A cat weighs 8.5 pounds on Earth. how much would this cat weigh on Neptune?

A gasoline tank has the shape of an inverted right circular cone with base radius 4 meters and height 5 meters. Gasoline is bein

RSB [31]

Answer:

h'=0.25m/s

Explanation:

In order to solve this problem, we need to start by drawing a diagram of the given situation. (See attached image).

So, the problem talks about an inverted circular cone with a given height and radius. The problem also tells us that water is being pumped into the tank at a rate of $8m^{3}/s$ . As you may see, the problem is talking about a rate of volume over time. So we need to relate the volume, with the height of the cone with its radius. This relation is found on the volume of a cone formula:

$V_{cone}=\frac{1}{3} \pi r^{2}h$

notie the volume formula has two unknowns or variables, so we need to relate the radius with the height with an equation we can use to rewrite our volume formula in terms of either the radius or the height. Since in this case the problem wants us to find the rate of change over time of the height of the gasoline tank, we will need to rewrite our formula in terms of the height h.

If we take a look at a cross section of the cone, we can see that we can use similar triangles to find the equation we are looking for. When using similar triangles we get:

$\frac {r}{h}=\frac{4}{5}$

When solving for r, we get:

$r=\frac{4}{5}h$

so we can substitute this into our volume of a cone formula:

$V_{cone}=\frac{1}{3} \pi (\frac{4}{5}h)^{2}h$

which simplifies to:

$V_{cone}=\frac{1}{3} \pi (\frac{16}{25}h^{2})h$

$V_{cone}=\frac{16}{75} \pi h^{3}$

So now we can proceed and find the partial derivative over time of each of the sides of the equation, so we get:

$\frac{dV}{dt}= \frac{16}{75} \pi (3)h^{2} \frac{dh}{dt}$

Which simplifies to:

$\frac{dV}{dt}= \frac{16}{25} \pi h^{2} \frac{dh}{dt}$

So now I can solve the equation for dh/dt (the rate of height over time, the velocity at which height is increasing)

So we get:

$\frac{dh}{dt}= \frac{(dV/dt)(25)}{16 \pi h^{2}}$

Now we can substitute the provided values into our equation. So we get:

$\frac{dh}{dt}= \frac{(8m^{3}/s)(25)}{16 \pi (4m)^{2}}$

so:

$\frac{dh}{dt}=0.25m/s$

3 0

3 years ago

Connie teaches her children to call adults "sir" and "ma'am" and to say "please" and "thank you." These rituals are known as

Nat2105 [25]

Manners. they are known as manners.

5 0

3 years ago

A parallel-plate vacuum capacitor has 7.72 J of energy stored in it. The separation between the plates is 3.30 mm. If the separa

maxonik [38]

Answer

3.340J

Explanation;

Using the relation. Energy stored in capacitor = U = 7.72 J

U =(1/2)CV^2

C =(eo)A/d

C*d=(eo)A=constant

C2d2=C1d1

C2=C1d1/d2

The separation between the plates is 3.30mm . The separation is decreased to 1.45 mm.

Initial separation between the plates =d1= 3.30mm .

Final separation = d2 = 1.45 mm

(A) if the capacitor was disconnected from the potential source before the separation of the plates was changed, charge 'q' remains same

Energy=U =(1/2)q^2/C

U2C2 = U1C1

U2 =U1C1 /C2

U2 =U1d2/d1

Final energy = Uf = initial energy *d2/d1

Final energy = Uf =7.72*1.45/3.30

(A) Final energy = Uf = 3.340J

4 0

3 years ago

What is the fraction of the hydrogen atom's mass (11h) that is in the nucleus? the mass of proton is 1.007276 u, and the mass of

Alex_Xolod [135]

The mass fraction of the hydrogen atom is 0.9995 u.

<h3>Calculation:</h3>

We know that mass fraction can be determines as,

Mass fraction = Mass of proton/mass of H atom

Given,

Mass of proton = 1.007276 u

Mass of H atom = 1.007825 u

Put the values in the formula,

Mass fraction = Mass of proton/mass of H atom

Mass fraction = 1.007276/1.007825

= 0.9995 u

Hence, the mass fraction of the hydrogen atom is 0.9995 u.

Learn more about mass fraction here:

brainly.com/question/9639161

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3 0

2 years ago

Which of acceleration, age, speed, temperature, and velocity are vector quantities?.

ollegr [7]

Velocity and acceleration are vector quantities whereas speed, temperature and age are not.

<h3>What is a vector quantity?</h3>

Vector is a quantity that has both magnitude and direction and is represented by an arrow whose direction is same as that of the quantity and length is proportional to the quantity's magnitude.

Vector has magnitude and direction but it does not have position. Velocity and acceleration both are vector quantities as they have magnitude and direction.

If the speed of an object remains same but direction changes then the object is accelerating. It is important to remember that acceleration and velocity aren't always in the same direction.

To know more about vector quantity, refer

brainly.com/question/626479

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4 0

1 year ago