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 above. At what rate is the height of the cone increasing when the height is 2 cm form the base of the cone?​

Answers

Answer 1

Answer:

[tex]\displaystyle \frac{dh}{dt} = \frac{1}{10 \pi}[/tex]

Explanation:

Volume of a cone:

[tex]\displaystyle V=\frac{1}{3} \pi r^2 h[/tex]

We have [tex]\displaystyle \frac{dV}{dt} = \frac{10 \ cm^3}{sec}[/tex] and we want to find [tex]\displaystyle \frac{dh}{dt} \Biggr | _{h\ =\ 6}= \ ?[/tex] 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:

[tex]\displaystyle V =\frac{1}{3} \pi (5h)^2 h[/tex]   [tex]\displaystyle V =\frac{1}{3} \pi \ 25h^3[/tex]

Differentiate this equation with respect to time t.

[tex]\displaystyle \frac{dV}{dt} =\frac{25}{3} \pi \ 3h^2 \ \frac{dh}{dt}[/tex] [tex]\displaystyle \frac{dV}{dt} =25 \pi h^2 \ \frac{dh}{dt}[/tex]

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

[tex]\displaystyle 10 = 25 \pi (2)^2 \ \frac{dh}{dt}[/tex] [tex]\displaystyle 10 = 100 \pi \ \frac{dh}{dt}[/tex]  

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

[tex]\displaystyle \frac{10}{100 \pi} = \frac{dh}{dt}[/tex] [tex]\displaystyle \frac{dh}{dt} = \frac{1}{10 \pi}[/tex]

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


Related Questions

When paper is burned, the mass of the remaining ash is less than the mass of the original paper. Which statement best explains this result?

A. The ash has less volume than the paper.
B. Some of the matter is destroyed during the reaction.
C. The mass of the ash cannot be accurately determined
D. Some of the products of the reaction were given off as a gas.

Answers

Answer:

d

Explanation:

According to law of conservation of mass, mass  is conserved during burning of paper although the mass of ash is less than paper as some of the products are  given out as gas.

What is law of conservation of mass?

According to law of conservation of mass, it is evident that mass is neither created nor destroyed rather it is restored at the end of a chemical reaction .

Law of conservation of mass and energy are related as mass and energy are directly proportional which is indicated by the equation E=mc².Concept of conservation of mass is widely used in field of chemistry, fluid dynamics.

Law needs to be modified in accordance with laws of quantum mechanics under the principle of mass and energy equivalence.This law was proposed by Antoine Lavoisier in the year 1789.

Learn more about law of conservation of mass ,here:

https://brainly.com/question/13383562

#SPJ5

What is the molarity of a HCl solution that
contains 6.27 g of HCl in 163 mL of solution?
Answer in units of M.

Answers

Answer:

M = 1.04 M

Explanation:

Given data:

Molarity of solution = ?

Mass of HCl = 6.27 g

Volume of solution = 163 mL (163 mL× 1L /1000 mL = 0.163 L)

Solution:

Molarity is used to describe the concentration of solution. It tells how many moles are dissolve in per litter of solution.

Formula:

Molarity = number of moles of solute / L of solution

Number of moles of HCl:

Number of moles = mass/molar mass

Number of moles = 6.27 g / 36.5 g/mol

Number of moles = 0.17 mol

Molarity:

M = 0.17 mol/ 0.163 L

M = 1.04 M

Answer:

4.6 M HCI

Explanation:

on edge

compound
element + element
1:Synthesis
2:Decomposition
3:Single Replacement
4:Double Replacement
5:Combustion

Answers

Answer:

4

Explanation:

Because of single replacement the ideal shape comes in form

Question 1
The Relationship of Potential Energy is that when
increases or
increases, Potential Energy will increase also.
A
speed in a given direction
B
the amount of matter in an object
С
is a measurement for the amount of energy
D
Mass, Height
E
Mass, Velocity

Answers

b? i think b i took this class last year tho

For the chemical reaction:
ALOH3 (s)
= Al2O3 (s)
+ H20 (l)
Calculate the mass of water formed when 100 g of Al(OH)3 is heated. (AI = 27: 0 - 16; H = 1)​

Answers

Answer:

35.1 g

Explanation:

Given data:

Mass of Al(OH)₃ = 100 g

Mass of water formed = ?

