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Bess [88]
2 years ago
9

Yea yea you know i need help my brains tiny thank you for everything and everyone helping

Mathematics
2 answers:
Darina [25.2K]2 years ago
4 0

Answer: r=6

Step-by-step explanation:

<u>Step 1: Substitute for the known variables</u>

we know that the formula to find the volume of a cylinder is <u>V= πr²h</u>

π= 3.14

h= 12

r= ?

v=1,357

Plugging the numbers we know into the formula, we get:

1,357= 3.14xr²x12

1,357= 3.14x12xr² (because with the commutative property of multiplication you can multiply in any order)

1,357= 37.68 x r²

<u>Step 2: Get the variable term (the letter term) on the left</u>

37.68 x r²= 1,357

Now, divide by 37.68. (I know to divide because when you switch the 37.68x r² the other way around to  r²x37.68, you are clearly multiplying and must do the inverse operation (opposite of multiplication; division) to solve the problem.

So,

r²= 1357÷37.68

r²= 36.0138004 ----> about 36.

r²= 36

This equation isn't over yet because we still have the exponent on the r. Whenever you see a letter squared (to the power 2) in an equation, the "inverse operation" is to take the square root of both sides. Look:

r²= 36

The square root of  r² is just r, because r x r =  r²

The square root of 36 is 6, because 6x6=36.

Now we have :

r= 6

Step 3: Check

Now we have all the variables. To check to make sure the radius is correct, "plug in"

V= π r²h

1,357= 3.14x6²x12

1,357= 3.14x36x12

1,357= 113.04x12

1,357= 1356.48

They said in the question that the volume is APPROXIMATLEY 1357, so I can just round 1356.48 --> 1356.5---> 1357. Now I am sure that the radius is 6.

Hope this helps :)) also brainliest would be appreciated  :D

Anni [7]2 years ago
4 0
Answer r=6 I won’t put you through the reading
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Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four
Alina [70]

Answer:

Step-by-step explanation:

(a)

Suppose we came up with an ideology whereby we pick a value for the length including the length dividing the inside into 4 parts(5 parallel sides), then we can get the value for breath by using the following process.

Let assume the length of the rectangle is 50;

Then, the breath can be calculated as follows:

= 50 × 5 = 250   ( since the breath is divided into 5 parallel sides)

The fencing is said to be 950 ft

So, 950 - 250 = 700

Then divided by 2, we get:

= 700/2

= 350

So for the first diagram; the length = 50 and the breath = 350

The area = 50 × 350 = 17500 ft²

Now, let's go up a little bit.

If the length increase to 100;

Then 100 × 5 = 500

⇒ 950 - 500 = 450

⇒ 450/2 = 225

The area = 225 × 100 = 22500 ft²

Suppose the length increases to 150

Then 150 × 5 = 750

⇒ 950 - 750 = 200

⇒ 200/2 = 100

The area = 150 × 100 = 15000 ft²

The diagrams for each of the outline above can be seen in the image attached below.

(b) The diagram illustrating the general solution can be seen in the second image provided below.

(c) The expression for  the total area A in terms of both x and y is:

Area A = x×y

(d) Recall that:

The fencing is said to be 950 ft.

And the length is divided inside into 5 parallel sides;

Then:

5x + 2y = 950  (from the illustration in the second image below)

2y  = 950 - 5x

y = \dfrac{950}{2} - \dfrac{5}{2}x

y = 475- \dfrac{5}{2}x

(e)

From (c); replace the value of y in (d) into (c)

Then:

Area A = x×y

f(x)= x\times ( 475 -\dfrac{5}{2}x)

Open brackets

f(x)= ( 475 x-\dfrac{5}{2}x^2)

(f)

By differentiating what we have in (e)

f(x)= ( 475 x-\dfrac{5}{2}x^2)

f'(x)= ( 475 (1)-\dfrac{5}{2}(2x))

f'(x)= 475 -5x

\implies  475 = 5x

x = 475/5

x = 95

From (d):

y = 475- \dfrac{5}{2}x

y = 475- \dfrac{5}{2}(95)

y =237.5

∴

Area A = x × y

Area A = 95 × 237.5

Area A = 22562.5 ft²

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