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).
I believe that the answer is p+7
You're looking for the answers to both X and Y, correct?<span />
Question:
2x + y = 3, x - 2y = –1.
If equation one is multiplied by 2 and then the equations are added, the result is _____.
(A) 3x = 2
(B) 3x = 5
(C) 5x = 5
Answer:
Option C:
5x = 5
Solution:
Given equations are
2x + y = 3 – – – – (1)
x – 2y = –1 – – – – (2)
Let us first multiply equation (1) by 2, we get
(1) × 2 ⇒ 4x + 2y = 6 – – – – (3)
Now, add equation (3) to equation (2).
⇒ x – 2y + 4x + 2y = –1 + 6
Combine like terms together.
⇒ x + 4x – 2y + 2y = –1 + 6
⇒ 5x = 5
So, if equation one is multiplied by 2 and then the equations are added, the result is 5x = 5.
