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Galina-37 [17]
3 years ago
12

Find the unknown side length, x. Write your answer in simplest radical form.

Mathematics
1 answer:
velikii [3]3 years ago
8 0
The answer should be 16√5
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At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The di
lawyer [7]

Answer:

0.0063 ft / min

Step-by-step explanation:

From the problem statement we have that the variation in volume with respect to time is equal 10, like this:

dV / dt = 10 ft ^ 3 / min

We know that the volume of the cone is given by the equation:

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

Now, we are mentioned that the diameter of the base of the cone is approximately three times the altitude, therefore:

2r = 3h, solving for r we have:

r = (3/2) * h, replacing the volume equation:

V = (1/3) * Pi * [(3h / 2) ^ 2] * h, solving we have:

V = (3/4) * Pi * h ^ 3

They ask us to calculate the change in height with respect to time, that is dh / dt

Therefore we derive both sides with respect to time, we have to:

dV / dt = (3/4) * Pi [3 * (h ^ 2) dh / dt] = (9/4) * pi * (h ^ 2) * dh / dt

reorganizing for dh / dt, we have:

dh / dt = [4/9 * pi * (h ^ 2)] * dV / dt

Knowing that h is 15 and dV / dt is 10, we replace these values:

dh / dt = [4/9 * 3.14 * (15 ^ 2)] * 10 = 0.0063 ft / min

0.0063 ft / min would be the change in height with respect to time.

4 0
3 years ago
Find the volume of the shape
jeka57 [31]

Answer:

i think. 8 times 12 = 96 times 20 = 1,920

7 0
2 years ago
If a girl cuts the grass in 3 hours and a boy cuts it in 2 hours what would be the time if they cut it toghther.?
svet-max [94.6K]

Answer:

d

Step-by-step explanation:

the answer is d because if you do 3+2 it equals 5 so therefore it is b

4 0
3 years ago
Read 2 more answers
Given AB= BC<br> FINDIND <br> X=<br> AB=<br> BC=<br> AC=
tester [92]

Answer:

see explanation

Step-by-step explanation:

Given AB ≅ BC, then

AB = BC = x + 6 , and

AC = AB + BC ← substitute values

3x - 31 = x + 6 + x + 6, that is

3x - 31 = 2x + 12 ( subtract 2x from both sides )

x - 31 = 12 ( add 31 to both sides )

x = 43

Hence

AB = BC = x + 6 = 43 + 6 = 49

AC = 3x - 31 =(3 × 43) - 31 = 129 - 31 = 98

8 0
3 years ago
Can you help me or at least guide me through writing a proof on this?<br> I'm a bit stuck
Andrew [12]

Answer:basically if what they want you to prove is correct say it is correct and why is it correct

Step-by-step explanation:

5 0
3 years ago
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