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
sladkih [1.3K]
3 years ago
13

Gravel is being dumped from a conveyor belt at a rate of 20 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 15 ft high
Mathematics
1 answer:
pantera1 [17]3 years ago
8 0

Answer:

The height of the pile is increasing at the rate of  \mathbf{ \dfrac{20}{56.25 \pi}   \ \ \ \ \  ft/min}

Step-by-step explanation:

Given that :

Gravel is being dumped from a conveyor belt at a rate of 20 ft³ /min

i.e \dfrac{dV}{dt}= 20 \ ft^3/min

we know that radius r is always twice the   diameter d

i.e d = 2r

Given that :

the shape of a cone whose base diameter and height are always equal.

then d = h = 2r

h = 2r

r = h/2

The volume of a cone can be given by the formula:

V = \dfrac{\pi r^2 h}{3}

V = \dfrac{\pi (h/2)^2 h}{3}

V = \dfrac{1}{12} \pi h^3

V = \dfrac{ \pi h^3}{12}

Taking the differentiation of volume V with respect to time t; we have:

\dfrac{dV}{dt }= (\dfrac{d}{dh}(\dfrac{\pi h^3}{12})) \times \dfrac{dh}{dt}

\dfrac{dV}{dt }= (\dfrac{\pi h^2}{4} ) \times \dfrac{dh}{dt}

we know that:

\dfrac{dV}{dt}= 20 \ ft^3/min

So;we have:

20= (\dfrac{\pi (15)^2}{4} ) \times \dfrac{dh}{dt}

20= 56.25 \pi \times \dfrac{dh}{dt}

\mathbf{\dfrac{dh}{dt}= \dfrac{20}{56.25 \pi}   \ \ \ \ \  ft/min}

The height of the pile is increasing at the rate of  \mathbf{ \dfrac{20}{56.25 \pi}   \ \ \ \ \  ft/min}

You might be interested in
Please answer this question as soon as possible
Taya2010 [7]

Answer: The graph is shifted vertically, but not horizontally

Step-by-step explanation:

Since the added constant is outside the x term, the constant will only shift the graph vertically.

6 0
3 years ago
PLEASE HELP ASAP HURRY
bulgar [2K]

Answer: The amount she pays for admission

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Hello, could anyone help me on part A and part B
solniwko [45]

Answer:

9 answer ok like floow on

7 0
3 years ago
B Identify the coefficient and the number of terms in the
Elenna [48]
It’s D because the number that have an (x) is a COEFFICIENT and I hope it helps :)
8 0
2 years ago
Solve for x. Please Help
IceJOKER [234]
I’m pretty sure it would be C
4 0
3 years ago
Read 2 more answers
Other questions:
  • Solve 4x − 2(x + 1) = 3x + 10. −12 12 −8 8
    14·2 answers
  • Solve the inequality
    7·1 answer
  • Given the function f(x) = 2(3)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
    11·1 answer
  • Simplify 3 over 2 x 3 over 2 exact answer
    10·2 answers
  • Help solving this math problem
    13·2 answers
  • Solve for x:<br> 51 = 3x
    12·2 answers
  • Find an equation of a line with the x- and y-intercepts below. Use exact fractions when necessary.
    14·1 answer
  • 1. Find Cos 0 if Sin 0 = 0.7771 if 0 so&lt;<br> a. 0.6293<br> b. +0.6293<br> C. 0.3961<br> d. -03961
    7·1 answer
  • HELP ME ON 9 AND 10 PLEASE THIS IS DUE 8AM!!!
    13·2 answers
  • the bellah's pool is leaking. The pool leaked 3/4 gallon in 20 minutes, or 1/3 hour. how many gallon is the pool leaking each ho
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!