Is a sugar crystal a mineral? Explain

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

I NEED HELP PLEASE, THANKS! :) Why does the pattern of colors repeat in a thin soap film?

Nadusha1986 [10]

Answer:

When white light shines on the bubble, it acts as a prism. While some of the white light bounces back off, some of them pass through the prism forming fringes of colors. But then, they too bounce off the inner part of the film. So one set of light rays shine into a soap bubble, but two sets of rays come back out again. When they emerge, the waves that bounce off the inner film have traveled a tiny bit further than the waves that bounced off the outer film. So, we have two sets of light waves. After that, the waves starts merging (Just like the ripples in the pond) . Some add together while some cancel out. That is why we see the pattern of colors repeating in the thin film soap.

7 0

3 years ago

Consider this situation: A rope is used to lift an actor upward off the stage. Of the forces listed, identify which act upon the

Katarina [22]

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6 0

4 years ago

Read 2 more answers

*photo attached* The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.67 m and 1.01 m, respectivel

stiks02 [169]

(a) The speeds of the tips of both rotors; main rotor <u>178.3 m/s</u> and tail rotor <u>218.4 m/s</u>.

(b) The speed of the main rotor is <u>0.52</u> speed of sound, and the speed of the tail rotor is <u>0.64</u> speed of sound.

<h3>Linear speed of main motor and tail rotor</h3>

v = ωr

where;

ω is the angular speed (rad/s)
r is radius (m)

v(main rotor) = (444 rev/min x 2π rad x 1 min/60s) x (0.5 x 7.67 m)

v(main rotor) = 178.3 m/s

v(tail rotor) = (4,130 rev/min x 2π rad x 1 min/60s) x (0.5 x 1.01 m)

v(tail rotor) = 218.4 m/s

<h3>Speed of the rotors with respect to speed of sound</h3>

% speed (main motor) = 178.3/343 = 0.52 = 52 %

% speed (tail motor) = 218.4/343 = 0.64 = 64 %

Thus, the speed of the main rotor is 0.52 speed of sound, and the speed of the tail rotor is 0.64 speed of sound.

Learn more about linear speed here: brainly.com/question/15154527

#SPJ1

5 0

2 years ago

The final stages of a star's life depend on its mas. true or false?

Diano4ka-milaya [45]

Answer:

TRUE

Explanation:

Low mass stars last lots longer.

5 0

4 years ago