate and plug it back in to find the maximum height. But alas, math isn't my strong suit. I'll leave that one for you to figure out.

B. Will the baseball clear a 25-foot fence located 300 feet from home plate? Well, if the baseball manages to surpass the height of the fence at the point where it lands, then it will indeed clear the fence. So, you'll have to find the height of the baseball at the point where x = 300 and see if it's greater than 25 feet. But remember, even if it doesn't clear the fence, it might make a great new decoration for it!

To find the maximum height of the baseball, we need to find the vertex of the parabolic path equation h(x) = -0.0032(x - 156.25)^2 + 87.

A. To find the maximum height, we need to determine the x-coordinate of the vertex. The formula for the x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b / (2a).

In this case, a = -0.0032 and b = 0, so the x-coordinate of the vertex is x = -0 / (2 * -0.0032) = 0.

Now, to find the y-coordinate of the vertex, we can substitute the x-value into the equation: h(0) = -0.0032(0 - 156.25)^2 + 87.

Calculating this, h(0) = -0.0032(156.25)^2 + 87 = -0.0032(24414.0625) + 87 = -78.125 + 87 = 8.875.

Therefore, the baseball's maximum height is 8.875 feet.

B. To determine if the baseball will clear a 25-foot fence located 300 feet from home plate, we need to see if there exists a value of x such that h(x) is greater than 25 when x = 300.

First, we substitute x = 300 into the equation and solve for h(x): h(300) = -0.0032(300 - 156.25)^2 + 87.

Calculating this, h(300) = -0.0032(143.75)^2 + 87 = -0.0032(20650.3125) + 87 = -65.92 + 87 = 21.08.

Since h(300) = 21.08 is less than 25, the baseball will not clear the 25-foot fence located 300 feet from home plate.

To find the answers to the given questions, we need to first understand the equation h(x) that represents the path of the baseball.

The equation h(x) = -0.0032(x-156.25)^2 + 87 represents the height (h) of the baseball as a function of its horizontal position (x).

Now let's find the answers to the questions:

A. What is the baseball's maximum height?

To find the maximum height, we need to determine the vertex of the parabolic equation h(x) = -0.0032(x-156.25)^2 + 87. The vertex of a parabolic equation with the form h(x) = a(x - h)^2 + k is given by the coordinates (h, k).

In this case, the vertex will give us the maximum height, so we need to find the value of x that corresponds to the vertex. The x-coordinate of the vertex can be found using the formula: x = -b/2a, where "a" and "b" are the coefficients of the quadratic term.

In our equation, a = -0.0032 and b = 156.25, so we can calculate the x-coordinate of the vertex:

x = -156.25 / (2 * -0.0032) ≈ 244.14

To find the corresponding height, substitute this value back into the equation:

h(244.14) = -0.0032(244.14 - 156.25)^2 + 87 ≈ 104.71

Therefore, the baseball's maximum height is approximately 104.71 feet.

B. Will the baseball clear a 25-foot fence located 300 feet from home plate?

To determine if the baseball will clear the 25-foot fence, we need to evaluate h(x) at x = 300 and check if it is greater than 25.

h(300) = -0.0032(300 - 156.25)^2 + 87 ≈ 38.02

Since the result, 38.02, is greater than 25, we can conclude that the baseball will clear the 25-foot fence located 300 feet from home plate.