Solution:

Chemical equation:

2Al(OH)₃      →        Al₂O₃ + 3H₂O

Number of moles of Al(OH)₃:

Number of moles = mass/molar mass

Number of moles = 100 g/ 78 g/mol

Number of moles = 1.3 mol

now we will compare the moles of Al(OH)₃ with water.

                          Al(OH)₃         :          H₂O

                             2                :            3

                             1.3              :           3/2×1.3 = 1.95

Mass of water produced:

Mass = number of moles ×molar mass

Mass = 1.95 mol × 18 g/mol

Mass = 35.1 g

Passengers get on a plane in Phoenix at 8:00 A.M. and fly to Los Angeles and land at 8:00 A.M. How can that possible?

Answers

Answer:

Because of time zones?

Explanation: The only thing that would make sense to me is the time zones.

Plz solve
A 20-g sample of sugar is dissolved in 59 g of water. The concentration of the solution is

Hint Water is a solvent​

Answers

Answer:

0.98 M

Explanation:

Given data:

Mass of sugar = 20 g

Mass of water = 59 g

Concentration of solution = ?

Solution:

1 g = 0.01 L

59 g× 0.01 L/1 g

0.059 L

Concentration formula:

C = m/v

m = moles of solute

v = volume of solution

Number of moles of sugar:

Number of moles = mass/molar mass

Number of moles = 20 g/ 342.3 g/mol

Number of moles = 0.058 mol

Now we will calculate the concentration:

C = 0.058 mol/0.059 L

C = 0.98 mol/L

C = 0.98 M

Calculate the mole fraction of each solute and solvent in the solution of 46.85 g of codeine, C 18 H 21 NO 3 , in 125.5 g of ethanol, C 2 H 5 OH.

Answers

mol fraction Codein : 0.054

mol fraction Ethanol : 0.946

Further explanation

Given

46.85 g of codeine

125.5 g of ethanol

Required

mol fraction

Solution

The mole fraction : the mole ratio of a substance to the mole of solution /mixture  

mol Codeine, C₁₈H₂₁NO₃(MW=299.4 g/mol) :

[tex]\tt mol=\dfrac{46.85}{299.4 g/mol}\\\\mol=0.1565[/tex]

mol Ethanol, C₂H₅OH(MW=46.07 g/mol)

[tex]\tt mol=\dfrac{125.5}{46.07}=2.7241[/tex]

mol of solution :

[tex]\tt mol~codein+mol~ethanol=0.1565+2.7241=2.8806[/tex]

mol fraction Codein :

[tex]\tt \dfrac{0.1565}{2.8806}=0.054[/tex]

mol fraction Ethanol :

[tex]\tt \dfrac{2.7241}{2.8806}=0.946[/tex]

If the enantiomeric excess of a mixture is 81 %, what are the percent compositions of the major and minor enantiomer?

Answers

Answer:

major enantiomer = 90.5 %

minor enantiomer = 9.5 %

Explanation:

Assuming that the  major isomer is in excess;

From, ee/2 + 50

ee = enantiomeric excess = 81%

%  major =81/2 + 50 = 90.5 %

%  minor = 100% - 90.5 %

%  minor = 9.5 %

Identify this instrument.



Microscope
Refracting telescope
Reflecting telescope
Radio Telescope

Answers

I think it might be a refracting telescope, but I do know it is between refracting telescope and reflecting telescope

Answer:

I believe the answer is Reflecting Telescope

Explanation:

-leeknowishawt

hich of the following is a typical cost associated with renting?
a.
closing costs
b.
down payment
c.
property tax
d.
security deposit

Answers

Answer:

D

Explanation:

The other three are related to

a. selling a home

b. buying a home

c. owning a home

click heart to give thanks :)

What advantage does a heterogeneous catalyst provide over a homogeneous catalyst in industrial processes?

