Answer:
Farmers growing high-yield crops are more likely to be self-sufficient and thus require less support from the rest of society.
Explanation:
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I will assume you mistyped this question. For y = -1/16x^2 + 4x + 3, the answers to this question are
a) 3 feet
b) 67 feet
c) 64.741 feet
For a) we note that at x = 0, that is the instant where the ball leaves the hand. y(0) = 0.
For b), we find the vertex of y = -1/16x^2 + 4x + 3
y = -1/16x^2 + 4x + 3
y = -1/16(x^2 - 64x) + 3
y = -1/16(x^2 - 64x + 1024 - 1024) + 3
y = -1/16((x-32)^2 - 1024) + 3
y = -1/16(x-32)^2 + 64 + 3
y = -1/16(x-32)^2 + 67
The vertex is at (32,67) so 67 is the maximum height.
For c), we find the x-intercepts with the quadratic formula on
y = -1/16x^2 + 4x + 3=0:
x = [ -b <span>± √b^2 - 4ac ] / (2a)</span><span>
x = [ -4 ± √4^2 - 4(-1/16)(3) ] / (2(-1/16))
x = -0.741, 64.741
Only the positive solution, so 64.741 feet </span>
We can define the base of each equilateral section as

since this is the distance from the x-axis to the function

.
An equilateral triangle's area can have a function defined solely by the base. Since all sides are equal, the height of the triangle can be found via pythagorean theorem as:

But we know that the base

is a function of x. We also can then state that Area

is also a function of x. Specifically:

.
Then if we integrate the area function A(x) from 0 to pi, we get the total volume:
The most economic activities were agriculture.