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ICE Princess25 [194]
3 years ago
11

An expression on the total cost to download the movies

Mathematics
1 answer:
kari74 [83]3 years ago
8 0
Whata re the answers that i can oick from

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From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th
wel

Answer:

\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}

Step-by-step explanation:

The <u>width</u> of a square is its <u>side length</u>.

The <u>width</u> of a circle is its <u>diameter</u>.

Therefore, the largest possible circle that can be cut out from a square is a circle whose <u>diameter</u> is <u>equal in length</u> to the <u>side length</u> of the square.

<u>Formulas</u>

\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}

\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}

\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}

If the diameter is equal to the side length of the square, then:
\implies \sf r=\dfrac{1}{2}s

Therefore:

\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}

So the ratio of the area of the circle to the original square is:

\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}

Given:

  • side length (s) = 6 in
  • radius (r) = 6 ÷ 2 = 3 in

\implies \sf \textsf{Area of square}=6^2=36\:in^2

\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)

Ratio of circle to square:

\implies \dfrac{28}{36}=\dfrac{7}{9}

5 0
2 years ago
A 13-foot ladder leans against the side of a house with its base 3 feet from the house. Use the Pythagorean Theorem to approxima
scZoUnD [109]

Answer: 12.65 ft

Pythagorean theorem is a^{2} + b^{2} = c^{2}

So, a^{2} + 3^{2} = 13^{2}

169 - 9 = 160

\sqrt{160} is 12.65.

Hope it helps.

4 0
3 years ago
3x\4=2y+6xy. what is "x" equal too? what is "y" equal too?
andreyandreev [35.5K]
 the answer is 
x=8y/3(1-8y)


y=3x/8(1+3x)

hope this helped l used cymath to solve this problem. 
good day : )
6 0
3 years ago
Sin-1 (2/3) rounded to nearest 10th
Luda [366]

the is answer 2 because if u round it 3

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The top of the fraction is the Y axis, count to 3 on the y axis and 5 on x axis
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