The number of apples produced by each tree in an apple orchard depends on how densely the trees are planted. if n trees are planted on an acre of land, then each tree produces 900 - 9n apples. so the number of apples produced per acre is a(n) = n(900 - 9n) how many trees should be planted per acre to obtain the maximum yield of apples?

50 trees should be planted to obtain the maximum yield

Step-by-step explanation:

In order to calculate the maximum yield of apples per acre, where

A(n) = n* (900 - 9 n)

A should be derived respect to n . The maximum value stands where the derivative equals 0. Thus,

A(n) = n* (900 - 9 n) = 900*n - 9* n²

therefore

dA/dn = 900 - 2*9*n = 0 → n= 900/(2*9) = 50 trees

the maximum yield of apples A will be

A(50) = 50* (900 - 9*50) = 22500 apples/acre when n=50 trees

Note

- Since the second derivative d²A/(dn)² = -18 < 0 we verify that is a maximum value

- n goes between 0 and 100 , with maximum at 50

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.