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snow_lady [41]
3 years ago
5

The area of a sector of a circle with a central angle of radians is . Find the radius of the circle. Do not round any intermedia

te computations. Round your answer to the nearest tenth.

Mathematics
1 answer:
Savatey [412]3 years ago
8 0

Answer:

<h3>3.5ft</h3>

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the complete question in the diagram attached.

Area of a sector = θ/360 * πr² where;

r is the radius

θ is the angle substended by the sector

Given parameters

Area of the sector = 9ft²

central angle θ = 1.5 radians

Since  1 radians = 57.2958°

1.5 radians = (1.5 * 57.2958)

1.5 rad = 85.9437°

Substituting the given values into the formula;

Area of a sector = θ/360 * πr²

9 = 85.9437/360 * (3.14)r²

9 = 0.2387325 * 3.14r²

9 = 0.74962005r²

r² = 9/0.74962005

r² = 12.00608

r = √12.00608

r = 3.4641

r = 3.5 ft (to the nearest tenth)

Hence the radius of the circle is 3.5ft

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The first five terms of a linear sequence are given below. 7 , 12 , 17, 22 , 27 , ... What is the next term of the sequence?
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2 years ago
Apply the method of undetermined coefficients to find a particular solution to the following system.wing system.
jarptica [38.1K]
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The corresponding homogeneous ODE has characteristic equation r^2-r+1=0 with roots at r=\dfrac{1\pm\sqrt3}2, thus admitting the characteristic solution

y_c=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x

For the particular solution, assume one of the form

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Substituting into the ODE gives

(-a\sin x-b\cos x)-(a\cos x-b\sin x)+(a\sin x+b\cos x)=\sin x

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\implies a=1,b=0

Then the general solution to this ODE is

\boxed{y(x)=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x+\sin x}

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Assume a solution of the form

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Substituting into the ODE gives

2e^x(a\cos x-b\sin x)-3e^x((a+b)\cos x+(a-b)\sin x)+2e^x(a\sin x+b\cos x)=e^x\sin x

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