An orange grower find that she gets an average yield of 40 bushels per tree when she plants 20 trees on an acre of ground. each time she adds a tree to an acre, the yield per tree decreases by 1 bushel, due to congestion.
how many trees per acres should she plant for maximum yield?

30 trees/acre

Step-by-step explanation:

Let n = the number of trees added to 1 acre

Let Y(n) = the yield in bushels/acre

Yield in bushels/acre = [bushels/tree] x [trees/acre]

Y(n) = (40-n)*(20+n)

       = 800 - 20n + 40n - n^2

       = n^2 + 20n + 800 (1)

The n-value of the vertex ( which is a peak )  is given by the formula:

n(max) = -b/2a

Putting values from equation (1) gives us

n(max) = 10

The grower started with 20 tree/acre and adds 10  more for max yield, so she should plant:  30 trees/acre

and

Maximum yield is 900 bushels/acre.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: