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grin007 [14]
3 years ago
6

The equation of a circle is given by (x + 3.5) ^ 2 + (y - 2.82) ^ 2 = 25 What is the area of a 52 degrees sector of this circle?

Round to the nearest hundredth of a square unit.
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
3 0

Answer:

≈ 11.34 units²

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 3.5)² + (y - 2.82)² = 25 ← is in standard form

with r² = 25 ⇒ r = \sqrt{25} = 5

The area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × \frac{52}{360}

   = π × 5² × \frac{52}{360}

   = π × 25 × \frac{52}{360}

   = \frac{25(52)\pi }{360}

   ≈ 11.34 units² ( to the nearest hundredth )

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125 divided by 32 equals what
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32 × 2 = 68
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So far we can conclude that the answer to your question lies somewhere between the numbers 3 and 4. To narrow down the answer some more, multiply 32 by 3.5 (a midway point between 3 and 4).

32 × 3.5 = 112
The number 112 tells us that the decimal we are looking for is higher than 3.5. (Because we need to get to 125, not 112.) Let's try some decimals between 3.5 and 4.

32 × 3.7 = 118.4
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As we narrow down our answer, we can see that the number we are looking for lies between 3.9 and 4 on the number line. Now we need to start testing some decimals between 3.9 and 4. 

32 × 3.905 = 124.96
Again, use the number five as a "midway" point to decide if you should use numbers that are higher or lower than 3.905. In this case, we need to use numbers higher than 3.905.

32 × 3.906 = 124.992
32 × 3.907 = 125.024

We are getting even closer to our number now that we know the decimal is somewhere between 3.906 and 3.907.

32 × 3.9065 = 125.008
With our midway point we can see that our number lies between 3.906 and 3.9065. Let's try a quarter point to see where our number lies from there.

32 × 3.90625 = 125
And BINGO! We have found the answer to the question. To be rephrased, our answer can be put like this:

\frac{125}{32} = 3.90625
6 0
3 years ago
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