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).
Answer and Step-by-step explanation:
If my calculations are correct,
A. 17b = w
B. 867 = w
C. 3 bottles for 51 fluid ounces of water
For B and C, just plug in the values.
For A, it was 17 ounces for every bottle (b), so that's why it is multiplied together. This is then equal to w, the total volume of water in fluid ounces.
Answer:
0.3
Step-by-step explanation:
The margin of error is calculated as ...
(standard deviation)/√(sample size) × (z*-score)
where the z*-score is chosen based on the desired confidence level.
Here, you have ...
- standard deviation = 2.7
- √(sample size) = √225 = 15
- z*-score for 90% confidence level = 1.645
Putting these values in the above expression for margin of error gives ...
2.7/15·1.645 = 0.2961 ≈ 0.3
30: x
60: xsqrt3
90: 2x (hypotenuse)
The answer is x >_ -2 and x >_ 7.
