A rectangular garden 800 square feet in area is to be fenced off against rodents. Find the dimensions that will require the least amount of fencing if one side of the garden is already protected by a barn.

Answers

Answer 1

Step-by-step explanation:

the area of a rectangle is

a × b

with a, b being the length and width (in any sequence).

a×b = 800

a = 800/b

the perimeter is

2a + 2b

one side is not needed, so we take one of them off. e.g. we take off one a.

a + 2b need to be a minimum

800/b + 2b

f(b) = 800/b + 2b

the extreme value(s) we find as the zero points of the first derivative.

f'(x) = -800/(b²) + 2 = 0

2 = 800/(b²)

2b² = 800

b² = 400

b = ±20 ft

negative lengths don't make sense, so, 20 ft is the solution.

a×b = 800

a×20 = 800

a = 40 ft

so, the minimum fencing is for

a = 40 ft

b = 20 ft (2 times)

the second a is covered by the barn.


Related Questions

The _________is where the line crosses the vertical axis.

Answers

Answer:

The Y intercept is the point where your line crosses the y-axis.

and always Does.... Well Some time it Dosen't, If It is A different Point

I NEED HELP ASAP PLEASE

Answers

Answer:

A and E

Step-by-step explanation:

B and D is unchangeable, species of bears and types of vegetables that existed in the world never changed.

C only consist of one data, temperature of Chicago at noon yesterday only.

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

Answers

Step-by-step explanation:

cos x = 59/95

x = 0.9007

round this and you have your answer

What is the value of l-6l - l-8l

Answers

Answer:

-2

Step-by-step explanation:

absolute value is the distance from zero. it will never be negative. so -6 is 6 away from zero, -8 is 8 away from zero. you can just take off the negative sign and use the number by itself.

|-6| - |-8|

6 - 8

-2

Answer:

[tex] - 2[/tex]

Step-by-step explanation:

[tex]|−6|−|−8|[/tex]

Simplify each term.

The absolute value is the distance between a number and zero. The distance between −6 and 0 is 6.

[tex]6−|−8|[/tex]

The absolute value is the distance between a number and zero. The distance between −8 and 0 is 8.

[tex]6−1 \times 8[/tex]

Multiply −1 by 8.

[tex]6−8[/tex]

Subtract 8 from 6.

[tex] - 2[/tex]

Hope it is helpful....

PLs help lots of points

Answers

Answer:

I believe it is cube A

Step-by-step explanation:

the volume of Cube B equaled 2073.6 in for me. so it would be less than cube A

Answer: They are the same

Explanation: same shape and size simple

What are the solutions to the equation x^2-4x-5=0?

Answers

Answer:

x = 5 ,  − 1

Step-by-step explanation:

If two expressions have the same factor or base. What happens to the exponents when the expression are dividing

Answers

Answer:

whats the question tho?

Step-by-step explanation:

The diameter of a cone-shaped storage tank is 14 feet and it's height is 9 feet. Find the volume of liquid the tank can hold. Round your answer to the integer, if necessary. Use the approximate of value of /pi , that is 3.14.

Answers

Answer:

Volume of cone shape tank  = 461.58 ft³ (Approx.)

Step-by-step explanation:

Given:

Diameter of cone shape tank = 14 feet

Height of of cone shape tank = 9 feet

Find:

Volume of cone shape tank

Computation:

Radius of cone = 14 / 2

Radius of cone = 7 feet

Volume of cone = (1/3)(π)(r²)(h)

Volume of cone shape tank  = (1/3)(3.14)(7²)(9)

Volume of cone shape tank  = (1/3)(3.14)(49)(9)

Volume of cone shape tank  = 1,384.74 / 3

Volume of cone shape tank  = 461.58 ft³ (Approx.)

14. 10th
term of arthmetic
Sequence is 32 more than 7th term.If the first term is -14
find the 2nd term of the sequence​

Answers

Answer:

5

Step-by-step explanation:

1

Given the point (18, -10), apply the rule and tell the image after the translation as an ordered pair with no spaces.

