A field bordering a straight stream is to be enclosed. The side bordering the stream is not to be fenced. If 1000 yards of fencing material is to be used, what are the dimensions of the largest rectangular field that can be fenced? What is the maximum area?

Answers

Answer 1

Answer:

x  =  500 yd

y  =  250 yd

A(max) = 125000 yd²

Step-by-step explanation:

Let´s call x the side parallel to the stream ( only one side to be fenced )

y the other side of the rectangular area

Then the perimeter of the  rectangle  is  p  =  2*x  + 2* y  ( but only 1 x will be fenced)

p  =  x  +  2*y

1000  =  x   +  2 * y         ⇒    y  =  (1000 - x )/ 2

And   A(r)  =  x * y

Are as fuction of x

A(x)  =  x  *  (  1000  -  x ) / 2

A(x)  =   1000*x / 2 -  x² / 2

A´(x)  =  500  -  2*x/2

A´(x)  =  0              500   -  x   =  0

x  =  500 yd

To find out if this value will bring function A to a maximum value we get the second derivative

C´´(x)  =  -1         C´´(x) < 0  then efectevly we got a maximum at  x  = 500

The side  y  = ( 1000  -  x ) / 2

y  =  500/ 2

y  =  250 yd

A(max)  =  250 * 500

A(max) = 125000 yd²


Related Questions

Find the following value

Answers

Answer:

∠ BCA = 45°, ∠ AWD = 90°

Step-by-step explanation:

All angles are right angles by definition.

Diagonals bisect the angles , so

∠ BCA = 45°

Diagonals are perpendicular bisectors of each other, so

∠ AWD = 90°

In the figure below, what is the measurement of GH ?

Answers

Answer:

C. 4

Step-by-step explanation:

first off, we know we need the value of HJ to solve for GH. Luckily for us HJ is congruent to JK, and we have the values to solve for that using pythagorean theorum.

4^2 + JK^2 = 5^2

16 + JK^2 = 25

JK^2 = 9

JK = 3

now we can solve for GH

3^2 + GH^2 = 5^2

9 + GH^2 = 25

GH^2 = 16

GH = 4

help me plsssssssssssss

Answers

Answer:

do you still need help

Step-by-step explanation:

???

9c+1 = 10
What is c?

Answers

Answer:

c=1

Step-by-step explanation:

9c+1 = 10

Subtract 1 from each side

9c+1-1=10-1

9c = 9

Divide by 9

9c/9 = 9/9

c = 1

The function f(x) is graphed below. what is f(1)?

Answers

Answer:

f(1) = - 3

Step-by-step explanation:

Locate x = 1 on the x - axis, then go vertically down to (1, - 3 ) , then

f(1) = - 3

2. Liam and Sam shared a chocolate bar Liam ate 3/5
and Sam ate 4/ 10 Who ate more? How much
more?​

Answers

Liam ate more
Explanation:
first convert one of the fractions to the same denominator as the other one. personally, I chose to simplify 4/10 to 2/5. this leaves us with a common denominator of 5, and it makes the problem much easier/simpler to look at.

3/5 - 2/5 = 1/5
Liam ate 1/5 more chocolate than Sam

PLEASEEEE help I will give you BRAINLEST

Answers

Y= x+6

I hope you pass

Answer:

y=2x+3

Step-by-step explanation:

Write an inequality for the graph below.


DO NOT PUT A LINK!

Answers

Answer:

y=1/4x+1

i think

Step-by-step explanation:

Solve for x. Round to the nearest tenth of a degree, if necessary

Answers

Answer:

39

Step-by-step explanation:

sin^-1(x)= 39/62

x= 38.97

x=39

The answer would be 39

25/24 as a decimal and round it to the nearest hundredth

Answers

Answer:

1.04

Step-by-step explanation:

25/24=1.04166667

round: 1.04

Adam wants to compare the fractions and He wants to order them from least to greatest and rewrite them so they all have the same denominator. Explain how Adam can rewrite the fractions.

Answers

Answer:

[tex]\frac{1}{6},\ \frac{3}{12},\ \frac{1}{3}[/tex]

Step-by-step explanation:

Given

The fractions are:

[tex]\frac{3}{12},\ \frac{1}{6},\ \frac{1}{3}[/tex]

Required

How the fractions can be rewritten

The fractions can be rewritten by taking the LCM of the denominators.

