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1 year ago

12

What is the explicit formula of the arithmetic sequence? -9, -6, -3, 0....

1 answer:

luda_lava [24]1 year ago

4 0

Answer:

Tn= -9+(n-1)×3

Step-by-step explanation:

d= t2-t1 =t3-t2....

=-6-(-9)=3

We realize that this is an arithmetic sequence

Therefore Tn= a + (n-1)d, whereby a if the first term= - 9,d=3

Tn=-9+(n-1)×3

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2 years ago

Newton's law of cooling is:

Mnenie [13.5K]

Answer:

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Step-by-step explanation:

For this case we have the following differential equationÑ

$\frac{du}{dt}= -k (u-T)$

We can reorder the expression like this:

$\frac{du}{u-T} = -k dt$

We can use the substitution $w = u-T$ and $dw =du$ so then we have:

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IF we integrate both sides we got:

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We can also express the solution in the following terms:

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For this case we know that $k =-0.15 hr$ since w ehave a cooloing, $T_{i}= 70 F, T_{amb}=11F$ , we have this model:

$u(t) = (70-11) e^{-0.15t} +11$

And if we want that the temperature would be 32F we can solve for t like this:

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If we apply natural logs on both sides we got:

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