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Citrus2011 [14]
3 years ago
15

Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 5 cubic feet

per minute. If the pool has radius 6 feet and height 9 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 5 feet
Physics
1 answer:
Marina86 [1]3 years ago
7 0

Answer:

\frac{dH}{dt}=0.044\;\;feet\;per\;min

Explanation:

Given,

Radius R = 6 feet

Height H = 9 feet

Depth of the water = 5 feet

Volume of right circular cylinder,

V=\pi R^2 H\\

Differentiate with respect to the H

\frac{dV}{dH}=\pi R^2\\\frac{dV}{dH}=36\pi

Now,

\frac{dV}{dH}.\frac{dt}{dt} =36\pi\\\frac{dV}{dt}.\frac{dt}{dH}=36\pi\\  5.\frac{dt}{dH}=36\pi\\\frac{dH}{dt}=\frac{5}{36\pi}\\\frac{dH}{dt}=0.044\;\;feet\;per\;min

Hence, the rate of chage of height of water is 0.044 feet per min.

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Question 9
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Answer: it means object initially possessed equal number of positive and negative charges.

Explanation:

Object looks uncharged when it's in neutral state. That's positive charge equals negative charge.

The moment the transfer of charges take place, one gains electron while the other loses electron.

The gainer of electron becomes negatively charged while the looser of electron becomes positively charged.

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3 years ago
How do you solve this problem?
Katarina [22]

The particle has acceleration vector

\vec a=\left(-2.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)\,\vec\imath+\left(4.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)\,\vec\jmath

We're told that it starts off at the origin, so that its position vector at t=0 is

\vec r_0=\vec0

and that it has an initial velocity of 12 m/s in the positive x direction, or equivalently its initial velocity vector is

\vec v_0=\left(12\,\dfrac{\mathrm m}{\mathrm s}\right)\,\vec\imath

To find the velocity vector for the particle at time t, we integrate the acceleration vector:

\vec v=\vec v_0+\displaystyle\int_0^t\vec a\,\mathrm d\tau

\vec v=\left[12\,\dfrac{\mathrm m}{\mathrm s}+\displaystyle\int_0^t\left(-2.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)\,\mathrm d\tau\right]\,\vec\imath+\left[\displaystyle\int_0^t\left(4.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)\,\mathrm d\tau\right]\,\vec\jmath

\vec v=\left[12\,\dfrac{\mathrm m}{\mathrm s}+\left(-2.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t\right]\,\vec\imath+\left(4.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t\,\vec\jmath

Then we integrate this to find the position vector at time t:

\vec r=\vec r_0+\displaystyle\int_0^t\vec v\,\mathrm d\tau

\vec r=\left[\displaystyle\int_0^t\left(12\,\dfrac{\mathrm m}{\mathrm s}+\left(-2.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t\right)\,\mathrm d\tau\right]\,\vec\imath+\left[\displaystyle\int_0^t\left(4.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t\,\mathrm d\tau\right]\,\vec\jmath

\vec r=\left[\left(12\,\dfrac{\mathrm m}{\mathrm s}\right)t+\left(-1.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t^2\right]\,\vec\imath+\left(2.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t^2\,\vec\jmath

Solve for the time when the y coordinate is 18 m:

18\,\mathrm m=\left(2.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t^2\implies t=3.0\,\mathrm s

At this point, the x coordinate is

\left(12\,\dfrac{\mathrm m}{\mathrm s}\right)(3.0\,\mathrm s)+\left(-1.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)(3.0\,\mathrm s)^2=27\,\mathrm m

so the answer is C.

7 0
3 years ago
A cyclist maintains a constant velocity of
Feliz [49]
The answer is 509 m.

Let point B be 253 m from point A. Let point C be 64 s away from point B.
Let d1 be the displacements from point A to point B and d2 and be the displacements from point B to point C
Step 1. Calculate the displacement from the point B after 64 s.
Step 2. Calculate the displacement from the point A by summing up two distances (d1 and d2).

Step 1.
v = d2/t
v = 4 m/s
d2 = ?
t = 64s
____
4 = d2/64
d2 = 64 * 4 = 256 m


Step 2:
d = d1 + d2
d1 = 253 m
d2 = 256 m
d = 253 + 256 = 509m

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Alenkasestr [34]

Kinematics is the branch of physics and a subdivision of classical mechanics concerned with the geometrically possible motion of a body or system of bodies without consideration of the forces involved. :)

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12345 [234]

Explanation:

Since the equation is not given in this case, you can follow this explanation to balance it up.

A balanced chemical equation is one in which the law of conservation of matter is strictly obeyed.

According to the laws, we know that the total mass of the reacting substances must be equal to that of the product.

To do this, coefficients are usually assigned to chemical species.

In order to know the right coefficient one can use;

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learn more:

Balanced equation brainly.com/question/2612756

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