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Nadya [2.5K]
1 year ago
7

A home gardener estimates that 18 apple trees will produce an average yield of 80 apples per tree. But because of the size of th

e garden, for each additional tree planted, the yield will decrease by four apples per tree. How many trees should be planted to maximize the total
Mathematics
1 answer:
aliina [53]1 year ago
4 0

19 trees should be planted to maximize the total

<h3>How many trees should be planted to maximize the total</h3>

From the question, we have the following parameters:

Number of apples, x = 18

Yield, f(x) = 80 per tree

When the number of apple trees is increased (say by x).

We have:

Trees = 18 + x

The yield decreases by four apples per tree.

So, we have

Yield = 80 - 4x

So, the profit function is

P(x) = Apples * Yield

This gives

P(x) = (18 + x) *(80 - 4x)

Expand the bracket

P(x) = 1440 - 72x + 80x - 4x^2

Differentiate the function

P'(x) = 0 - 72 + 80 - 8x

Evaluate the like terms

P'(x) = 8 - 8x

Set P'(x) to 0

8 - 8x = 0

Divide through by 8

1 - x = 0

Solve for x

x = 1

Recall that:

Trees = 18 + x

So, we have

Trees = 18 + 1

Evaluate

Trees = 19

Hence, 19 trees should be planted to maximize the total

Read more about quadratic functions at:

brainly.com/question/12120831

#SPJ1

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If the blue radius below is perpendicular to the green chord and the segment BC is 7.6 units long, what is the length of the cho
galina1969 [7]

Answer:

The correct answer is A. 15.2 units

Step-by-step explanation:

The segment AB is congruent to the segment BC  eg AB≅BC Why?

We can prove it with the triangle congruent theorem, postulate side-side-angle

We are watching triangle ΔABO and triangle ΔCBO, they are congruent

first element side OB=OB - common side

second element side OA=OC=r - radius of the circle

third element angle ∡ABO≅∡CBO=90°

According to the postulate side-side-angle we can conclude that triangles

ΔABO≅ΔCBO (triangles are congruent)

If they are congruent all of their elements are also congruent and therefore also

side AB=BC  => AB+BC=AC,  which is chord  => 7.6+7.6=15.2 units

AC= 15.2 units ( chord )

Good luck!!!


6 0
3 years ago
What is 30/45 simplest form
Marysya12 [62]
\dfrac{30}{45}=\dfrac{30:15}{45:15}=\dfrac{2}{3}
5 0
3 years ago
1/3 = x/12 what is x?​
marishachu [46]

Answer:

x = 4

Step-by-step explanation:

Given

\frac{1}{3} = \frac{x}{12} ( cross- multiply )

3x = 12 ( divide both sides by 3 )

x = 4

5 0
3 years ago
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PLSS HELP ILL GIVE BRAINLIEST IF YOU HELP ME AND EXPLAIN UR ANSWER
kherson [118]

Answer:

It is the second choice.

Step-by-step explanation:

Divide both side by pi r squared. Boom.

3 0
2 years ago
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6x+4y=42 -3x+3y=-6 by elimination
creativ13 [48]

Answer:

x=5, y=2

Step-by-step explanation:

To solve this system, we need to find x and y. First, let's find x. In the first equation (6x+4y=42), subtract 4y on both sides to isolate 6x. This will result in 6x=42-4y. Divide by 6 on both sides to isolate x and get x=7-\frac{2}{3}y. Now we know what x equals. Go to the second equation ad plug this into it. So instead of -3x+3y=-6, you'll have -3(7-\frac{2}{3}y)+3y=-6. Use the distributive property to get -21+2y+3y=-6. Add 2y and 3y to get -21+5y=-6. Add 21 to both sides to isolate 5y and get 5y=15. Divide by 5 on both sides to isolate y and get y=3. Now that we know that y=3, we can plug this back into the equation that was bolded above so that we can find x, so we'll have x=7-\frac{2}{3}(3) since y=3, and we'll get x=7-\frac{6}{3}, or x=7-2, or x=5.

x=5

y=2

6 0
3 years ago
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