A farmer finds that if she plants 25 trees per acre, each tree will yield 41 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 1 bushel. How many trees should she plant per acre to maximize her harvest?

17

Step-by-step explanation:

Let F be the number of fruit per acre  

F = (25 + x) × (41 - x)  

F=1025 -25x + 41x -x²

F=-x²+16x+1025

The maximum yield is at the maximum of that expression, which is at

x=8

So apparently she currently has far too many trees per acre. To get the maximum yield, she needs to reduce the number of trees per acre by 8.

So the number of trees per acre for maximum yield is 25-8 = 17.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).