Use a proportion to convert the measurement. Round your answer to two decimal places.

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

Rewrite the equation y-3=2(x+4) into slope form

soldi70 [24.7K]

Answer:

Step-by-step explanation:

So we have y-3=2(x+4)

So the first thing we want to do is distribute the 2 in front of the (x+4)

2(x+4) = 2x+8

Which means we have:

y-3=2x+8

Remember we need to get it into the form y=mx+b

As you can see here the 3 is preventing our equation from being in that form to we need to add it to both sides. This leaves us with:

y - 3 + 3 = 2x+8+3

Which gives: y = 2x+11

Therefore the slope form of this equation is y = 2x+11

4 0

3 years ago

Adam tried to compute the average of his 6 test scores. he mistakenly divided the correct sum of all of his test scores by 5, wh

kipiarov [429]

Sum/5 = 90
so Sum = 450 which should be divided by 6
450/6 = 75 as the real average.

5 0

3 years ago

Solve 5 ÷ 4. Express your answer as a mixed number.

Georgia [21]

use photomath

5/4

1 whole

1 1/4

8 0

3 years ago

Find the slope of the line passing through the points and ( -6, -5 ) and (4, 4)

Andrew [12]

Answer:

Slope: 9/10

Step-by-step explanation:

We need to find the slope of the line that passes through the coordinates given.

To find the slope, we would use the slope formula: m = y2-y1/x2-x1

Plug in your coordinates and solve:

m = 4-(-5)/4-(-6)

m = 4+5/4+6

m = 9/10

Since we can't simplify further, the slope of the line would be 9/10.

8 0

3 years ago