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stealth61 [152]
3 years ago
7

Create a system of equations that are parallel to the y-axis.

Mathematics
1 answer:
pishuonlain [190]3 years ago
4 0

Answer:

the y-axis equation that are parallel is x-axis

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(6,4)

Step-by-step explanation:

This question asks you to dilate by a factor of 2, and from the origin. Because it is from the origin, we can simply multiply the coordinates of Y by 2

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2*2=4

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Help with numer 5 please. thank you​
Alex17521 [72]

Answer:

See Below.

Step-by-step explanation:

We are given that:

\displaystyle I = I_0 e^{-kt}

Where <em>I₀</em> and <em>k</em> are constants.

And we want to prove that:

\displaystyle \frac{dI}{dt}+kI=0

From the original equation, take the derivative of both sides with respect to <em>t</em>. Hence:

\displaystyle \frac{d}{dt}\left[I\right] = \frac{d}{dt}\left[I_0e^{-kt}\right]

Differentiate. Since <em>I₀ </em>is a constant:

\displaystyle \frac{dI}{dt} = I_0\left(\frac{d}{dt}\left[ e^{-kt}\right]\right)

Using the chain rule:

\displaystyle \frac{dI}{dt} = I_0\left(-ke^{-kt}\right)  = -kI_0e^{-kt}

We have:

\displaystyle \frac{dI}{dt}+kI=0

Substitute:

\displaystyle \left(-kI_0e^{-kt}\right) + k\left(I_0e^{-kt}\right) = 0

Distribute and simplify:

\displaystyle -kI_0e^{-kt} + kI_0e^{-kt} = 0 \stackrel{\checkmark}{=}0

Hence proven.

4 0
3 years ago
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