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babymother [125]
2 years ago
12

Evaluate each function. 14) g(x)= 3x² - 1; Find g(-3)

Mathematics
2 answers:
adelina 88 [10]2 years ago
5 0

g(x) =3x^2 -1\\\\g(-3)=3(-3)^2 -1 \\ \\~~~~~~~~~=3(9) -1 \\\\~~~~~~~~~=27-1\\\\~~~~~~~~~=26

ololo11 [35]2 years ago
4 0

Answer:

g(26)

Step-by-step explanation:

 

substitute -3 for x.

g(x)=3x^{2}-1

g(-3)=3(-3)^{2} -1\\g(-3)= 3(9)-1\\g(-3)= 27-1\\g(-3)=26

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VGravel is being dumped from a conveyor belt at a rate of 50 ft3/min. It forms a pile in the shape of a right circular cone whos
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Step-by-step explanation:

To solve we must follow the following steps:

First, the volume of a cone is given by the equation:

Vc = (1/3) * Pi * (r ^ 2) * h

where r is the radius and h is the height.

they tell us that the height is equal to twice the radius, therefore

h = 2r; r = h / 2

replacing r in the volume of the cone:

Vc = (1/3) * Pi * ((h / 2) ^ 2) * h

solving we have:

Vc = (1/3) * Pi * (1/4) * (h ^ 2) * h

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They give us the change in volume with respect to time, that is, dV / dt = 50

It can also be expressed in the following way:

dV / dt = (dV / dh) * (dh / dt)

We know V, so we can derive with respect to h, we are like this:

dV / dh = 3 * (1/12) * Pi * h ^ 2

dV / dh = (1/4) * Pi * h ^ 2

we know that h is equal to 14, therefore:

dV / dh = (1/4) * Pi * 14 ^ 2

dV / dh = (1/4) * 3.14 * 196 = 153.86

Now if we replace

dV / dt = (dV / dh) * (dh / dt)

50 = 153.86 * (dh / dt)

(dh / dt) =  50/158.36

(dh / dt) =  0.3249

This means that the change in height with respect to time is 0.325 feet per minutes.

4 0
3 years ago
Read 2 more answers
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