An apple grower finds that if she plants 40 trees per acre, each tree will yield 150 bushels of apples. She also estimates that for each additional tree that she plants per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest

41 trees per acre

Step-by-step explanation:

For each tree per acre

Yield = 150 bushels of Apple

: Each tree tree will have :

150/40 = 3.75 bushels of Apple

Now;

For an additional tree(= 41 trees)

We would normally have for an acre to be

( 150/40) × 41 = 153.75 bushels of apples

But since in this case, there is a decrease of three bushel, we have

For the 41 trees per acre to be

153.75 - 3 = 150.75

Hence,

For each tree, we would have:

150.73 / 41 = 3.677 bushels of Apple

Conclusion:

40 trees yields 150 bushels of Apple per acre

41 yields 150.75 bushels of Apple per acre

10/60

step-by-step explanation:

if you divide 10 by 60 the answer is 0.166666 while if you divide or solve the other problems it equals 0.6

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81