(x,y) --> (x - 11, y - 9)

Answers

Answer:

The answer is (7,-19)

Step-by-step explanation:

Remember, 18 is x, and -10 is y. The rule says to subtract 11 from 18, which would be 7. For y, you add -9 to -10, which would be -19.

Therefore, your answer should be (7,-19)

Hope this helps!

By applying the rule and image after the translation as an ordered pair with no spaces is the point (7, -19).

What is translation?

Translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way.

Given point = (18, -10)

(x, y) --> (x - 11, y - 9)

(18, -10) = (18 - 11, -10 - 9)

New point = (7, -19)

Hence, by applying the rule and image after the translation as an ordered pair with no spaces is the point (7, -19).

Learn more about translation here

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I need help ASAP rn please 6th grade math btw

Answers

Answer:

first

Step-by-step explanation:

A= r*pi*r = pi*r²

Answer:

A.

Step-by-step explanation:

The rearranged segments form a rectangle with length (pi)r and width r.

A = LW

A = (pi)r * r

A = (pi)r^2

Answer: A.

a T-shirt increased in price by 1/7 after the increase it was a priced at £56. what was the original price?​

Answers

Answer: £48

Explanation: divide £56 by 7. each of the seven parts is equal to £8. Subtract £8 from £56 and the original price is £48.

What is the value of x when 1/3x = 9 1/2​

Answers

I'll help.

[tex] \frac{1}{3}x = 9 \frac{1}{2} [/tex]

[tex]x = ?[/tex]

[tex] \frac{1}{3} x = \frac{19}{2} [/tex]

[tex]x = \frac{57}{2} [/tex]

"How it can be 57 ?"

The number 19 is multiplied by the number 3 at the bottom left.

19 × 3 = 57.

What does a country need to do to keep a republic, and not fall under the power of a dictator?

Answers

Answer:

Continue to provide equality for all!

Step-by-step explanation:

When rules and regulations are in place, the government runs smoothly but also people still need to have a voice because without us - there is no government(social contract). We the people(constitution) have the power to prevent a dictator.

Hope this helps:)

Please help me with this:
The gas meter readings at the beginning and end of a period were:
6
4
9
6

6
7
8
5

The cost of the gas is 13p for each unit.
There is also a fixed charge of £21.45.
Calculate the cost of the gas.
You must show your working.​

Answers

Answer:

£59.02

Step-by-step explanation:

find the amount of gas used: 6785-6496 = 289find the cost of the gas by multiplying the 289 by 13p = 3757p = £37.57add the cost of the gas to the fixed delivery charge £37.57+£21.45 = £59.02

The number of units in meter readings will be 289. Then the cost of the gas will be £59.02.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of units and 'y' be the total cost. Then the equation is given as,

y = 0.13x + 21.45

The number of units is calculated as,

x = 6785 - 6496

x = 289

The cost of the gas will be given as,

y = 0.13(289) + 21.45

y = 37.57 + 21.45

y = £59.02

The number of units in meter readings will be 289. Then the cost of the gas will be £59.02.

More about the linear equation link is given below.

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A baseball pitching coach charges $90 for 2.5 hours of training. If you train for 9 hours in one week, how much will that cost for the week, in dollars?

Answers

Answe$324

Step-by-step explanation:

First you divide 9 by 2.5 to get 3.6 which is how many times you practiced for 2.5 hours

Next you multiply 3.6 by 90 to get 324

What the guy above me said

26 months 7 days from 51 months.

Answers

Answer:

Uhhh get it i guess

Step-by-step explanation:

Answer: Well 7 days = 1 week, also 26 months = 2.16667 year or 790.834 days. I DON'T GET IT

Step-by-step explanation:

Find y and choose the answer for brainlest

Answers

Answer:

Last answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

angle y =128 degree reason-angles x and y are supplementary angles

Help
Which choice is equivalent to the product below when x > 0

Answers

Answer:

D

Hope this help

Step-by-step explanation:

the answer would be D

150 round 2 decimal places

Answers

Answer:

[tex]150 = 150.00[/tex]

4. What is the greatest common factor of 12
and 30?

Answers

Answer:

6

Step-by-step explanation:

