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Doss [256]
3 years ago
6

The diameter of a circle if five times the length of a recatngle. The length of a rectangle is three times the width of the rect

angle. All three measurements are integers (in other words, they are not fractions or decimals). The area of the rectangle is 12 square feet. What is the area of the circle? Use 3.14 as pi. Do not round the answer.​
Mathematics
1 answer:
Leno4ka [110]3 years ago
8 0

Answer:

706.5 ft²

Step-by-step explanation:

A. Width of the rectangle

The formula for the area of a rectangle is

A = lw

But, l = 3w, so,

A = (3w)w

= 3w² = 12

      w² = 4         Divided each side by 3

      w   = 2 ft     Took the square root of each side

B. Length of rectangle

l = 3w = 6 ft

C. Diameter of circle

d = 5l = 5 × 6 = 30 ft

D. Radius of circle

d = 2r

r = d/2     Divided each side by 2

r = 30/2 = 15 ft

E. Area of circle

A = πr² = 3.14 × 15² = 3.14 × 225 = 706.5 ft²

The area of the circle is 706.5 ft².

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Answer:

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Step-by-step explanation:

5+2x-7x

Combine like terms:

2x-7x+5\\

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-5x+5

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The movie ended at 7:15 p.m. and lasted 2 hours 40 minutes. What time did the movie begin?
nekit [7.7K]

Answer:

The movie started in 4:35 pm

Step-by-step explanation:

the easy way to do this

Step one: subtract 2 hours from 7:15 pm which is 5:15 pm

step two: to subtract 30 min from 5:15 which is 4:45 pm

step three: to subtract 10 min from 4:45 pm which is 4:35 pm

<h3>∴ The movie started in 4:35 pm</h3>
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Step-by-step explanation:

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3 years ago
Find the dimensions of an open rectangular box with a square base that holds 2000 cubic cm and is constructed with the least bui
Vesnalui [34]
<h3>The dimensions of the given rectangular box are:</h3><h3>L  =   15.874 cm  , B  =  15.874 cm   , H = 7.8937 cm</h3>

Step-by-step explanation:

Let us assume that the dimension of the square base = S x S

Let us assume the height of the rectangular base = H

So, the total area of the open rectangular box  

= Area of the base +  4 x ( Area of the adjacent faces)

=  S x S  +  4 ( S x H)   = S² +  4 SH   ..... (1)

Also, Area of the box  = S x S x H  =  S²H

⇒ S²H = 2000

\implies H = \frac{2000}{S^2}

Substituting the value of H in (1), we get:

A = S^2 + 4 SH =  S^2 + 4 S(\frac{2000}{S^2}) =  S^2 + (\frac{8000}{S})\\\implies A  =  S^2 + (\frac{8000}{S})

Now, to minimize the area put :

(\frac{dA}{dS} ) = 0 \implies 2S  - \frac{8000}{S^2}  = 0\\\implies S^3 = 4000\\\implies S  = 15.874 \approx 16 cm

Putting the value of S  = 15.874 cm in the value of H , we get:

\implies H = \frac{2000}{S^2}  =  \frac{2000}{(15.874)^2} = 7.8937 cm

Hence, the dimensions of the given rectangular box are:

L  =   15.874 cm

B  = 15.874 cm

H = 7.8937 cm

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