Answers

A heterogeneous catalyst can be easily separated from reactants.

Answer:

A heterogeneous catalyst can be easily separated from reactants.

Explanation:

A perfectly spherical balloon occupied 35°C of neon gas under a pressure of 2 atm.
The radius of the balloon is 15 cm. The balloon is then released up in the air until it
reached the temperature of -20°C under 0.3 atm. Determine its volume at that instant.

Answers

Answer:

V₂ =  116126.75 cm³

Explanation:

Given data:

Radius of balloon = 15 cm

Initial pressure = 2 atm

Initial temperature = 35 °C (35 +273 = 308K)

Final temperature = -20°C (-20+273 = 253 K)

Final pressure = 0.3 atm

Final volume = ?

Formula:  

P₁V₁/T₁ = P₂V₂/T₂  

P₁ = Initial pressure

V₁ = Initial volume

T₁ = Initial temperature

P₂ = Final pressure

V₂ = Final volume

T₂ = Final temperature

Solution:

Initial volume of balloon:

V = 4/3πr³

V = 4/3×22/7×(15cm)³

V = 14137.17 cm³

V₂ = P₁V₁ T₂/ T₁ P₂  

V₂ = 2 atm × 14137.17 cm³ × 253 K / 308 K × 0.3 atm

V₂ = 7153408.02 atm .cm³. K / 61.6 K.atm

V₂ =  116126.75 cm³

How many liters of 0.305 m K3PO4 solution are necessary to completely react with 187 ml of 0.0184M NiCl2 according to the balanced chemical reaction:

2 K3PO4(aq) + 3NiCl2(aq)>Ni3(PO4)2(s) +6 KCl(aq)

Answers

Answer:

0.00752L of 0.305M K₃PO₄

Explanation:

Based on the balanced chemical equation, 2 moles of K₃PO₄ react with 3 moles of NiCl₂.

To find the volume of K₃PO₄ we need to determine the moles of this compound required for a complete reaction finding moles of NiCl₂ and using the chemical equation:

Moles NiCl₂:

187mL = 0.187L * (0.0184mol / L) = 0.00344 moles NiCl₂

Moles K₃PO₄:

As 2 moles of K₃PO₄ react with 3 moles of NiCl₂:

0.00344 moles NiCl₂ * (2 mol K₃PO₄ / 3 moles NiCl₂) =

0.002294 moles of K₃PO₄

Volume of 0.305M K₃PO₄:

0.002294 moles of K₃PO₄ * (1L / 0.305moles K₃PO₄) =

0.00752L of 0.305M K₃PO₄

whats the answer giving brainliest please help

Answers

Answer:

C               (I think)

Explanation:

the levels are higher than they have ever been

please help!!!!!!!
according to the laws of conservation of mass how much zinc was present in the zinc carbonate
a. 40 g
b. 88 g
C. 104 g
d. 256 g​

Answers

the answer is c. 104 g because 152-64 equals 88 and 192-88 equals 105

During science lab, Jacob mixes together sodium hydroxide (NaOH) and hydrochloric acid (HCl). The two chemicals react to form sodium chloride (NaCl) and water (H2O).

Which of the following are reactants in the chemical reaction described above?
A.
hydrochloric acid and water
B.
sodium hydroxide and hydrochloric acid
C.
sodium hydroxide and sodium chloride
D.
sodium chloride and water

Answers

B. Sodium hydroxide and Hydrochloric acid

Further explanation

Chemical equations can be expressed in terms of

word reaction formula reaction

In a chemical reaction, there are several components, including reactants, products, and compounds that react in the form of solids, gases, and liquids

Reactants are compounds that react and form products

The reactants are generally to the left of the chemical equation and the products are to the right of the reaction

The statement of the word reaction above can be expressed by the reaction formula