Which function represents the area of the rectangle? 6x2 – 8x + 36 6x2 – 27x + 36 6x2 – 35x + 36 6x2 + 35x + 36

Answers

Answer:

[tex]Area = 6x^2 - 35x + 36[/tex]

Step-by-step explanation:

Given

[tex]g(x)=3x-4[/tex]

[tex]f(x)=2x-9[/tex]

Required

The area

This is calculated as:

[tex]Area = f(x) * g(x)[/tex]

[tex]Area = (3x -4) * (2x - 9)[/tex]

Open bracket

[tex]Area = 6x^2 - 27x - 8x + 36[/tex]

[tex]Area = 6x^2 - 35x + 36[/tex]

Answer:

6x2 – 35x + 36

Step-by-step explanation:

If a spinner for a game is spun once, there is a 25% chance it will land on
orange. What is the chance that the spinner will not land on orange on both
the first and second spin in a game? Calculate the probability as a decimal
rounded to the nearest TENTH.

Answers

Answer:

[tex]Pr = 0.6[/tex]

Step-by-step explanation:

Given

Let

[tex]O \to Orange[/tex]

So:

[tex]P(O) = 25\%[/tex] --- probability of O

[tex]n=2[/tex] --- Number of spin

Using the complement rule, the probability that a spin will not land on orange is:

[tex]P(O') = 1 - P(O)[/tex]

[tex]P(O') = 1 - 25\%[/tex]

Express as decimal

[tex]P(O') = 1 - 0.25[/tex]

[tex]P(O') = 0.75[/tex]

On two spins, the probability that it will not land on orange is:

[tex]Pr = P(O') * P(O')[/tex]

So, we have:

[tex]Pr = 0.75* 0.75[/tex]

[tex]Pr = 0.5625[/tex]

[tex]Pr = 0.6[/tex] --- approximated

how to write 3600 in babylonian numerals?

Answers

Answer:

Each vertical bar | (pipe) equals a unit and each < (corner wedge or bracket) equals a tenth. The change of power of sixty (60 ^ 1 = 60, 60 ^ 2 = 3600, 30 ^ 3 = 216000, etc.) is represented by a space.

A band of 17 pirates stole a sack of gold coins. When they tried to divide the fortune into equal portions, 3 coins remained. In the ensuing brawl over who should get the extra coins, one pirate was killed. The wealth was redistributed, but this time an equal division left 10 coins. Again an argument developed in which another pirate was killed. But now the total fortune was evenly distributed among the survivors. What was the least number of coins that could have been stolen

Answers

Answer:

The least number of coins that could have been stolen is 3,930.

Step-by-step explanation:

In the beginning, there are N coins to be distributed among 17 pirates, and we know that if we divide evenly these coins, there are 3 coins remaining.

Then we can write the total number of coins as a multiple of 17 plus 3.

N = 17*k + 3

where k is an integer.

After that, a pirate is killed, so now we have 16 pirates, and now there are 10 coins left, so now we can write N as a multiple of 16 plus 10:

N = 16*j + 10

where j is an integer.

Finally, having 15 pirates, the total number of coins can be divided evenly, then N is a multiple of 15

N = 15*m

where m is an integer.

So we have these 3 equations:

N = 17*k + 3

N = 16*j + 10

N = 15*m

So we can express equations like:

15*m = 16*j + 10

15*m = 17*k + 3

Where we need to find solutions such that both of these variables are integers.

For the first one we can write:

15*m - 16*j = 10

One way to do it, is to write this like a linear equation:

m = (16*j + 10)/15

Graph this, and find the pairs of points in the line that have bot integer values, or we can just find some values of j such that:

16*j + 10 is a multiple of 15.

For example, with j = 5 we have:

m = (16*5 + 10)/15 = 6

so j = 5 and m = 6 is a possible solution.

Now if we use m = 6 in the other equation:

15*m = 17*k + 3

we can see if k is also an integer:

k = (15*m - 3)/17

replacing m by 6:

k = (15*6 - 3)/17 = 5.1

This solution does not work.

