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vladimir1956 [14]
3 years ago
14

QUESTION 1

Mathematics
1 answer:
Kitty [74]3 years ago
3 0

It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.

Let <em>θ</em> be the angle between the force vector <em>F</em> and the displacement vector <em>r</em>. The work <em>W</em> done by <em>F</em> in the direction of <em>r</em> is

<em>W</em> = <em>F</em> • <em>r</em> cos(<em>θ</em>)

The cosine of the angle between the vectors can be obtained from the dot product identity,

<em>a</em> • <em>b</em> = ||<em>a</em>|| ||<em>b</em>|| cos(<em>θ</em>)   ==>   cos(<em>θ</em>) = (<em>a</em> • <em>b</em>) / (||<em>a</em>|| ||<em>b</em>||)

so that

<em>W</em> = (<em>F</em> • <em>r</em>)² / (||<em>F</em>|| ||<em>r</em>||)

For instance, if <em>F</em> = 3<em>i</em> + <em>j</em> + <em>k</em> and <em>r</em> = 7<em>i</em> - 7<em>j</em> - <em>k</em> (which is my closest guess to the given vectors' components), then the work done by <em>F</em> along <em>r</em> is

<em>W</em> = ((3<em>i</em> + <em>j</em> + <em>k</em>) • (7<em>i</em> - 7<em>j</em> - <em>k</em>))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))

==>   <em>W</em> ≈ 5.12 J

(assuming <em>F</em> and <em>r</em> are measured in Newtons (N) and meters (m), respectively).

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Match each number with its estimated power of 10
zheka24 [161]

The matching numbers are:

1) 0.0000225 = 2 x 10⁻⁵

2) 219,000 = 2 x 10⁵

3) 3,40,000 = 3 x 10⁶

4) 297,000 = 3 x 10⁵

5) 0.0000034 = 3 x 10⁻⁶

What are Exponents?

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

We have to match the following terms :

1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵

2) 219,000 =  2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵

3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶

4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵

5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶

Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶

To learn more about Exponents click on the link
brainly.com/question/11975096
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First add all the numbers together:
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Next, divide 175 (the total) by 5 (because there are 5 numbers)

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Answer:

The answer is r < or equal to 15.5.

Step-by-step explanation:

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the basketball court in the park is rectangle two of the sides are 84 feet long and the other two sides are 50 ft long what is t
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Hello!

So, we know that the length of the rectangular basketball court is 84 ft, and the width is 50 ft.

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This means that we need to multiply the length by two and the width by two as well.

Substitute:

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