[tex]\tt NaOH+HCl\rightarrow NaCl+H_2O[/tex]

This reaction is called a neutralization reaction because it involves acids(HCl) and bases(NaOH) and produces salt(NaCl)and water(H₂O)

From the reaction above, the reactants on the left are NaOH and HCl compounds

What is the oxidation number for S in the compound SO3? (Recall that o has an oxidation number of -2.)
0
O +2
O +4
O +6

Answers

The oxidation number for S in the compound SO₃ : +6

Further explanation

The formula for determining Oxidation Numbers :

1. Single element atomic oxidation number = 0.

Group IA (Li, Na, K, Rb, Cs, and Fr): +1

Group IIA (Be, Mg, Ca, Sr and Ba): +2

H in compound = +1, except metal hydride compounds (Hydrogen which binds to groups IA or IIA) oxidation number H = -1, for example, LiH, MgH₂, etc.

2. Oxidation number O in compound = -2, except OF₂ = + 2 and in peroxide (Na₂O₂, BaO₂) = -1 and superoxide, for example KO₂ = -1/2.

3 The oxidation number in an uncharged compound = 0,

Total oxidation number in ion = ion charge, Example NO₃⁻ = -1

The oxidation number for S in SO₃ :

[tex]\tt oxidation~number~of~S+3\times oxidation~number~of~O=0\\\\oxidaton~number~of~S+3\times(-2)=0\\\\oxidation~number~of~S=+6[/tex]

Acetylene gas is often used in welding torches because of the very high heat produced when it reacts with oxygen O2 gas, producing carbon dioxide gas and water vapor. Calculate the moles of oxygen needed to produce 1.3mol of carbon dioxide. Be sure your answer has a unit symbol, if necessary, and round it to 2 significant digits.

Answers

Answer:  

3.2 moles of carbon dioxide

Explanation:

When C₂H₂ reacts with O₂ the chemical reaction is:

C₂H₂ + 5/2O₂ → 2CO₂ + H₂O

Where 1 mole of acetylene produce 2 moles of carbon dioxide.

Based on the chemical equation of this reaction, there are produced twice the moles of acetylene in moles of carbon dioxide assuming a compete reaction.

If 1.6 moles of acetylene reacts there are produced:

1.6 moles Acetylene * (2 moles Carbon Dioxide / 1 mole Acetylene) =

3.2 moles of carbon dioxide

When an element loses electrons, it forms *
Negative ions or anions
Positive ions or cations
neutral atoms or neutrons
alpha and beta particles

Answers

Answer: Positive ions or cations

Explanation:

The ions are formed when an atom gains or lose electrons.

The ions are classified into two which are called the cations and anions. The cation is classified as the positive charge formed by the loss of electrons. Example: [tex]Na^+[/tex] is formed by the loss of one electron by [tex]Na[/tex]

The anion is classified as the negative charge ion formed by the gain of electrons. Example : [tex]F^-[/tex] is formed the gain of one electron by [tex]F[/tex]

Thus when an element loses electrons, it forms positive ions or cations.

1
Aluminum metal and oxygen gas combine to produce aluminum oxide.
Which of these is the balanced equation for this reaction? *

Answers

Answer:

4 Al(s) + 3 O₂(g) ⇒ 2 Al₂O₃(s)

Explanation:

Let's consider the unbalanced molecular equation when aluminum metal and oxygen gas combine to produce aluminum oxide. This is a combination reaction.

Al(s) + O₂(g) ⇒ Al₂O₃(s)

We can balance O  atoms by multiplying O₂ by 3 and Al₂O₃ by 2.

Al(s) + 3 O₂(g) ⇒ 2 Al₂O₃(s)

Finally, we multiply Al by 4 to get the balanced equation.

4 Al(s) + 3 O₂(g) ⇒ 2 Al₂O₃(s)

List the symbol and the bonding capacity of the 4 most common elements found in
organic compounds.

