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yan [13]
2 years ago
9

Can you please help me​

Physics
1 answer:
g100num [7]2 years ago
7 0

Answer: Hello Miko here to help!

Explanation: The answer is c!

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The radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing when the diameter is 40 mm?
marin [14]

Using <span>r </span> to represent the radius and <span>t </span> for time, you can write the first rate as:

<span><span><span><span>dr</span><span>dt</span></span>=4<span>mms</span></span> </span>

or

<span><span>r=r<span>(t)</span>=4t</span> </span>

The formula for a solid sphere's volume is:

<span><span>V=V<span>(r)</span>=<span>43</span>π<span>r3</span></span> </span>

When you take the derivative of both sides with respect to time...

<span><span><span><span>dV</span><span>dt</span></span>=<span>43</span>π<span>(3<span>r2</span>)</span><span>(<span><span>dr</span><span>dt</span></span>)</span></span> </span>

...remember the Chain Rule for implicit differentiation. The general format for this is:

<span><span><span><span><span>dV<span>(r)</span></span><span>dt</span></span>=<span><span>dV<span>(r)</span></span><span>dr<span>(t)</span></span></span>⋅<span><span>dr<span>(t)</span></span><span>dt</span></span></span> </span>with <span><span>V=V<span>(r)</span></span> </span> and <span><span>r=r<span>(t)</span></span> </span>.</span>

So, when you take the derivative of the volume, it is with respect to its variable <span>r </span> <span><span>(<span><span>dV<span>(r)</span></span><span>dr<span>(t)</span></span></span>)</span> </span>, but we want to do it with respect to <span>t </span> <span><span>(<span><span>dV<span>(r)</span></span><span>dt</span></span>)</span> </span>. Since <span><span>r=r<span>(t)</span></span> </span> and <span><span>r<span>(t)</span></span> </span> is implicitly a function of <span>t </span>, to make the equality work, you have to multiply by the derivative of the function <span><span>r<span>(t)</span></span> </span> with respect to <span>t </span> <span><span>(<span><span>dr<span>(t)</span></span><span>dt</span></span>)</span> </span>as well. That way, you're taking a derivative along a chain of functions, so to speak (<span><span>V→r→t</span> </span>).

Now what you can do is simply plug in what <span>r </span> is (note you were given diameter) and what <span><span><span>dr</span><span>dt</span></span> </span> is, because <span><span><span>dV</span><span>dt</span></span> </span> describes the rate of change of the volume over time, of a sphere.

<span><span><span><span><span>dV</span><span>dt</span></span>=<span>43</span>π<span>(3<span><span>(20mm)</span>2</span>)</span><span>(4<span>mms</span>)</span></span> </span><span><span>=6400π<span><span>mm3</span>s</span></span> </span></span>

Since time just increases, and the radius increases as a function of time, and the volume increases as a function of a constant times the radius cubed, the volume increases faster than the radius increases, so we can't just say the two rates are the same.

7 0
3 years ago
Acid rain is caused by human activity. Please select the best answer from the choices provided T F
olasank [31]

It is actually caused by the environment, so its false. :)

5 0
3 years ago
If toner particles in a laser printer have a negative charge, then what charge do you think the surface of the paper in the prin
Elina [12.6K]

Answer:

Explanation:

As it moves along, the paper is given a strong negative electrical charge by another corona wire. When the paper moves near the drum, its negative charge attracts the positively charged toner particles away from the drum.

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2 years ago
A patient arrives at an emergency room complaining of pain in her ankle. The nurse examines the patient’s ankle, looking for ski
Bond [772]

Answer:

Superficial anatomy.

Explanation:

Superficial anatomy can be defined as the physical examination of the external parts of a living organism such as ankle, nose, skin, knee, toes, fingers, cornea etc.

Hence, superficial anatomy is also popularly referred to as surface anatomy.

In this scenario, a patient arrives at an emergency room complaining of pain in her ankle. The nurse examines the patient’s ankle, looking for skin discoloration or swelling. The nurse is relying mostly on his knowledge of superficial anatomy by studying or examining the patient's ankle for any sign of decoration or swelling on the skin.

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An electron (m= 9.11 x 10 ^-31 kg) moves in a circle whose radius is 2.00 x 10^-2 m. If the force acting on the electron is 4.60
Rina8888 [55]
Oh wow!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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