The maximum grain yield for corn is achieved by planting at a density of 37,000 plants per
acre. A farmer wants to maximize the yield for the field represented on the coordinate grid.
Each unit on the coordinate grid represents one foot. How many corn plants, to the nearest
thousand, does the farmer need? (Hint: 1 acrt = 43,560 ft?)
у
500 fx
E
F
X
-500
0
500
G
-500
H
The farmer needs approximately
corn plants.

     [tex]I=\displaystyle \int \dfrac{\sqrt x}{\sqrt x -4} ~dx\\\\\text{Let,}\\\\~~~~u=\sqrt x-4\\\\\implies \dfrac{du}{dx} = \dfrac d{dx} \left( \sqrt x -4 \right)\\\\\implies \dfrac{du}{dx} = \dfrac 1{2 \sqrt x} \\\\\implies dx =2\sqrt x~ du\\\\\\I= \displaystyle \int \dfrac{u+4}{u+4 -4 } 2(u+4) du\\\\\\~~~=2\displaystyle \int \dfrac{(u+4)^2}{u} du\\\\\\~~~=2\displaystyle \int \dfrac{u^2+ 8u+16}{u} du\\\\\\~~~=2\displaystyle \int \left(u+8+\dfrac{16}u\right) du\\\\\\[/tex]

    [tex]~~~=2\left(\displaystyle \int u ~ du + \displaystyle \int 8 ~ du + \displaystyle \int \dfrac{16} u ~ du\right) \\\\\\~~~=2\left( \dfrac {u^2}2 + 8u+16\ln |u| \right) +C\\\\\\~~~~= u^2 + 16u+ 32 \ln |u|+C\\\\\\~~~~=\left( \sqrt x -4 \right)^2 + 16\left( \sqrt x -4 \right) +32 \ln |\sqrt x -4|+C\\\\\\~~~~= x-8\sqrt x+16 +16\sqrt x -64 +32 \ln \left|\sqrt x-4 \right|+C\\\\\\\~~~~=x+8\sqrt x -48 +32\ln|\sqrt x -4| +C[/tex]

Using proportions, given the density value, it is found that the ballons contain 9.8 kilograms of helium.

A proportion is a fraction of a total amount.

In this problem, we have that each ballon contain 0.14 kilograms per cubic meter.

You get 5 ballons, each with 14 cubic meters, hence the total volume is given by:

V = 5 x 14 = 70 m³.

Applying the density, we have that the total mass is given by:

M = 0.14 x 70 = 9.8 kilograms.

More can be learned about proportions at https://brainly.com/question/14398287

#SPJ1

The probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is (29/37).

The probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The number of times the experiment was done is 37 (15+14+8). The number of times apple chew came as a result of the experiment is 14, while the number of times peach chew came as a result of the experiment is 15. Therefore, the probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is

[tex]\rm Probability = \dfrac{\text{Number of times apple chew or peach chew was selected}}{\text{Total number of times experiment was performed}}\\\\\\Probability = \dfrac{14+15}{37} = \dfrac{29}{37}[/tex]

Hence, the probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is (29/37).

Learn more about Probability:

https://brainly.com/question/795909

#SPJ1

The length of the diagonal brace when Jonathan is building a box in the shape of a rectangular prism is 17 inches.

From the information given, the dimensions are given as 8 inches by 12 inches by 9 inches.

Therefore, the length of the diagonal brace will be:

= ✓12 + ✓8 + ✓9

= ✓289

= 17

In conclusion, the correct option is 17 inches.

Learn more about rectangles on:

https://brainly.com/question/25292087

#SPJ1

f(x) = x becomes g(x) = (1/5)x through vertical compression by a factor of 5.

Answer:

6,597 cups

Step-by-step explanation:

y=0.9x x=7,330 7,330 x 0.9= 6,597

Answer:

1/2652

Step-by-step explanation:

52 cards    one jack spades      1/52

now 51 cards left   one jack diamonds   1/51

1/52 * 1/51 = 1 / 2652

Answer:

That corresponds to a width of 3.5 feet, so a yard of paper covers an area of 3 x 3.5 = 10.5 square feet

Answer:

x = 10

Step-by-step explanation:

Answer:

[tex]\bf x=10[/tex]

Step-by-step explanation:

[tex]\tt 4x+3(x-1)=67[/tex]

Use the distributive property to multiply 3 by x-1:-

[tex]\tt 4x+3x-3=67[/tex]

Combine 4x and 3x = 7x:-

[tex]\tt 7x-3=67[/tex]

Add 3 to both sides:-

[tex]\tt 7x=70[/tex]

Divide both sides by 7:-

[tex]\tt \cfrac{7x}{7} =\cfrac{70}{7}[/tex]

[tex]\tt x=10[/tex]

Answer:

75%

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

1) domain is: x≥7; range f(x)≥9.

