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agasfer [191]
3 years ago
12

The formula to find the period of orbit of a satellite around a planet is (T^2) = (4pi^2/ gm) r3 where r is the orbit’s mean rad

ius, M is the mass of the planet, and G is the universal gravitational constant. If you are given all the values except r, how do you rewrite the formula to solve for r?

Mathematics
1 answer:
Inga [223]3 years ago
7 0
See the attached graphic to see this solved for "r".
You should be very careful about stating the units for each of those variables.
time in seconds
radius in meters
mass in kilograms
G = 6.674 x 10^-11 m^3 / (kilograms * seconds²)
Also, it would be worth your while to go to this web page http://www.1728.org/kepler3a.htm
It has a calculator and other information about Kepler's Third Law.


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Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,
kompoz [17]

If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

V_{flask}=V_{sphere}+V_{cylinder}.

Use following formulas to determine volumes of sphere and cylinder:

V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

  • V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;
  • V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;
  • V_{flask}=V_{sphere}+V_{cylinder}\approx 47.71+2.36=50.07.

Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.

Then

\dfrac{V_{\text{new flask}}}{V_{\text{flask}}} =\dfrac{8}{1}=8.

Answer 2: correct choice is D.


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4 years ago
Can the sides of a triangle have lengths 1, 3, and 10?
Troyanec [42]

Answer:

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3 0
3 years ago
Please help me I think the answer is 12 cm .
-Dominant- [34]

You can find the value of the hypotenuse if you apply the Pythagorean Theorem, which is show below:


 h²=a²+ b² ⇒ h=√(a² + b²)


 h: hypotenuse (the opposite side of the right angle and the longest side of the triangle).

 a and b: legs (the sides that form the right angle).


 Then, you have:


 h²=a² + b²

 h²=12²+12²

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Short-term investments characteristics  are:

  • More affected by rapid market changes.
  • Taxed at a higher rate.
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  • Incurs more annual brokerage fees.

<h3>What are Long-Term Investments?</h3>

Others are:

Long-term investments characteristics  are:

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Long-term investments are known to be a kind of assets that people or a firm intends to keep for a long period of time that is usually more than three years.

Note that Long-term investors usually take on a high degree of risk when one is said to be after higher returns.

Learn more about investments  from

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