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Vaselesa [24]
3 years ago
9

A wheel has a radius of 15 cm . approximately how far does it travel in 4 revolutions?

Mathematics
1 answer:
storchak [24]3 years ago
8 0
C Because 15 x pie(3.14)=47.1 and 47.1 x 4= 188.4
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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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Darian is asked to determine the volume of a cylindrical pipe for his dad’s plumbing business. The pipe has a diameter of 7 inch
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Check the picture below.

bearing in mind that an angle bisector segment will cut the angle A in two equal halves, thus θ will be half of A.

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Answer:

It is arithmetic and it has a common difference of -99

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