1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
UNO [17]
3 years ago
6

g Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that it forms a pile in the sh

ape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 ft high
Mathematics
1 answer:
Maslowich3 years ago
7 0

Answer:

0.3537 feet per minute.

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

\dfrac{dV}{dt}=10$ ft^3/min

\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h

If the Base Diameter = Height of the Cone

The radius of the Cone = h/2

Therefore,

\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}

\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}

Therefore: \dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10

We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.

When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute

When the pile is 6 feet high, the height of the pile is increasing at a rate of 0.3537 feet per minute.

You might be interested in
Jen has $60 in a savings account that earns 5% interest per year. the interest is not compounded. How much interest will she ear
Stolb23 [73]

Answer:

$9

Step-by-step explanation:

Firstly, I want to say, if the interest is not compounded that means it is simple interest.

Simple interest is also called non-compounding interest.

We've, Principal(p)= $60

Rate of Interest (R)=5%

Time (T)= 3 years

Interest (I) = ?

By formula of Simple Interest,

S.I = PTR/100

=(60×3×5)/100

=900/100

=9

THEREFORE, the interest amount is $9.

Thank You.

3 0
3 years ago
Z squared divided by z​
Rufina [12.5K]

Answer:

z^2/z=z

Step-by-step explanation:

3 0
3 years ago
Will give brainliest
anastassius [24]
9 sq units down and 6 sq units to the left
5 0
3 years ago
Sean drew a shape with 2 fewer sides than an octagon.Which shape did he draw?
Katena32 [7]
He drew a hexagon
hexa = 6
4 0
3 years ago
Read 2 more answers
MULTIPLE CHOICE QUESTION
inn [45]

Answer

are you answering this your self?

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • William bought a new sweater at the store when they were having a 45% off sale.
    12·2 answers
  • The sector of a circle with a 12 inches radius has a central angle measure of 60°.
    7·2 answers
  • Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to:_______
    11·1 answer
  • Estimate the measure of the clockwise angle formed by the minute hand and the second hand, then classify the angle.
    7·1 answer
  • if 129.5 meters of cable connected the boat to the parasail, approximately how many meters above the lake was the man?
    8·2 answers
  • Write each fraction or mixed number as a decimal. Use bar notation if the decimal is a repeating decimal.
    6·2 answers
  • Help please!!! the question is number 2 help me plzz
    15·1 answer
  • Find the measure of angle 6
    12·2 answers
  • The trail is a loop that is 3/4 of a mile long. On Monday, Selma land the loop in 1/6 of an hour. What is selmas unit rate in mi
    6·1 answer
  • Which equation in point slope form is shown in the graph below
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!