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klio [65]
3 years ago
5

PLZ HELP ASAP AREA OF A SECTOR

Mathematics
1 answer:
xxTIMURxx [149]3 years ago
5 0
The relationship of arcs is:
 S '/ S = ((1/9) * pi * 3) / (2 * pi * 3)
 Rewriting we have:
 S '/ S = ((1/9)) / (2)
 S '/ S = 1/18
 Therefore, the area of the shaded region is:
 A '= (S' / S) * A
 Where A: area of the complete circle:
 A '= (1/18) * pi * r ^ 2
 A '= (1/18) * pi * (3) ^ 2
 A '= (1/18) * pi * 9
 A '= (1/2) * pi
 Answer:
 
The area of the shaded region is:
 A '= (1/2) * pi
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Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =
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Answer:  The required solution is y=50e^{0.1386t}.

Step-by-step explanation:

We are given to solve the following differential equation :

\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

\dfrac{dy}{y}=kdt.

Integrating both sides, we get

\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]

Also, the conditions are

y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50

and

y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.

Thus, the required solution is y=50e^{0.1386t}.

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3 years ago
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What dose this sign mean in math ( )
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Step-by-step explanation:

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vesna_86 [32]

Answer:

30

Step-by-step explanation:

Quotient means were dividing, so divide 900.37 by 28.9

900.37/28.9=30 rounded up.

The estimated quotient of 900.37 and 28.9 is 30.

Hope this helps!

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