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DiKsa [7]
3 years ago
11

For brainliest please help!

Mathematics
1 answer:
Advocard [28]3 years ago
8 0

Answer:

negative multiples of 3 less than -3

Step-by-step explanation:

if m <9, then

m ={8,7,6,5,4,3,2,1,0,-1,-2,....,..........}

And |6m-55|

So is said that,

when, m= 8

6(8)-55=-6

when, m=7

6(7)-54=-12

when, m = 6

6(6)-54=-18

Since the trend is negative multiples of 3 less than -3

this is my answer

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Step-by-step explanation:

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4 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

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