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zhenek [66]
3 years ago
9

Describe the geometric meaning of the following mappings in spherical coordinates.

Mathematics
1 answer:
bearhunter [10]3 years ago
8 0

Answer:

A. (iv)-There is a rotation by π around the x-axis.

B. (v)-There is a reflection across the xy plane.

C. None of the above, There is a rotation by π/2 about the x-axis with a radial expansion by a factor of 2.

Step-by-step explanation:

A. In spherical coordinates, for some point in R³, the angle θ is designed to be the angle between the x-axis and the projection of the line that goes from (0,0,0) to that point into the xy plane.

So, if you add π to the angle it only rotate 180 degrees or π units about the x-axis

B.  In spherical coordinates, for some point in R³, the angle ϕ is designed to be the angle between the z-axis and the diagonal from (0,0,0) to that point.

So, if you subtract π to the angle it would flip the diagonal in the negative part of z (assuming ϕ<π/2, otherwise, originally the diagonal would be in the negative part of z and it would flip to the positive part of z) and this could be interpreted as a reflection around the xy plane. Notice if ϕ=π/2, then π − ϕ=π/2 so everything stays the same for points that belong to xy plane (i.e that ϕ=π/2)

C.  In spherical coordinates, for some point in R³, ρ is designed to be the length of the diagonal from (0,0,0) to that point. So if we multiply ρ by 2, we are expanding the length of the diagonal.

But as we´ve seen before, adding something to θ means a rotation about x-axis by what we are adding (π/2)

Then the answer is that there is a rotation by π/2 about the x-axis with a radial expansion by a factor of 2.

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Step-by-step explanation:

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Answer: Cylinder is the correct answer

Hope this helps.

4 0
3 years ago
Which pair of angles are corresponding angles?
Effectus [21]

Corresponding angles are angles that are the same, and occupy the same relative position.

1 and 2: Incorrect - These are supplementary angles

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Hope this helps!! :)

7 0
3 years ago
ACCTUALLY HELP ME??!!!!!!! NEEDED FOR TOMORROW AND 50 POINTS! will award brainliest for first answer!!
drek231 [11]

Answer:

a:c = 35:24

a:c = 20:27

a:c = 35:22

a:c = 28:27

Step-by-step explanation:

a:b = 7:3

Using cross products

3a = 7b

Divide by 7

3a/7 = b

Now we want

8b = 5c

Substitute in 3a/7 for b

8 (3a/7) = 5c

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Multiply by 7

24/7a *7 = 5*7c

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Divide by c

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Divide by 24

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Using cross products

9a = 4b

Divide by 4

9a/4 = b

Now we want

3b = 5c

Substitute in 9a/4 for b

3 (9a/4) = 5c

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Multiply by 4

27/4a *4 = 5*4c

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Divide by c

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Divide by 27

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Using cross products

11b = 5c

Divide by 11

b = 5c/11

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2a = 7b

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2a = 7(5c/11)

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Multiply by 11

2a*11 = 35c

22a = 35c

Divide by c

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Divide by 22

a/c = 35/22

a:c = 35:22

b:c = 14:3

Using cross products

3b = 14c

Divide by 3

b = 14c/3

Now we want

9a = 2b

Substitute in 14c/3 for b

9a = 2(14c/3)

9a = 28c/3

Multiply by 3

9a*3 = 28c

27a = 28c

Divide by c

27 a/c = 28

Divide by 27

a/c = 28/27

a:c = 28:27

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SpyIntel [72]
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svetoff [14.1K]

Answer:

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Step-by-step explanation:

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