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
Nutka1998 [239]
2 years ago
6

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 16 cubic feet per minute. The di

ameter of the base of the cone is approximately three times the altitude. At what rate (in ft/min) is the height of the pile changing when the pile is 2 feet high
Mathematics
1 answer:
kogti [31]2 years ago
6 0

The rate at which the height of the pile is changing when the height is 2 ft. is 0.5659 ft./min. Computed using differentiation.

The sand is falling onto a conical pile, thus we get the pile in the shape of a cone, whose volume is given as:

<u>V = (1/3)πr²h</u>,

where V represents the volume of the cone, r represents its radius, and h represents its height.

In the question, we are given that the rate of piling is 16 ft.³/min, which implies that:

dV/dt = 16 ... (i)

We are also given that the diameter is three times the altitude (height), which can be shown as:

2r = 3h,

or, r  = (3/2)h.

Thus, the volume can now be shown as:

V = (1/3)π{(3/2)h}²h,

or, V = (3πh³)/4.

Differentiating this with respect to time, we get:

dV/dt = (3π/4)(3h²)dh/dt.

Now, we need to calculate the rate of change of height, when the height is  2 feet, thus we take h = 2

Using dV/dt = 16 from (i), we can write:

16 = (3π/4)(3(2)²)dh/dt.,

or, 16 = 9π(dh/dt),

or, dh/dt = 16/9π = 0.5659 ft./min.

Thus, the rate at which the height of the pile is changing when the height is 2 ft. is 0.5659 ft./min.

Learn more about differentiation at

brainly.com/question/13461339

#SPJ4

You might be interested in
What is the slope of the line shown below ?
ElenaW [278]

Answer:

4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(6-(-2))/(3-1)

m=(6+2)/(2)

m=8/2

m=4

7 0
3 years ago
Simplify the expression 3(x + 9) by distributing. Which expression is equivalent?
notsponge [240]

3(x+9)

3 multiply both x and 9

3x+27

hope it's helpful ❤❤❤

THANK YOU.❤

8 0
3 years ago
In 4 years, Harry’s age will be the same as Jim’s age is now. In 2 years, Jim will be twice as old as Harry will be. Find their
ololo11 [35]
Jim is 6 / Harry is 2 

In 4 years Harry will be 6 
In 2 years Jim will be 8 and Harry will be 4 which is twice as much Harry's age.


hope this helps!
5 0
3 years ago
Read 2 more answers
The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experi- mental conditio
zzz [600]

Answer:

see explaination

Step-by-step explanation:

Data : 32.1 , 30.6 , 31.4 , 30.4 , 31.0 , 31.9

Mean X-bar = 31.23

SD = 0.689

a)

Null Hypothesis : Xbar = mu

Alternate Hypothesis : Xbar > mu

z = (Xbar - mu) / (SD/sqrt(n))

= (31.23 - 30 ) /(0.689/sqrt(6))

= 4.372

P-value = ~0

Since P-vale < 0.01 , we will reject null hypothesis.

The data suggest that true average stopping ditance exceeds the maximum.

b)

i) SD = 0.65

mu = 31

z = (Xbar - mu) / (SD/sqrt(n))

= (31.23 - 31) /(0.65/sqrt(6))

= 0.867

P-value = 0.3859 Answer

ii) SD = 0.65

mu = 32

z = (Xbar - mu) / (SD/sqrt(n))

= (31.23 - 32) /(0.65/sqrt(6))

= -2.9

P-value = 0.0037 Answer

c)

i) SD = 0.8

mu = 31

z = (Xbar - mu) / (SD/sqrt(n))

= (31.23 - 31) /(0.8/sqrt(6))

= 0.704

P-value = 0.4814 Answer

ii) SD = 0.8

mu = 32

z = (Xbar - mu) / (SD/sqrt(n))

= (31.23 - 32) /(0.8/sqrt(6))

= -2.357

P-value = 0.0184 Answer

The probabilities obtained in part c are comparatively higher than that of part b.

d)

i) For alpha =0.01

z = (Xbar - mu) / (SD/sqrt(n))

=> -2.32 = (31.23 - 31) /(0.65/sqrt(n))

=> (0.65/sqrt(n)) = (31.23 - 31)/-2.32

=> sqrt(n) = (0.65*(-2.32)) / (31.23 - 31)

=> n = 43 Answer

ii) For beta =0.10

z = (Xbar - mu) / (SD/sqrt(n))

=> -1.28 = (31.23 - 31) /(0.65/sqrt(n))

=> (0.65/sqrt(n)) = (31.23 - 31)/-1.28

=> sqrt(n) = (0.65*(-1.28)) / (31.23 - 31)

=> n = 13 Answer

4 0
3 years ago
Find a number which when divided by 3 gives the quotient 20 and remainder
Westkost [7]

Solution:

<em>the</em><em> </em><em>answer</em><em> </em><em>please</em><em> </em><em>mark</em><em> </em><em>as</em><em> </em><em>brainly ness</em><em> </em>

<em>your</em><em> </em><em>welcome</em>

8 0
2 years ago
Other questions:
  • How many micrometers long is one edge of a centimeter cube
    8·2 answers
  • HELP PLEAAESEEEEEEeee
    14·1 answer
  • Expand the binomial (a+2)^4
    7·2 answers
  • You have decided to start your own business selling friendship bracelets. It will
    9·2 answers
  • What is -5 to the 4 power in expanded form
    6·2 answers
  • Select all that apply.
    12·1 answer
  • On number 6 what should i color in
    11·1 answer
  • Given 2x⁵-6x³-4x²-2x+4 =0 solve for x
    11·1 answer
  • Rafe and Sebastian both rode in a 5 mile bike race. There were so many riders that they started groups at different times. Rafe
    10·1 answer
  • Write a system of equations to describe the situation below, solve using any method, and fill
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!