A farmer finds that if she plants 50 trees per acre, each tree will yield 80 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest?

Answers

Answer 1

Answer:

28

Step-by-step explanation:

From the given information:

Let x be the number of trees.

F(x) = (50 +x) (20 - 3x)

F(x) = 1000 - 150x + 20x - 3x²)

F(x) = -3x² - 130x + 1000

Differentiating F(x) with respect to x;

[tex]F'(x) = \dfrac{d}{dx}( -3x^2- 130x + 1000)[/tex]

[tex]F'(x) = ( -3(2x)- 130(1) +0)[/tex]

F'(x) = -6x -130

Now; we set F'(x) to be equal to zero to determine the critical value;

-6x - 130 = 0

x = - 130/6

Differentiating F''(x) with respect to x

[tex]F''(x) = \dfrac{d}{dx}( -6x- 130)[/tex]

[tex]F''(x) = ( -6(1))[/tex]

F''(x) = -6 (<0)

Thus; by the second derivative, the revenue function F(x) is maximum when x = -130/6

Therefore, the number of trees she should plant per acre to maximize her harvest is:

50 + x = 50 - 130/6

= 85/3

[tex]\simeq[/tex] 28

Therefore, the number of trees per acre to maximize the harvest is 28


Related Questions

Factor -6 out of 18z - 15

Answers

Answer: -6(-3z+15/6)
Divide both 18z and -15 by -6 and then put -6 outside the parentheses with the quotients on the inside so the -6 can be distributed to create 18z-15

In mathematics, a factor is an integer or algebraic expression which divides another number or expression evenly, giving no remainder, and the further calculation can be defined as follows:

Given:

[tex]\bold{-6\ out \ of (18z - 15)}\\\\[/tex]

To find:

Factor=?

Solution:

[tex]\to \bold{-6\ out \ of (18z - 15)}\\\\\to \bold{-6\times \frac{(18z - 15)}{-6}}\\\\\to \bold{-6\ (-3z + \frac{5}{2})}}\\\\[/tex]

Therefore, the final answer is "[tex]\bold{-6\ (-3z + \frac{5}{2})}}[/tex]".

Learn more:

brainly.com/question/19310237

For signing up for the rewards program at a pizzeria, Haley got a card with 15 points. For each pizza she orders, she earns 8 points. Once she hits 175 points, she gets a free pizza. How many pizzas will she need to order to get a free one?

Answers

8x+15=175
8x= 160
20 pizzas

Answer:

20 pizzas

Step-by-step explanation:

Jackie and her family went out for dinner for her birthday. The cost of the dinner before sales tax was $76.45. The family decides to tip 20% for the good service they received. How much did Jackie's family leave as a tip for her birthday meal?

Answers

Answer:

15.29 i think

Step-by-step explanation:

Thomas went to the store to buy a couple of items for his mother at the store. He purchased a gallon
of milk for $2.15, a gallon of orange juice for $4.68, and a loaf of bread for $2.49.
If the sales tax is 8.25%, what is the total cost?

Answers

Answer:

$10.09

Step-by-step explanation:

2.49 + 2.15 + 4.68 = 9.32

9.32 * 0.825 = 0.77

9.32 + 0.77 = 10.09

I hope this helped, please mark Brainliest, thank you!!

Select the correct answer.
Select the place of the digit 9 in this number.

269,478


ten thousands

hundreds

one thousands

ones

hundred thousands

tens

Answers

I think answer should be thousands please give me brainlest I hope this helps let me know if it’s correct or not okay thanks
the correct name for the place that the digit 9 stands in is , one thousand .

A local hamburger shop sold a combined total of 721 hamburgers and cheeseburgers on Thursday. There were 71 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Thursday?

Answers

Answer:771-71/2= 350 hamburgers and 350 +71 cheeseburgers

Step-by-step explanation:

Solve for the roots: x3-2x2+3x-6

Answers

Answer:

x = 2, i[tex]\sqrt[]{3}[/tex],  -i [tex]\sqrt{3}[/tex]

x^3 - 2x^2+ 3x - 6 = 0

Hint: Solve by grouping.

Store A sells 3 candy bars for $3.45.
Store B charges $5.45 for 5 candy bars.
Store C sells 7 candy bars for $7.56.
Which store offers the best value?

Answers

Answer:

Store C

Step-by-step explanation:

$7.56÷7=$1.08 a candy bar

-5(-2)..............

Answers

Answer:

10 is answer

Step-by-step explanation:

because minos minos = plus


The sum of two numbers is 38. The smaller number is 22 less than the larger number. What are the numbers?

Answers

Answer:

30 and 8

Step-by-step explanation:

30 - 8 = 22

The table shows the mean number of basketball goals made by four random samples of players from the school team during this year’s season. Sample # Sample Mean Number of Goals 1 7 2 4 3 5 4 8 Is a valid prediction for the mean of the population possible using these samples? No, there are not enough samples. Yes, the sample means are all less than 10. Yes, the variation of the sample means is small. No, the variation of the sample means is too great.

Answers

Answer:

Answer is C

Step-by-step explanation:

There is not enough samples.

Answer:

 Yes, the variation of the sample means is small.

Step-by-step explanation:

When x = 19,
y = 209. Find
the value of x
when y = 143.

Answers

Answer:

13

Step-by-step explanation:

19=209

 ?=143

19*143

=2717

2717/209

=13

Remember that whole numbers that are next to each other, for example, 2 and 3, or 43, 44, and 45 are called consecutive numbers.

If n is the smallest of three consecutive integers, write an expression for the largest number.

