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DENIUS [597]
3 years ago
12

Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shap

e of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 12 ft high? (Round your answer to two decimal places.)
Mathematics
1 answer:
gayaneshka [121]3 years ago
7 0

Answer:

0.13 ft/min

Step-by-step explanation:

We are given that

\frac{dV}{dt}=15ft^3/min

We have to find the increasing rate of change of height of pile  when the pile is 12 ft high.

Let d be the diameter of pile

Height of pile=h

d=h

Radius of pile,r=\frac{d}{2}=\frac{h}{2}

Volume of pile=\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3

\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}

h=12 ft

Substitute the values

15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}

\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}

\frac{dh}{dt}=0.13ft/min

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Ivanna is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a num
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Answer:

The spinner has 6 equal-sized slices, so each slice has a 1/6 probability of showing up.

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number 4: wins $7

number 5: losses $8

number 6: loses $8

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We know that the probability for all the events is 1/6, so we have:

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3 years ago
What is 7+2t+3t in its simplest form?
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Can u guys PLEASE answer this question ASAP. A fat cat that was initially 12 kg reduces its weight by 10% each month. How long d
Mkey [24]

Answer:

It takes at least 7 months for the cat to be at least 6 kg lighter than the original weight.

Step-by-step explanation:

Use exponential decay formula:

A = P (1-r)t

A = amount decreased to

P = original amount

r = rate of decrease

t = time

 

6 ≥ 12 (1-0.10)t      divide both sides by 12

0.5 ≥ (0.9)t            take log of both sides

log (0.5) ≥ log (0.9)t     power rule of logs lets the exponent t drop to front of log to become a factor

log (0.5) ≥ t log(0.9)     divide both sides by log(0.9) which is negative so reverse the inequality sign

log (0.5) / log (0.9) ≤ t     use calculator

6.57 ≤ t

 

It takes at least 7 months for the cat to be at least 6 kg lighter that original weight.

 

check:

12 (0.9)7≈ 5.73

12 (0.9)6 ≈ 6.37

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