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mrs_skeptik [129]
4 years ago
6

A farmer finds that if she plants 85 trees per acre, each tree will yield 80 bushels of fruit. She estimates that for each addit

ional tree planted per acre, the yield of each tree will decrease by 4 bushels. How many trees should she plant per acre to maximize her harvest
Mathematics
1 answer:
vova2212 [387]4 years ago
5 0

Answer:

52 Trees

Step-by-step explanation:

If she plants 85 trees per acre, each tree will yield 80 bushels of fruit.

Yield = 85 X 80

Let x be the additional tree planted per acre.

For each additional tree planted per acre, the yield of each tree will decrease by 4 bushels.

Therefore, the yield:

F(x)=(85+x)(80-4x)\\F(x)=6800-260x-4x^2

Next, we maximize F(x) by taking its derivatives and solving for its critical point.

F'(x)=-260-8x\\$Setting $F'(x)=0,$ we have:$\\-260-8x=0\\8x=-260\\$Divide both sides by 8$\\x=-32.5

F''(x)=-8, $therefore we have a maximum

It is apparent that she currently has too many trees per acre. To get a maximum harvest, she needs to reduce the number of trees by approximately 32.5 trees.

Therefore, number of trees per acre she should plant:

85+(-32.5)

=85-32.5

=52.5 Trees

Since the number of trees can only be an integer and it cannot be greater than 52.5, the number of trees to be planted per acre to maximize her harvest is 52.

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Aneli [31]

Answer:

Volume of the prism is 648cm^3

Step-by-step explanation:

Given:

Base of the prism is rectangular in shape

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To Find:

Volume of the prism=?

Solution:

Volume of the prism ,

V= Base area of the prism x  Height of the prism

Here in the figure  base of the prism is in  Rectangular form

So the base area of the prism = area of the rectangle

We know that the area of the rectangle is = length x height

Substituting the values

Area of the Rectangle = 12 x 9

Area of the Rectangle = 108

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7 0
3 years ago
5/y + 7/x =24<br> 12/y + 2/x =24 ,find the ratio of x to y.
rosijanka [135]

Answer:

Step-by-step explanation:

5/y + 7/x =24.........(1)

12/y + 2/x =24........(2)

Let 1/y = a and 1/x = b

5a + 7b = 24 ...........(3)

12a + 2b = 24...........(4)

Multiply (3) by 2 and (4) by 7

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84a + 14b = 168.........(6)

Substracting (5) from (6)

84a - 10a = 168 - 48

74a = 120

a = 120/74

a = 60/37

Putting a = 60/37 in (3)

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5(60/37) + 7b = 24

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Multiply each term 37

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259b = 888 - 300

259b = 588

b = 588/259

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Cross multiply

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Also

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Cross multiply

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x = 259/588

7 0
4 years ago
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dybincka [34]

Answer:

AC=-160

BC is the midpoint of AC meaning half of AC

-160/2=-80

4 0
4 years ago
What's 23 divided by 186
egoroff_w [7]
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Hope this helps :))
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4 years ago
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Step-by-step explanation: simply

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