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Lina20 [59]
3 years ago
15

A square is inscribed in a circle with an area of 10 pi square inches. what is the area of the square

Mathematics
1 answer:
Naddik [55]3 years ago
8 0
We need to determine the radius and diameter of the circle.  If the area of the circle is 10 pi in^2, then, according to the formula for the area of a circle,

A = 10 pi in^2 = pi*r^2.  Thus, 10 in^2 = r^2, and r = radius of circle = sqrt(10) in.

Thus, the diam. of the circle is 2sqrt(10) in.  This diam. has the same length as does the hypotenuse of one of the triangles making up the square.

Thus, [ 2*sqrt(10) ]^2 = x^2 + x^2, where x represents the length of one side of the square.  So, 4(10) in^2 = 2x^2.  Then:
                                 40 in^2  = 2x^2, or 20 in^2 = x^2, and so the length x of one side of the square is sqrt(20).  The area of the square is the square of this result:

Area of the square = x^2 = [ sqrt(20) ]^2 = 20 in^2 (answer).  Compare that to the 10 pi sq in area of the circle (31.42 in^2).
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Answer:

  (c)  III

Step-by-step explanation:

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Another way to simplify the equation is to subtract the right side from both sides. If that simplifies to 0 = 0, then there are an infinite number of solutions.

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8 0
2 years ago
Determine the nth term for each of the following sequences: 2,5,8,11,14,..
Tanya [424]
To determine the nth term, we must create a function.

f(n) = 1st term + common difference (n - 1)

n = term you are looking for
1st term = 1st number in the sequence
common difference = the difference between two consecutive numbers in the sequence.

based on the above sequence, the 1st term is 2, its common difference is 3.

f(n) = 2 + 3(n-1)

Assuming we are looking for the 5th term
f(5) = 2 + 3(5-1)
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f(5) = 14   as you can see in the above sequence 14 is the 5th term.

For any other value of the nth term, simply substitute n by the number of the term and solve the equation.
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3 years ago
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Art [367]
Let's make things easier by simplifying things.

y = 8 and x = 3 is more likely to be understood as a ratio. So for the rest of the answer, their relationship would be represented as y:x

Thus: y:x = 8:3

The problem would be finding y when x = 45

Let us proceed on using the previous equation and substitute x with 45 which would look like this:

y:45 = 8:3

Ratios can also be expressed as fractions which would make things more understandable and easy to solve. So the new form of our equation would be like this:

y/45 = 8/3

Then we proceed with a cross multiplication where the equation becomes like as what is shown below:

3y = 45 * 8

From there, you can solve it by multiplying 45 and 8 then dividing the product with 3 to get y

3y = 360

y = 120

Another way of looking at the problem, especially problems like these, is to take the whole question or statement as an equation. it would probably look like this:

y = 8 when x = 3 : y = ? when x = 45

This would make you understand what approach you can use to solve the given problem.
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The answer is (7,-3)
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3 years ago
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