2) answer C

Answer:

Step-by-step explanation:

Jim drank 2 and 4/5 orange juice

2and 4/5=14/5 orange juice

jack drank  1and 1/10 less than Jim= 11/10 less than Jim

I introduce the whole numbers into the fractions

we will convert the number 14/5 into a fraction that has the denominator 10, by multiplying by 2 both numerator and denominator

(14/5 )*2=28/10

Now we can find out how much juine Jack drank

28/10- 11/10= 17/10

so Jack drank 17/10 orange juice , the fraction can be written also as

1 and 7/10

Answer:

x=13

Step-by-step explanation:

Side Splitter Theorem states that If a line is parallel to one side of a triangle and intersects the other two sides, it divides both sides proportionally.

21/14 =1.5

6x1.5 = 9

x-4=9

x=13

The circle is an illustration of tangent and secant lines, and the length of FE in the circle is 9.3 units

The lengths are given as:

Start calculating the length DF using:

DE * DF = CD²

So, we have:

12 * DF = 16²

Evaluate the exponent

12 * DF = 256

Divide both sides by 12

DF = 21.3

The length FE is then calculated using:

DF = FE + DE

Substitute DE = 12 and DF = 21.3

21.3 = FE + 12

Subtract 12 from both sides

FE = 21.3 - 12

Evaluate the difference

FE = 9.3

Hence, the length of FE in the circle is 9.3 units

Read more about tangents and secants at:

https://brainly.com/question/14697178

Answer:

y = -1/4x + 1

Step-by-step explanation:

Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

The y-intercept of the line is 1, so in slope-intercept form, b will be 1.

Now, the line also intersects the y-axis at (4, 0). We can plug these two points into slope formula to find the slope: (0-1)/(4-0) = -1/4.

Therefore, the equation of the line is y=-1/4x + 1

Answer:

Mean Absolute Deviation: 4

Step-by-step explanation:

A mean absolute deviation is measured how much the values in the data set are likely to differ from the mean.

Answer:

f(g(x)) = =2(-x^2+5)-3

=-2x^2+10-3

=-2x^2+7

Sorry, I'm not sure about g(f(x)).

Step-by-step explanation:

f(g(x))=f(-x^2+5)=2x-3

=2(-x^2+5)-3

=-2x^2+10-3

=-2x^2+7

Answer:

between 31 and 29 classes

Step-by-step explanation:

The best estimate of the number of times out of 32 that Lexie is on time to class is 30.4.

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

The probability that Lexie is on time for given class is 95% and there are 32 classes during the semester.

So,

=32 * 0.95

= 30.4

Learn more about his concept here:

https://brainly.com/question/16310350

#SPJ5

Answer:

c 2.00 in vec ay se the back yard

Answer:

Every third student who enters each homeroom

Step-by-step explanation:

This would produce the least biased results as every third student gives a 3/x for students and there are y homerooms, giving the least biased results.

Answer:

B.

Step-by-step explanation:

Because if you look closely you will be able to tell which answer it is by looking at the way the shape formed andjust breakaprt the shape .

Answer: 3 inches

Step-by-step explanation:

Answer:

The slope is 6

Step-by-step explanation:

m = y2 - y1/x2 - x1

ΔX = 3 – 2 = 1

ΔY = 7 – 1 = 6

6/1 = 6

Answer:

n=45

Step-by-step explanation:

Sum of interior angles can be calculated using formula: 180(number of sides - 2).

Hexagon has: 720 degrees. we subtract two right angles and get 4x=540. The x is the angle supplement to n. x=135 => 180-x=35 => n=45.

Answer:

the answer is C

Step-by-step explanation:

Answer:

  x = 50

Step-by-step explanation:

The marked angles are vertical angles, so are congruent.

  3x -3 = 147 . . . . congruent angles have equal measures

  x -1 = 49 . . . . . divide by3

  x = 50 . . . . . . add 1

Answer:

The length of the diagonal of Stacy's ceiling was found to be 31 feet using both Pythagorean theorem and trigonometry.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let d represent the length of the diagonal, Usinng Pythagoras:

d² = 22² + 22²

d = 31 feet

Using trigonometric identity:

sin(45) = 22/d

d = 31 feet

The length of the diagonal of Stacy's ceiling was found to be 31 feet using both Pythagorean theorem and trigonometry.

Find out more on equation at: brainly.com/question/2972832

Step-by-step explanation: