At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season when about 700 vines are planted per acre. for each additional vine that is planted, the production of each vine decreases by about 1 percent. so the number of pounds of grapes produced per acre is modeled by a(n) = (700 + n)(10 − 0.01n) where n is the number of additional vines planted. find the number of vines that should be planted to maximize grape production.

Number of vines that should be planted are 150.

Step-by-step explanation:

The number of pounds of pounds of grapes produced per acre is represented by the expression

Where n = additional vines planted

To maximize the production of grapes we will find the derivative of A(n) and equate it to zero.

For

3 - 0.02n = 0

0.02n = 3

n =

n = 150

To check whether the maximum value of the function is at n = 150, we will find the second derivative A(n).

Which shows A"(n) < 0

Therefore, A(n) has the maximum value at n = 150.

Therefore, number of vines that should be planted are 150.

1,8,15,22,29,36,43,50

step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.