The [tex]LCM[/tex] of [tex]12; 6\ and\ 3[/tex] is [tex]12[/tex]

So, we have:

[tex]\frac{3}{12},\ \frac{2*1}{12},\ \frac{4*1}{12}[/tex]

Simplify the numerators

[tex]\frac{3}{12},\ \frac{2}{12},\ \frac{4}{12}[/tex]

Now, the fractions can be ordered based on the numerators

[tex]\frac{2}{12},\ \frac{3}{12},\ \frac{4}{12}[/tex]

Return to original form

[tex]\frac{1}{6},\ \frac{3}{12},\ \frac{1}{3}[/tex]

5 (3z-3) =30 it’s from delta math 8 grade

Answers

Answer:

[tex]5[/tex]

Step-by-step explanation:

Substitute the value of the variable into the equation and simplify.

5 (3z-3) = 30

15 z - 15 = 30

15 z = 30+ 15

15z = 45

z= 45/ 15

z= 3

A manager at a shipping company will purchase boxes in the shape of right rectangular prisms. He wants the volume of each box to be exactly 98 cubic feet. Which figure shows a box with the dimensions, in feet (ft), that the manager will purchase?

You have 4 options... which one do you think is correct
winner gets brainlest!! along with 50 points

Answers

Answer:

the first one

Step-by-step explanation:

To find the answer we want to find the volume of each rectangular prism

Which ever prism has an exact volume of 98 is the correct answer

( note that volume of a rectangular prism = length times width times height )

For the first answer choice

4 * 3.5 * 7 = 98

We get an outcome of 98, which means that the first one could possibly be the correct answer however lets find the volume of the rest of the prisms just to be safe.

For the second one

6.25 * 7 * 2 = 87.5

87.5 ≠ 98 therefore the second choice is not correct

For the third one

3 * 6.5 * 5 = 97.5

97.5 ≠ 98 therefore the third choice is not correct

For the fourth one

7.5 * 1 * 14 = 105

105 ≠ 98 therefore the fourth choice is not correct

So we can conclude that the first answer choice is correct

Solve for x: 3(x - 2) = -9
1. 1
2. -1
3. - 7/3
4. 3/7

Answers

Answer:

2) -1

Step-by-step explanation:

Answer:

the answer is 2. -1...............

Please help. Thank you....

Answers

The answer is B

Hopefully this helps

Janet uses 2 cups of strawberries to make 4 cups of strawberry jam. How many cups of strawberries are required to make 10 cups of strawberry jam?

Answers

5 cups of strawberries are required to make 10 cups of strawberry jam.

Because we know from the information given that the number of strawberry jam cups will be 2 times the number of strawberry cups

Someone that can help ?!?!

Answers

Answer:

D

Step-by-step explanation:

just by my experience and the look of it, but its super easy to put these in "MathPapa Algebra Calculator", and check. I use it for everything!

I am pretty sure it is answer D

Evaluate: - 5 - 3 3/4 - 1/6 + 1/6 + 3 3/4 + 10

A 15

B 10 1/4

C 5

D -5 1/12

Answers

Answer:

the answer is c

Step-by-step explanation:

True or false? f (x) = 2 · (1/5)^x represents an exponential function growth.

Answers

Hi there!

[tex]\large\boxed{\text{False.}}[/tex]

f(x) = 2(1/5)ˣ

Recall the form of an exponential function:

f(x) = a(b)ˣ where:

a = initial value

b = rate of decay/growth

If b > 1, the function is undergoing exponential growth. If b < 1, then the function is undergoing exponential decay.

1/5 < 1, so the function is undergoing exponential decay, not growth.

Lee took 10 pictures with a camera and 2 of them were pictures of airplanes.
What percent of the pictures that Lee took were pictures of airplanes?

Answers

Answer:

20%.

Step-by-step explanation:

100/20 is 20%, but so is 10/2 because it is the same, but simplified.

This probability distribution shows the

typical grade distribution for a Geometry

course with 35 students.

Grade

A

B

с

DF

Frequency 5

10

15

3

2

Find the probability that a student earns a

grade of B.

p = [?]

Enter a decimal rounded to the nearest hundredth.

Answers

Answer:

0.29

Step-by-step explanation:

Total grade frequency = (5 + 10 + 15 + 3 + 2) = 35

Frequency of grade B = 10

Probability = required outcome / Total possible outcomes

Required outcome = frequency of grade B = 10

Total possible outcomes = total grade frequency = 35

P(B) = 10 / 35

P(B) = 0.2857

P(B) = 0.29

Question 38
Two cuboids are congruent. Which statement about their properties

a.Each face has the same area

b.One is larger than the other

c.They have the same volume

d.The sum of the angles is 360°​

Answers

a because the face are always going to be the same.

