A brass lid screws tightly onto a glass jar at 20 degrees C. To help open the jar, it can be placed into a bath of hot water. Af

Let L be the length of the inclined plane. The work done by gravity on the block is calculated as the product of force and distance traveled, which amounts to mg sinθ x L, where m stands for the mass of the block and θ denotes the angle of inclination. This translates into the potential energy of the compressed spring represented by 1/2 k x² = mgL sin31, with k as the spring constant. Compression x measures 0.37. Solving this gives: 0.5 x 3400 x 0.37² = 33 x 9.8 x sin31 L yields L = 1.4 m, indicating the incline measures 1.4 meters.

Answer:

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Explanation:

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The volumes are 200cm3 and 0.0002m3

Answer:

≈ 3077.34

Explanation:

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

F(x,y,z) = y i − x j + 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:

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 + k

The normal vector N is computed as

Where:

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, >. < 2v sin v, -2v cos v, u >

F(S(u,v)).N = 2uv + u

Thus

≈ 3077.34