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3 years ago

HELP ME IM TERRIBLE AT THIS

Mathematics

1 answer:

OLEGan [10]3 years ago

8 0

Answer:

a. $14.50

b. $43.5

Step-by-step explanation:

a. $7.00 + $7.50 = $14.50

b. y = 14.5x x=3

y = $14.5 x 3 = $43.5

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The values of a and be are:

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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

Sarah walks 20 feet away from her house and places a mirror on the ground. She backs 5 feet away from the mirror so that she can

Vikki [24]

Answer:

16 feet

Step-by-step explanation:

As said in the problem statement, the angles between the top of the house, the mirror, and the ground and between Sarah's eyes, the mirror, and the ground are congruent.

We also know that Sarah and the house are perpendicular to the ground.

So if we draw a triangle from the top of the house, to the mirror, to the bottom of the house, and another triangle from Sarah's eyes, to the mirror, to Sarah's feet, we get two triangles that have the same angles. Therefore, the triangles are similar, and we can write a proportion:

4 / 5 = h / 20

h = 16

The house is 16 feet tall.

4 0

3 years ago