Answers

Answer:

The four elements most commonly found in living things are carbon, nitrogen, hydrogen, and oxygen.

Explanation:

The four elements most commonly found in living things are carbon, nitrogen, hydrogen, and oxygen.

What do asteroids have in common with earth?

Answers

they rotate around the central axis

Which term refers to the process by which land is worn away by natural forces or human activity?

Answers

Answer:

erosion

Explanation:

erosion is the term that refers to the process by which land is worn away by natural forces or human activity.

Answer:

Erosion

Explanation:

Just took the test, hope it helps!

Calcium Carbonate reacts with dilute hydrochloric acid. The equation for the reaction is shown. CaCo3 + 2Hcl = Cacl2 + H2O + Co2 1 g of calcium Carbonate is added to 50cm3 of 0.05mol/dm3 hydrochloric acid. Which volume of carbon dioxide is made in this reaction?

Answers

Answer:

Approximately [tex]0.224\;\rm L[/tex], assuming that this reaction took place under standard temperature and pressure, and that [tex]\rm CO_2[/tex] behaves like an ideal gas. Also assume that the reaction went to completion.

Explanation:

The first step is to find out: which species is the limiting reactant?

Assume that [tex]\rm CaCO_3[/tex] is the limiting reactant. How many moles of [tex]\rm CO_2[/tex] would be produced?

Look up the relative atomic mass of [tex]\rm Ca[/tex], [tex]\rm C[/tex], and [tex]\rm O[/tex] on a modern periodic table:

[tex]\rm Ca[/tex]: [tex]40.078[/tex].[tex]\rm C[/tex]: [tex]12.011[/tex].[tex]\rm O[/tex]: [tex]15.999[/tex].

Calculate the formula mass of [tex]\rm CaCO_3[/tex]:

[tex]\begin{aligned} & M(\rm CaCO_3) \\ &= 40.078 + 12.011 + 3 \times 15.999 \\&= 100.086\; \rm g \cdot mol^{-1}\end{aligned}[/tex].

Calculate the number of moles of formula units in [tex]1\; \rm g[/tex] of [tex]\rm CaCO_3[/tex] using its formula mass:

[tex]\begin{aligned}& n(\mathrm{CaCO_3})\\&= \frac{m(\mathrm{CaCO_3})}{M(\mathrm{CaCO_3})} \\ &= \frac{1\; \rm g}{100.086\; \rm g \cdot mol^{-1}} \approx 1.00\times 10^{-2}\; \rm mol\end{aligned}[/tex].

In the balanced chemical equation, the ratio between the coefficient of [tex]\rm CaCO_3[/tex] and that of [tex]\rm CO_2[/tex] is [tex]\displaystyle \frac{n(\mathrm{CO_2})}{n(\mathrm{CaCO_3})} = 1[/tex].

In other words, for each mole of [tex]\rm CaCO_3[/tex] formula units consumed, one mole of [tex]\rm CO_2[/tex] would be produced.

If [tex]\rm CaCO_3[/tex] is indeed the limiting reactant, all that approximately [tex]1.00\times 10^{-2}\; \rm mol[/tex] of [tex]\rm CaCO_3\![/tex] formula would be consumed. That would produce approximately [tex]1.00\times 10^{-2}\; \rm mol\![/tex] of [tex]\rm CO_2[/tex].

On the other hand, assume that [tex]\rm HCl[/tex] is the limiting reactant.

Convert the volume of [tex]\rm HCl[/tex] to [tex]\rm dm^{3}[/tex] (so as to match the unit of concentration.)

[tex]\begin{aligned}&V(\mathrm{HCl})\\ &= 50\; \rm cm^{3} \\ &= 50\; \rm cm^{3} \times \frac{1\; \rm dm^{3}}{10^{3}\; \rm cm^{3}} \\ &= 5.00\times 10^{-2}\; \rm dm^{3} \end{aligned}[/tex].

