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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 diagram shows a right-angled triangle.<br> a<br> 12 cm<br> 24 cm<br> Find the size of angle x.
Vlada [557]

Given that , Length of Base and Hypotenuse is 12 cm and 24 cm , respectively .

Need To Find : The measure of Angle x .

<em>As </em><em>We </em><em>know </em><em>that </em>,

Cos ∅ = Base / Hypotenuse

ㅤㅤ <u>By </u><u>Substituting </u><u>known </u><u>Values </u><u>:</u>

ㅤ⤀Cos x = 12/24

ㅤ⤀Cos x = ½

ㅤ⤀Cos 60⁰ = ½

Therefore,

  • Value of Angle x is 60⁰
6 0
2 years ago
Thomas rents a car for his vaccation the milliage included with the 54 miles forer every mile he drives over 54 miles he needs t
Sauron [17]

Answer:

$27

Step-by-step explanation:

Thomas rents a car for his vacation. The mileage include with the rental is 54 miles. For every mile he drives over 54 miles, he needs to pay $1 4/5. If he drives 69 miles, how much extra does he need to pay?

Total mileage included with the rental = 54 miles

Additional cost per mile after 54 miles = $1 4/5

Total miles Thomas drives = 69 miles

Extra miles Thomas drives = 69 miles - 54 miles

= 15 miles

how much extra does he need to pay?

Extra cost Thomas needs to pay = Additional cost per mile after 54 miles * Extra miles Thomas drives

= $1 4/5 * 15 miles

= 9/5 * 15

= (9 * 15) / 5

= 135/5

= 27

Extra cost Thomas needs to pay = $27

4 0
2 years ago
If the area of a parallelogram is found by multiplying the base times the height, A=bh.
Ostrovityanka [42]

Answer:

A: 96

Step-by-step explanation:

Multiply 12 by 8.

5 0
3 years ago
A ladder reaches the top of a 20 foot building. the ladder is 4.5 feet away from the building. how long is the ladder?
KATRIN_1 [288]

Answer:

C

Step-by-step explanation:

do that with pithagoras:

20² + 4,5² = x²

400 + 20,25 = x²

420,25 = x²

x = \sqrt{420,25}

x ~ 20,5

Letter C: 20,5 feet

4 0
3 years ago
Write an equation of the line with the given slope and y-intercept,(4,3) and (0,1)
PSYCHO15rus [73]

Answer:

y=1/2x+1

Step-by-step explanation:

First use slope formula.

\frac{y2-y1}{x2-x1}

Plug in the information needed.

\frac{1-3}{0-4}=\frac{-2}{-4}=\frac{1}{2}

The slope is \frac{1}{2}.

Now, use point-slope formula.

y-y1=m(x-x1)

Plug in the information needed.

y-3=1/2(x-4)

y-3=1/2x-2

y=1/2x+1

The equation of the line in slope-intercept form is y=1/2x+1.

Hope this helps!

If not, I am sorry.

5 0
2 years ago
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