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horrorfan [7]
3 years ago
15

The radius of a circle is 13miles. what is the area of a sector bounded by a 20 degree arc

Mathematics
1 answer:
Stolb23 [73]3 years ago
5 0

Answer:

Area of the sector = 29.48 square miles.

Step-by-step explanation:

Given:

Radius of a circle = 13 miles

Angle bounded by the arc = 20 deg

To find

Area of the sector bounded by 20 degrees.

Note: Area of a sector = \frac{(\theta)}{360}\times \pi\times r^2

Plugging the values in the equation.

⇒ \frac{(\theta)}{360}\times \pi\times r^2

⇒ (\frac{20}{360})\times  3.14\times 13^2

⇒ 29.48 square-miles

So the area of the sector bounded by 20 degree arc is 29.48 square miles.

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2 years ago
A storage tank contains a liquid radioactive element with a half-life of 96 years. It will be relatively safe for the contents t
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Answer:

The tank must remain intact for 1183 years.

Step-by-step explanation:

Exponential equation for decay:

The amount of a substance after t years is given by:

A(t) = A(0)e^{rt}

In which A(0) is the initial amount and r is the decay rate.

A storage tank contains a liquid radioactive element with a half-life of 96 years.

This means that A(96) = 0.5A(0), and we use this to find r.

A(t) = A(0)e^{rt}

0.5A(0) = A(0)e^{96r}

e^{96r} = 0.5

\ln{e^{96r}} = \ln{0.5}

96r = \ln{0.5}

r = \frac{\ln{0.5}}{96}

r = -0.0072

So

A(t) = A(0)e^{-0.0072t}

It will be relatively safe for the contents to leak from the tank when 0.02% of the radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?

This is t for which A(t) = 0.0002A(0). So

A(t) = A(0)e^{-0.0072t}

0.0002A(0) = A(0)e^{-0.0072t}

e^{-0.0072t} = 0.0002

\ln{e^{-0.0072t}} = \ln{0.0002}

-0.0072t = \ln{0.0002}

t = -\frac{\ln{0.0002}}{0.0072}

t = 1183

The tank must remain intact for 1183 years.

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3 years ago
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Step-by-step explanation:

hope this helps

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