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3 years ago

Please help answer this I need to get this done

Mathematics

1 answer:

Jobisdone [24]3 years ago

5 0

I think it is 3/4 I am not sure this one

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(-3, -5); parallel to y = - 4x + 1

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What do you mean by that?

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3 years ago

Stephanie has 4,500 in her savings account. If it earns 6% interest every month how much money does Stephanie have her bank acco

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5,310

Step-by-step explanation:

6% of 4,500 is 270

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3 years ago

What is 2*6+6/777= plz help

Nana76 [90]

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3 years ago

Three lines intersect to form angles. If <2 is equivalent to (2x-8)°, what is the value of x?

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3 years ago

It is estimated that t-weeks into a semester, the average amount of sleep a college math student gets per day S(t) decreases at

goldenfox [79]

Answer:

s(15)= $\frac{-3}{2} e^{15^{2} } +9.6$

Step-by-step explanation:

Before to getting started ,we have to consider the function which represents sleep decline rate S'(t) = $-3te^{t^{2} } \\$

Since this function is interpreted in this case as a rate of change, we can deduce this funcion is the first derivative of the function of average amount of sleep (S(t)).

In order to find S(t), we will integrate S'(t)

$\int\limits^ {} -3t3e^{t^{2} } \, dx \\$

This case corresponds to intergration by substitution

Substituting u= $x^{2} \\$

Computting the differential of u

$\frac{du}{dt} =2tdt\\$

Now, let's go back to our integral and write it in terms of u, using both definition of u and its defferential.

$\int\limits^{}-3te^{u} \, \frac{1}{2t}du \\\\\int\limits^{}\frac{-3}{2} e^{u}du\\$

The integral of a exponential function is itself. So the result is:

$\frac{-3}{2} e^{u} +c$

Now substitute u back in:

$\frac{-3}{2} e^{t^{2} } +c$

This answer correspond to function of average amount of sleep.

We know that when the semester begins (t=0) , math students sleep an average of 8.1 hours per day so we will use this info in order to find the value of c.

$s(0)=\frac{-3}{2} e^{0^{2} } +c=8.1\\\\\frac{-3}{2} +c=8.1$

Solve this equation

c=8.1+ $\frac{3}{2}$

c=9.6

Replacing the value of c on S(t)

S(t)= $\frac{-3}{2} e^{t^{2} } +9.6$

Now, let's to find the average of amount of sleep when 15 weeks has elapsed since the start date of the semester.

s(15)= $\frac{-3}{2} e^{15^{2} } +9.6$

4 0

3 years ago