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LenKa [72]
2 years ago
8

Find the measure of arc FD

Mathematics
1 answer:
Mekhanik [1.2K]2 years ago
3 0

Answer: 49 degrees

Step-by-step explanation:

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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) =
irga5000 [103]

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}.

8 0
3 years ago
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Mr. Haines drives 12 kilometers from home to work each day. How many meters are equal to 12 kilometers?
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12000 meters

Step-by-step explanation:

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Does this graph has a minimum or maximum y=4x^2+4
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Answer:

It has a minimum and no maximum.

Step-by-step explanation:

This is the graph of a parabola that opens up, so it has a minimum but no maximum.

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Answer: The Answer is D.

Step-by-step explanation: IT is D because a FUNCTION DOES NOT suppose to hit more than 1 point. You can also use the vertical line test meaning take a pencil or pen hold it up and down and drag it across you screen or paper, and if it hits more than 1 point it is NOT a FUNCTION. Plus rate the Brainlest

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