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
GREYUIT [131]
3 years ago
10

Water is leaking out of an inverted conical tank at a rate of 6800 cubic centimeters per min at the same time that water is bein

g pumped into the tank at a constant rate. The tank has height 12 meters and the diameter at the top is 3 meters. If the water level is rising at a rate of 21 centimeters per minute when the height of the water is 3.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Mathematics
1 answer:
ivanzaharov [21]3 years ago
5 0

Answer:

1508527.582 cm³/min

Step-by-step explanation:

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 6800 cm³/min,

dV/dt = k - 6800

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 12 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

You might be interested in
53 pts! which of the following is equal to g(x)?
ziro4ka [17]

Answer:

B is the correct answer, as x - 2 in the exponent would move the graph to the right 2.

7 0
3 years ago
Can anyone help with problem 9.9 in the middle pls
ELEN [110]

Answer:

Angle 1: 53

Angle 2: 72

Angle 3: 55

Angle 4: 127

Angle 5: 53

Angle 6: 66

Angle 7: 125

3 0
3 years ago
Solve the following system by graphing and identify the point of intersection -5x+2y=-4 2x-y=2
FrozenT [24]

Answer: Point of intersection (0, -2)

Step-by-step explanation:

8 0
1 year ago
Read 2 more answers
(-10) - |(-20) – (+30) |
myrzilka [38]

ANSWER: -60

EXPLANATION: To solve for (-10) - |(-20) – (+30) |, we need to do:

−10−| −20 − 30|, which equals −10−|−50|. Next, we do −10−50, which is -60.

−10−|−20−30|

= −10−|−50|

= −10−50

= −60

6 0
2 years ago
Find the area of the triangle. Round the answer to the nearest tenth. Triangle is SSA. a= 3.7 b= 3.7 β= 70° ----- A.4.4 square u
Alexus [3.1K]

Answer:

  A.  4.40 square units

Step-by-step explanation:

The triangle is isosceles with base angles of 70°. The a.pex angle will be ...

  180° -2(70°) = 40°

The area of a triangle can be computed from two sides and the angle between them as ...

  A = (1/2)ab·sin(γ)

  A = (1/2)(3.7)(3.7)sin(40°) ≈ 4.40 . . .  square units

3 0
3 years ago
Other questions:
  • Alfred is practicing typing. The first time he tested himself, he could type 27 words per minute. After practicing for a week, h
    5·1 answer
  • Please help! Given the figure below, what is the value of x?
    5·2 answers
  • Its timed hurry lad <br> Evaluate the logarithm log8 (32)
    8·2 answers
  • What is the area of a square with a radius of 24 cm
    6·1 answer
  • Which values of x and y will make the expression 3(-2x - y)(2)
    9·1 answer
  • Help 6.5.AP-23 There were 675 people in line for a rock concert. Only 486 people got into the concert. Select the percent of peo
    11·1 answer
  • Can you help ASAP......
    12·2 answers
  • Use synthetic substitution to find |(3) for f(x) = x2 - 9x +5.
    11·1 answer
  • Mha fans be like..........
    5·2 answers
  • What is the slope of the line that passes through the points (1,0) and (5, 3)?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!