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).
Yup it has to be a greater divedend if not answer would be completly wrong
Answer:
- (4x -4)° +x° +(6x-3)° = 180°
- J = 99°
- K = 64°
- L = 17°
Step-by-step explanation:
The relation that helps you write an equation for x is, "the sum of angles in a triangle is 180°."
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<h3>equation</h3>
(4x -4)° +x° +(6x -3)° = 180° . . . . . sum of angles in this triangle
<h3>solution for x</h3>
11x -7 = 180 . . . . . . . divide by °, collect terms
11x = 187 . . . . . . . . add 7
x = 17 . . . . . . . . . divide by 11
<h3>angle values</h3>
m∠J = (6x -3)° = (6(17) -3)° = 99°
m∠K = (4x -4)° = (4(17) -4)° = 64°
m∠L = x° = 17°
45 degrees for x.
Do 180-160 = 20 (Since 180 is a straight line)
The 115, x, and 20 form another straight line, so take 180-20-115. You get 45.