Answers

Answer:

n +2

Step-by-step explanation:

If three numbers are consecutive, the 2nd number would be one more than the 1st number, and the 3rd number would be one more than the 2nd number.

Since the smallest number is n,

2nd consecutive number= n +1

3rd consecutive number

= n +1 +1

= n +2

Thus, the expression for the largest number is n +2.

Let's check!

If the smallest of the three consecutive number is 1, the 3rd consecutive number would be 3.

3rd consecutive number

= n +2

= 1 +2

= 3 (✓)

Thus, the expression is correct.

I need help solving these!!!!​

Answers

Answer:

4. y = -1/2x + 5

5. y = -1/3x + 3

6. y = 1

Step-by-step explanation:

For #4:

Because these lines are parallel, we know that they will have the same slope.

To get b, or the y-intercept, I just started at the point (4,4) and used the slope to work backwards to the y-axis. This is really not the best way to do it (especially with big numbers) but it works in a pinch. Also, I forgot the better way :/

For #5:

These lines are perpendicular. That means that the slopes are reciprocals of the other and, when multiplied with each other, the answer will be -1.

The reciprocal of 3 is -1/3.

To get the y-intercept, I did the same as above.

For #6:

x = 2 is a vertical line. To make a line perpendicular to it, that is, to make a line that intersects with it at 90°, the answer line will have to be horizontal.

That means that our answer is y = ?

We know that the line passes through a very specific point (2,1), and the line provided in the question already gives us the x value of this point. All we have to do is set y equal to the y value.

So, y = 1.

I hope this helps!

plsss help 6th grade math

Answers

Answer:  D

Step-by-step explanation:

If you put -5 and +5 on a number line and count their distance from zero they are both the same distance.

PLEASE HELP ASAP

Write the slope-intercept form of the equation of each line. Identify the slopes y-intercept

Answers

Answer:

10) m: 6

    b: 5

    y= 6x +5

12)  m: -2

     b: -1

     y= -2x-1

14)  m: 1

     b: 0

     y= x

Step-by-step explanation:

The slope-intercept form is the form y=mx+b

m is the slope. You can find it by finding two points that the line intersects, and counting the number of units between them.

Remember the slope is "rise over run", so, the difference in y over the difference in x.

b is the y-intercept. You can find it by looking at where the line crosses the y-axis.

Hope this helps you out!

Find the unit price for 9 colored pencils for $56

Answers

Answer:

6 2/9

Step-by-step explanation:

56/9

Read the following statement: Line segment MN is congruent to line segment OP.

Which of the following is an equivalent statement?


a
MN overbar is similar to OP overbar

b
MN overbar equals OP overbar

c
MN overbar is congruent to OP overbar

d
MN overbar is an element of OP overbar

Answers

Answer:c

Step-by-step explanation:

Over a period of 12 hours the temperature dropped 36°F what was the average change in temperature in one hour?

Answers

Answer:

3°F

Step-by-step explanation:

36 divided by 12 is 3

Answer:

3 degrees F

Step-by-step explanation:

36/12 = 3


--
What is the equation of g in terms of f?

Answers

Answer:

g(x) = f(x - horizontal shift) + vertical shift translates to g(x) = f(x - [-4])+[-7].

Step-by-step explanation:

I'm not to sure but I hope this helps

10 Lakh More Than 93,23,654​

Answers

Answer:

10,323,654

Step-by-step explanation:

Helpppppp pleaseeeee
Save me from this questionnnnn

Answers

y = 33
x = -3
Hoped I help

i need more help i'm so bad at this subject z/4 - 1/2 = 9? pls steps and test

Answers

answer: x=38

Step-by-step explanation:

hope I help you

What is the equation of this graphed line? Enter your answer in slope-intercept form in the box. please i really need help

Answers

Answer:

y = -9/8x+7

Step-by-step explanation:

First Find The Slope: 7--2/0-8=-9/8

Find Y Intercept=7

Than Write Equation: y=-9/8x+7

a transformation of a rectangle ABCD results in rectangle ABCD whch transformation maps the pre-image to the image

Answers

Answer:

dilation

Step-by-step explanation:

did it on edge 2020

Pls make me brainliest much appreciated

what is a square of 1.5cm ​

Answers

Answer:

a square with 1.5 cm width and height

Answer:

2.25

Step-by-step explanation:

1.5 * 1.5 = 2.25.


Round to the nearest 100 of 6,850..​

Answers

Answer: 6,900
Explanation: 800 is in the hundreds place therefore if it can round up it would round up to 6,900 instead of 7,000

help me (a) The total cost of rent is determined by recording x months of rent at $1400 per month, plus a $150 application fee.

Answers

Answer:

$1400x  + $150

Step-by-step explanation:

Let the total cost of rent used for a month be $1400 plus a $150 application fee.

This means that;

Total cost (1 month) = $1400(1) + $150 = $1550

TO calculate the cost for x months, we will simply multiply x with the cost of rent for 1 month as shown.

The cost of rent for x month = 1400x * $150

The cost of rent for x month = $1400x  + $150 (application fee are paid only once)

An exam has two probability problems, 1 and 2. If 37% of the students solved problem 1 and 12% of the students solved both problems 1 and 2, what is the percent of students who solved problem 2 given that they solved problem 1

Answers

Answer:

63%

Step-by-step explanation:

37% did not solve problem 2

100% - 37% = 63%

helppp pls 20 points !!

Answers

The answer is: -1 slope

Explanation: slope is rise over run and this slope rises 4 and goes back -4 so it would be 4/-4 which simplifies to -1
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