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dalvyx [7]
3 years ago
5

(a)b - 0.5b when a = 1 and b = 5​

Mathematics
2 answers:
Allisa [31]3 years ago
7 0

Answer:

(1)5 - 0.5(5) = 5 - 2.5 =======2.5

Step-by-step explanation:

MAXImum [283]3 years ago
3 0

Answer:

2.5

Step-by-step explanation:

(a)b-0.5b

Substitute 'a' and 'b' for the appropriate values:

(1)5-0.5(5)

Solve:

(1)5-0.5(5)\\\\5-2.5\\\\\boxed{2.5}

Hope this helps.

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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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