Let's find others:

if j = 20  (at this point we already know that the possible values of j "jump" by 15 units, like 5 + 15 = 20) then:

m = (16*20 + 10)/15 = 22

Then:

j = 20 and  m = 22 is another solution.

Same as before, let's use m = 22 in the equation for k:

k = (15*22 - 3)/17 = 19.2

Let's find another solution for m.

if  j = 35

m = (16*35 + 10)/15 = 38

Using this value of m in the k equation we get:

k = (15*35 - 3)/17 = 33.4

Let's find another solution for m.

if we take j = 50 we get:

m = (15*50 + 10)/15 = 54

Using this in the k equation we get:

k = (15*54 - 3)/17 = 47.5

Eventually, for j = 5  + 15*16 = 245 we get:  (arrived by iteration, just try each time using the previous value of j plus 15)

m = (16*245 + 10)/15 = 262

replacing this in the k equation we can find:

k = (15*262 - 3)/17 = 231.

So the first solution is:

j = 245, m = 262, k = 231

Then:

N = 262*15 = 3,930

The least number of coins that could have been stolen is 3,930.

Find sin S, sin R , cos S, and cos R.

Answers

Answer:

Step-by-step explanation:

sin S=21/75

sin R=72/75

cos S=72/75

cos R=21/75

Answer:

sin R = 72/75

cos R = 21/75

sin S = 21/75

cos S = 72/75

Step-by-step explanation:

sin = opposite side / hypotenuse

sin = adjacent side / hypotenuse

A pair of dice was rolled many times
and the results appear below. Based
upon these results, what is the
experimental probability of rolling a 2?
Outcome
2
3
4
5
6
7
8
9
10
11
12
Frequency
3
6
8
11
14
16
15
12
9
5
1
The percent probability is = [ ? ]%
Round to the nearest percent.

Answers

Answer:   3%

Most likely, you won't need to type in the percent symbol since that seems to be already done for you.

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

Explanation:

The outcome "2" shows up 3 times, as shown in the first column. Let A = 3.

Add up all the values in the bottom row: 3+6+8+11+14+16+15+12+9+5+1 = 100. Let B = 100. This is the total number of dice rolls.

Dividing the two values gets us A/B = 3/100 = 0.03 = 3%

The value "2" shows up 3% of the time, which is the experimental probability of getting a "2".

There are 4 oranges, 7 bananas, and 5 apples in a fruit basket. Mansour selects a piece of fruit at random and then
Mahmoud selects a piece of fruit at random. Find the probability that two apples are chosen​

Answers

Answer:1/12

Step-by-step explanation: 5/16 x 4/15 = 20/240= 1/12

Hi there I hope you are having an great day :) There are 4 oranges, 7 bananas, and 5 apples in a fruit basket. Mansour selects a piece of fruit at random and then  Mahmoud selects a piece of fruit at random. Find the probability that two apples are chose. (5/16)*(4/15) Mya selects a fruit and you want it to be an apple so that is 5 apples out of 16 fruits total. After Mya selects one fruit and it is an apple, there is one less fruit and apple. So 5-1/16-1. Since the is also in one case, not two separate ones, you multiply the two fractions so (5/16)*(4/15).

I need the answer pls I will mark brainlist just answer this

Answers

Answer:

The first one is B and the second is C :)

Answer:

C. 12 and A.5

Step-by-step explanation:

The number of people is 12 because 7 people who got 9 and 5 people who got ten ASSUMING this test means at least is more than or equals to

6-1 = 5

Your hose fills a swimming pool in 3 hours. When your friend's hose is used together with your hose, the pool is full in 1 hour. How long (in hours) does it take your friend's hose to fill the pool when working alone

Answers

Answer:

1.5 hours

Step-by-step explanation:

Given :

My hose = 3 hours ; my rate = 1/3

Let My friend's time = x ; his rate = 1/x

Combined time = 1 hour, combined rate = 1/1 = 1

Combined rate :

1/3 + 1/x = 1

1/x = 1 - 1/3

1/x = (3 - 1)/ 3

1/x = 2/3

Cross multiply :

3 = 2x

x = 3/2

x = 1.5 hours

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