Explain why 4x+1 is equal to 2x+12

Answers

i think
4x+1=2x+12
4x+1-2x=12-1
2x=11
x= 11/2
simplified version is x= 5.5
It’s a simultaneous equations:
4x+1=2x+12
So you have to move x to the same side means you have to switch the side for 1 and 2x (if you you are changing the side the value will be negative when it is switched but if the value is positive it will be negative when you switch the side)
4x-2x=-1+12
Now you have to simplify it.
2x=11
Now this is the last step. You need to change the value “2” to the another side. Since 2 is multiplying with x so when you switch the side it will divide with 11.
So, x=11/-2
It’s negative 2 because it switched the side.
Final answer is: x= -5.5
Now find the value for y.
Since you have found the value of x you can calculate the value of y: y=4(5.5)+1=23
y=2(5.5)+12=23
Now as you can see here that the value of y for both equations is the same so that’s why 4x+1 is equal to 2x+12

I hope you understand my explanations.

A Stats test has 5 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 5 questions, what is the probability that you get exactly 2 questions correct

Answers

Answer:

0.0512

Step-by-step explanation:

Probability of making a correct guess ; p = 1 / 5 = 0.2

q = 1 - p = 1 - 0.2 = 0.8

Number of questions, n = 5

Using the binomial probability relation :

P(x = x) = nCx * p^x * q^(n-x)

P(x = 3) = 5C3 * 0.2^3 * 0.8^2

P(x = 3) = 0.0512

Help me pls I’m giving brainlest plsss helpp

Answers

Wouldn’t the answer be 6.9? Because all of the other numbers are lower than 3. In this case, the number would need to be higher due to the fact that the x part is bigger than the 3?

In a group of 120 recruits at the police academy 80 are college graduates and 25 are army veterans. If 15 of the recruits are both college graduate and army veterans as shown above, how many are neither college graduate nor army veterans?

Answers

Answer:

the number of recruits neither be college graduate and nor army veterans is 30

Step-by-step explanation:

The computation of the number of recruits neither be college graduate and nor army veterans is as follows;

= Total recruits - (college students + army veterans - both college graduates & army veterans)

= 120 recruits - (80 + 25 - 15)

= 120 recruits - 90  

= 30

hence, the number of recruits neither be college graduate and nor army veterans is 30

A pie chart is being made with four sectors. Each sector will be a certain percentage of the total area. The table below shows the size of each sector as a percentage of the total area. Sector 1 = 5%
Sector 2 =30%
Sector 3 = 50%
Sector 4 = 15%

What will be the measure of the central angle of sector 4?
A. 27°
B. 54°
C. 5.4°
D. 57°​

Answers

Answer:

B. 54°

Step-by-step explanation:

There are 360° in a circle and sector 4 consists of 15% of it.

We just have to multiply the 2 numbers.

15% = 0.15

0.15(360) = 54

If a car can travel 250 miles on 10 gallons of fuel , how many gallons are requiered to travel 1325 miles

Answers

Answer:

53 gallons of fuel

Step-by-step explanation:

Step 1: Set up a fraction given the data (Let "x" represent the distance in miles.)

[tex]\frac{10}{250} = \frac{x}{1325}[/tex]

Step 2: Divide the given values (The given values are 10 over 250. We are doing this because we need to know the difference between those two figures.) (Trick: For this case, all you need to do is cancel both zeros and the answer is 0.04 once divided)

[tex]\frac{10}{250}\\\\10 \div 250\\\\= 0.04[/tex]

Step 3: Multiply the result to the last value (Since we've found the difference between them by division, we will have to do the opposite operation in order to find the answer.)

[tex]1325 \times 0.04\\\\= 53[/tex]

Therefore, 53 is the amount of gallons of fuel needed.

please help me !! this diagram is not to scale.

Answers

Answers:

sin(A) = 7/25cos(A) = 24/25tan(A) = 7/24

==============================================

Explanation:

We use these rules shown below

sin(angle) = opposite/hypotenusecos(angle) = adjacent/hypotenusetan(angle) = opposite/adjacent

For reference angle A, the side opposite it is BC = 7 which is as far as possible we can go from this angle. The closest we can get is AB = 24 which is the adjacent side. The hypotenuse is always the longest side, always opposite the largest angle (90 degrees).

Each fraction in bold shown above is reduced as much as possible. For example, 7/24 cannot be reduced since 7 and 24 have no factors in common other than 1.

Use SOH CAH TOA
for Sin it is opp over hyp
Cos = adjacent side over hyp
Then for Tan it's opposite over adjacenct

Find the volume of a sphere that has a radius of 6 in

Answers

Answer:

volume = 904.78 cubic inch

Step-by-step explanation:

[tex]Volume = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi \times 6 \times 6 \times 6 = 904.78in^3[/tex]

Answer:

904,32 in³

Step-by-step explanation:

The formula for finding the volume of a sphere with given radius is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

You simply substitute r³ with 6³:

[tex]V=\frac{4}{3} \pi 6^3[/tex]

Now you multiply 4/3 * 3,14 (pi) * 216 = 904,32 in³

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