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
Leona [35]
3 years ago
7

Salt is poured from a container at 10 cm³ s-¹ and it formed a conical pile whose height at any time is 1/5 the radius of the abo

ve. At what rate is the height of the cone increasing when the height is 2 cm form the base of the cone?​
Chemistry
1 answer:
Romashka-Z-Leto [24]3 years ago
7 0

Answer:

\displaystyle \frac{dh}{dt} = \frac{1}{10 \pi}

Explanation:

Volume of a cone:

  • \displaystyle V=\frac{1}{3} \pi r^2 h

We have \displaystyle \frac{dV}{dt} = \frac{10 \ cm^3}{sec} and we want to find \displaystyle \frac{dh}{dt} \Biggr | _{h\ =\ 6}= \ ? when the height is 2 cm.

We can see in our equation for the volume of a cone that we have three variables: V, r, and h.

Since we only have dV/dt and dh/dt, we can rewrite the equation in terms of h only.

We are given that the height of the cone is 1/5 the radius at any given time, 1/5r, so we can write this as r = 5h.

Plug this value for r into the volume formula:

  • \displaystyle V =\frac{1}{3} \pi (5h)^2 h  
  • \displaystyle V =\frac{1}{3} \pi \ 25h^3

Differentiate this equation with respect to time t.

  • \displaystyle \frac{dV}{dt}  =\frac{25}{3} \pi \ 3h^2 \ \frac{dh}{dt}
  • \displaystyle \frac{dV}{dt}  =25 \pi h^2 \ \frac{dh}{dt}

Plug known values into the equation and solve for dh/dt.

  • \displaystyle 10 = 25 \pi (2)^2  \ \frac{dh}{dt}
  • \displaystyle 10 = 100 \pi  \ \frac{dh}{dt}  

Divide both sides by 100π to solve for dh/dt.

  • \displaystyle \frac{10}{100 \pi} = \frac{dh}{dt}
  • \displaystyle \frac{dh}{dt} = \frac{1}{10 \pi}

The height of the cone is increasing at a rate of 1/10π cm per second.

You might be interested in
PLZZZZZZZZZZZZZZZ HELP IF RIGHT WILL GIVE BRAINLIEST
ioda

Answer:

I guess it all of these

as life cycle of an organism can be predicted and yeah it begins with birth hatching or germination for mammals, animals and plants respectively. then it's same for the organism of the same species .

7 0
2 years ago
Which of the following elements has the highest electronegativity?
olga55 [171]
Bromine has the highest
6 0
3 years ago
A cylinder is filled with 2.00 moles of nitrogen, 3.00 moles of argon, and 5.00 moles of helium.
Aleks [24]

PRACTICE MULTIPLE CHOICE QUESTIONS FROM UNIT 10

1.) A cylinder is filled with 2.00 moles of nitrogen, 3.00 moles of argon, and 5.00 moles of helium. If

the gas mixture is at STP, what is the partial pressure of the argon?

(A) 152 torr (B) 228 torr (C) 380. torr (D) 760. torr

2.) Compared to the average kinetic energy of 1 mole of water at 0 oC, the average kinetic energy

of 1 mole of water at 298 K is

(A) the same, and the number of molecules is the same

(B) the same, but the number of molecules is greater

(C) greater, and the number of molecules is greater

(D) greater, but the number of molecules is the same

3.) If the pressure on a given mass of gas in a closed system is increased and the temperature

remains constant, the volume of the gas will

(A) decrease (B) increase (C) remain the same

4.) Which gas has approximately the same density as C2H6 at STP?

(A) NO (B) NH3 (C) H2S (D) SO2

5.) At a temperature of 273 K, a 400. milliliter gas sample has a pressure of 760. millimeters of

mercury. If the pressure is changed to 380. millimeters of mercury, at which temperature will

this gas sample have a volume of 551 milliliters?

(A) 100 K (B) 188 K (C) 273 K (D) 546 K

Get the answers to these questions

Back to the Unit 10 Old Tests Page

Back to the Unit 10 Page

Back to the Main Page

5 0
3 years ago
Read 2 more answers
What anions generally form precipitates? What are the exceptions?
8_murik_8 [283]

Answer:

Carbonates (CO3-2), phosphates (PO4-3) and sulfides (S-2) are insoluble.

The exceptions are the alkali metals and the ammonium ion.

6 0
3 years ago
Read 2 more answers
Question 3 When the population size decreases over time, the total number of births the total number of deaths. O less than O eq
Neporo4naja [7]
The population decreases when the birth rate is less than the death rate.
4 0
2 years ago
Other questions:
  • a chemist encounters an unknown metal. They drop the metal into a graduated cylinder containing water, and find the volume chang
    5·1 answer
  • Write and balance the chemical equation that represents the reaction of aqueous sulfuric acid with aqueous sodium hydroxide to f
    9·1 answer
  • What is the heat required to vaporize 650 grams of a liquid with a heat of vaporization of 723 joules/grams?
    14·1 answer
  • What is the surface of Venus mainly composed of
    11·1 answer
  • The ph of a 0.30 m solution of a weak acid is 2.67. what is the ka for this acid?
    10·2 answers
  • The sun supplies about 1.0 kilowatt of energy for each square meter of surface area (1.0 kW/m^2 where a watt = 1 kJ/s) Plants pr
    5·1 answer
  • The amount of kinetic energy an object has depends on which feature of the object?
    8·1 answer
  • An artifact contains one-fourth as much carbon-14 as the atmosphere. how old is the artifact
    9·2 answers
  • Negative radical in the periodic table<br>​
    13·1 answer
  • How can fossil records be useful to determine the relative ages of rock layers and other fossils?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!