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3 years ago

6(x - 2) = 3x - 12 + 3x

Mathematics

1 answer:

Andrei [34K]3 years ago

3 0

6(x-2)=3x-12+3x
6x-12=6x-12

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2 years ago

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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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If f(x) = 2(x)^2 + 5 square root (x+2), complete the following statement (round your answer to the nearest hundredth): f(2) =

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$f(2) = 2(2)^{2} + 5 \sqrt{(2)+2}$

$f(2) = 2(4) + 5\sqrt{4}$

$f(2) = 8 + 5(2)$

$f(2)= 8+10$

f(2) = 18

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3 years ago