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Fofino [41]
3 years ago
9

A particle moves along line segments from the origin to the points (3, 0, 0), (3, 3, 1), (0, 3, 1), and back to the origin under

the influence of the force field F(x, y, z) = z2i + 3xyj + 3y2k. Find the work done.
Mathematics
1 answer:
Ierofanga [76]3 years ago
4 0

Answer:

[8i + 54j + 72k] joules per newton metre square.

Step-by-step explanation:

F(x,y,z) = z2i + 3xyj + 3y2k

F(3,0,0) = 0

F(3,3,1) = 1(2i) + 3(3)(3)j + 3(3)(2k)

= 2i + 27j + 18k

F(0,3,1) = 1(2i) + 3(0)(3)j + 3(3)(2k)

= 2i + 18k

The sum = [4i + 27j + 36k]

Since the particle moves back to the origin, we multiply the above Work Done by 2:

[8i + 54j + 72k]

And since work done is the product of Force and Distance, the S.I. unit is Joules/newton metre square

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The proportion of sophomores that do not own a car is equal to 0.93.

<h3>What is ratio?</h3>

Ratio is a mathematical expression that is used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

The proportion of sophomores that do not own a car is given by:

  • Number of sophomores that do not own a car = 398.
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Therefore, proportion = 398/427 = 0.93.

The proportion of all students who are seniors who own cars is given by:

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Therefore, proportion = 123/1192 = 0.10.

The proportion of non-car owners who are juniors is given by:

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Therefore, proportion = 339/976 = 0.35.

Read more on ratio here: brainly.com/question/13513438

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<u>Complete Question:</u>

At Central High School, there are 398 sophomores who do not own a car and 29 who do. There are 64 juniors who own a car and 339 who do not. There are 123 seniors who own a car, compared to 239 who do not. The above is a two-way table depicting this situation. Complete the following statements below by finding the ratio, then converting to a decimal. Round to the nearest hundredth.

The proportion of sophomores that do not own a car is?

The proportion of all students who are seniors who own cars is?

The proportion of non-car owners who are juniors is?

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