Calculate the number of moles of [tex]\rm HCl[/tex] molecules in that [tex]5.00\times 10^{-2}\; \rm dm^{3}[/tex] of this [tex]\rm 0.05\; \rm mol \cdot dm^{-3}[/tex]

[tex]\begin{aligned}& n(\mathrm{HCl}) \\ &= c(\mathrm{HCl}) \cdot V(\mathrm{HCl}) \\ &= 0.05\; \rm mol \cdot dm^{-3}\\ &\quad\quad \times 5.00\times 10^{-2}\;\rm dm^{3} \\ &= 2.50 \times 10^{-3}\; \rm mol\end{aligned}[/tex].

Notice that in the balanced chemical reaction, the ratio between the coefficient of [tex]\rm HCl[/tex] and that of [tex]\rm CO_2[/tex] is [tex]\displaystyle \frac{n(\mathrm{CO_2})}{n(\mathrm{HCl})} = \frac{1}{2}[/tex].

In other words, each mole of [tex]\rm HCl[/tex] molecules consumed would produce only [tex]0.5\;\rm mol[/tex] of [tex]\rm CO_2[/tex] molecules.

Therefore, if [tex]\rm HCl[/tex] is the limiting reactant, that [tex]2.50 \times 10^{-3}\; \rm mol[/tex] of [tex]\rm HCl\![/tex] molecules would produce only one-half as many (that is, [tex]1.25\times 10^{-3}\; \rm mol[/tex]) of [tex]\rm CO_2[/tex] molecules.

If [tex]\rm CaCO_3[/tex] is the limiting reactant, [tex]\rm 1.00\times 10^{-3}\; \rm mol[/tex] of [tex]\rm CO_2[/tex] molecules would be produced. However, if [tex]\rm HCl[/tex] is the limiting reactant, [tex]1.25\times 10^{-3}\; \rm mol[/tex] of [tex]\rm CO_2\![/tex] molecules would be produced.

In reality, no more than [tex]\rm 1.00\times 10^{-3}\; \rm mol[/tex] of [tex]\rm CO_2[/tex] molecules would be produced. The reason is that all [tex]\rm CaCO_3[/tex] would have been consumed before [tex]\rm HCl[/tex] was.

After finding the limiting reactant, approximate the volume of the [tex]\rm CO_2\![/tex] produced.

Assume that this reaction took place under standard temperature and pressure (STP.) Under STP, the volume of one mole of ideal gas molecules would be approximately [tex]22.4\; \rm L[/tex].

If [tex]\rm CO_2[/tex] behaves like an ideal gas, the volume of that [tex]\rm 1.00\times 10^{-3}\; \rm mol[/tex] of [tex]\rm CO_2\![/tex] molecules would be approximately [tex]\rm 1.00\times 10^{-3}\; \rm mol \times 22.4\; \rm L = 0.224\; \rm L[/tex].

Which of the following aqueous solutions
would conduct electricity?
Electroyte and Vonvlectrolyte Solution​

Answers

Answer:

H2CO

Explanation:

Which two things are produced when a plant breaks down sugar to release energy

Answers

Answer:

Glucose is combined with oxygen and releases usable energy, carbon dioxide, and water. Cells can use that extra energy to power their functions. The energy isn't just floating around. It's stored in an excitable compound called ATP (adenosine triphosphate).

Explanation:

Answer: ATP(adenosine triphosohate) is released with water and carbon dioxide as byproducts.

Explanation: Remember that water, CO2,and ATP are the products of cellular respiration.

how much is a dogggggggggggggggggg

Answers

Answer:

it is 7

Explanation:

dogs are 7 HOPE THIS HELPED kidding i don get the question

Explanation:

DON"T EAT MY DOG OR I"LL EAT YOU

You better watch outYou better not cryYou better not pout

CAN SOMEONE PLEASE SEND ME A FILE FOR THE PROJECT ​

Answers

Answer:

ca you attach these two pdf ?? or provide the link to this document

One sugar produced by photosynthesis is called

Answers

glucose is produced using sunlight or the process photosynthesis

mark me brainliest
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