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17 days ago

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Where is the center of mass of the Earth-Moon system? The radius of the Earth is 6378 km and the radius of the Moon is 1737 km.

Select one of the answers below: Choose the correct description of the location of the center of mass of the Earth-Moon system. Choose the correct description of the location of the center of mass of the Earth-Moon system. The center of mass is exactly in the center between the Earth and the Moon. The center of mass is nearer to the Moon than the Earth, but outside the radius of the Moon. The center of mass is nearer to the Earth than the Moon, but outside the radius of the Earth.

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An advertiser who calls a basement apartment a “garden apartment” is using the rhetorical device called

serg [3582]

I would choose B or D, based on the location. If it’s situated in South Kensington, London, then D might be appropriate. Conversely, if it’s in an underprivileged area, I'd opt for B.

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2 months ago

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

inna [3103]

Answer:

$\int\limits^2_0 {} \, \int\limits^{5\pi}_0 {F(S(u,v)).N} \,dvdu$ ≈ 3077.34

Explanation:

To calculate the flux of F (vector field) across surface S, where

F(x,y,z) = y i − x j + $z^{2}$ k

and S(u,v) = u cos v i + u sin v j + v k, 0 ≤ u ≤ 2, 0 ≤ v ≤ 5π

We will evaluate the following integral:

$\int\limits^2_0 {} \, \int\limits^{5\pi}_0 {F(S(u,v)).N} \,dvdu$

Substituting for the surface

x = u cos v

y = u sin v

z = v

Then

F(S(u,v)) = u sin v i - u cos v j + $v^{2}$ k

The normal vector N is computed as

$N = S_{u}XS_{v}$

Where:

$S_{u} = =$

$S_{v} = =$

N = < cos v, sin v, 0 > X <- u sin v, u cos v, 2v

N = < 2v sin v, -2v cos v, u >

F(S(u,v)).N = < u sin v, -u cos v, $v^{2}$ >. < 2v sin v, -2v cos v, u >

F(S(u,v)).N = 2uv + u $v^{2}$

Thus

$\int\limits^2_0 {} \, \int\limits^{5\pi}_0 {2uv}+u v^{2}\,dvdu$ ≈ 3077.34

8 0

2 months ago

The Lamborghini Huracan has an initial acceleration of 0.75g. Its mass, with a driver, is 1510 kg.

Maru [3345]

Answer:

11109.825 N

Explanation:

Provided Information:

mass = m = 1510 kg

initial acceleration (a) = 0.75g (where g = 9.81 m/s²)

Using the formula F=ma

= (1510)*(0.75*9.81)

= 11109.825 N

4 0

3 months ago

What mass needs to be attached to a spring with a force constant of 7N/m in order to make a simple harmonic oscillator oscillate

Sav [3153]

Answer:

The mass will be 4.437 kg

Explanation:

The force constant k is given as 7 N/m

The time period of oscillation T is 5 sec

Thus, angular frequency $\omega =\frac{2\pi }{T}=\frac{2\times 3.14}{5}=1.256rad/sec$

It is known that angular frequency is computed via

$\omega =\sqrt{\frac{k}{m}}$

$1.256 =\sqrt{\frac{7}{m}}$

Squaring both sides gives us

$1.577 =\frac{7}{m}$

The mass equals 4.437 kg

6 0

2 months ago