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

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: