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Stella [2.4K]
2 years ago
7

Please please help me with this

Mathematics
2 answers:
ololo11 [35]2 years ago
8 0

Answer:

x = 5 units

Step-by-step explanation:

Use the Pythagorean Theorem:

a^2 +  b^2 = c^2

Set Values for Variables:

Side Length - a = 12

Side Length - b = x

Hypotenuse - c = 13

<em>* Hypotenuse is always opposite from the right angle.</em>

Solve:

12^2 + b^2 = 13^2

144 + b^2 = 169  

<em>(Subtract 144 from both sides to get 25)</em>

b^2 = 25

<em>(Find square root of 25 and b^2)</em>

b = 5

Conclude:

Now you know x (otherwise known as the b-value), is equal to 5 units.

BartSMP [9]2 years ago
5 0

Answer:

x = 5

Step-by-step explanation:

Just use the Pythagorean Triangle:

13^2 - 12^2 = x^2

x^2 = 25

x = 5

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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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Answer:

0.325 ft/min

Step-by-step explanation:

To solve we must follow the following steps:

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

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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

Vc = (1/12) * Pi * h ^ 3

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.

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