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Ket [755]
3 years ago
10

A rope 10 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a funct

ion representing the area of both square and circle as a function of the length of one side of the square.
Mathematics
1 answer:
Brilliant_brown [7]3 years ago
8 0
10-x=C=2πr

(10-x)/(2π)=r

A=π(100-20x+x^2)/(4π^2)

A=(x^2-20x+100)/(4π)

...

x/4=s, x=4s  using this in the area of a circle we get:

A=(16s^2-80s+100)/(4π)

A=(4s^2-20s+25)/π

And of course the area of a square is s^2

A=(4s^2+πs^2-20s+25)/π
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RoseWind [281]

Answer:

m\angle KLM=53.13^o

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle KOM

In the triangle KOM

we have

KO=MO=r=5\ units

KM=8\ units

Applying the law of cosines

8^2=5^2+5^2-2(5)(5)cos(KOM)

64=50-50cos(KOM)

50cos(KOM)=50-64

50cos(KOM)=-14

cos(KOM)=-14/50

m\angle KOM=cos^{-1}(-14/50)

m\angle KOM=106.26^o

step 2

Find the measure of the arc KM

we know that

arc\ KM=m\angle KOM ----> by central angle

we have

m\angle KOM=106.26^o

so

arc\ KM=106.26^o

step 3

Find the measure of angle KLM

we know that

The inscribed angle is half that of the arc comprising  

m\angle KLM=\frac{1}{2}[arc\ KM]

we have

arc\ KM=106.26^o

substitute

m\angle KLM=\frac{1}{2}[106.26^o]

m\angle KLM=53.13^o

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Answer:

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Step-by-step explanation:

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