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Liula [17]
3 years ago
8

Work out the area of this quarter circle of radius 8cm, Give you answer in terms of pi

Mathematics
1 answer:
oee [108]3 years ago
3 0

Answer:

The area of the quarter circle is 16\pi\ cm^{2}

Step-by-step explanation:

we know that

The area of a quarter circle is equal to

A=\frac{1}{4}\pi r^{2}

we have

r=8\ cm

substitute the value

A=\frac{1}{4}\pi (8)^{2}

A=16\pi\ cm^{2}

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Notice there's an (x-4) on both top and bottom. So they cancel out. That leaves us with your answer of \frac{x}{(x+9)}

#3. We do the same thing as above then multiply and simplify. In the interest of space, I'll cut straight to some simplification. 

\frac{2(x+2)^{3} }{6x(x+2)} ( \frac{5}{(x-2)^{2} } )

Now we start cancelling. For the first fraction, there are 3 (x+2)'s on top and 1 on the bottom so we will cancel out the one on the bottom and leave 2 (x+2)'s on top. There are no more polynomials to cancel out so now we multiply across:

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10 and 6 share a GCF of 2 so we divide both of those by 2. This leaves us with the final answer of:

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#4. This equation introduces division and because of it, we must flip the second fraction to make the division sign into a multiplication symbol. Again for space, I'll flip the fraction and simplify in one step. 

\frac{3(x+2)(x-2)}{(x+4)(x-2)} ( \frac{x+4}{6(x+3)})

Now we do our cancelling. First fraction has (x - 2) in the top and bottom. They're gone. The first fraction has a (x + 4) on the bottom and the second fraction has one on the top. Those will also cancel. This leaves you with:

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\frac{x+2}{2(x+3)}

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\frac{(3+2x)(x-10)+(13+x)(10-x)}{(10-x)(x-10)}

Now we FOIL each to expand and then simplify by combining like terms. Again for space, I'm just showing the result of this; you end up with:

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Simplify to get:

\frac{3x}{5}  * ( \frac{25}{10x})

After simplifying again, you end up with your final answer: 

\frac{3}{2}




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