Answer: x = -30
Steps: 19 + x/2 = 4
Subtract 19 from both sides: 19 + x/2 - 19 = 4 - 19
Simplify: x/2 = 15
Multiply both sides by two: x/2 (2) = -15 (2)
Simplify: x = -30
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).
Write the folowing in standard form and you well get
#1 is 5b
#2 is b−8x+<span>4</span>
First find your slope! by doing
y2-y1/x2-x1
in this case it would be
2-(-3)/-1-(-6)
It would give you 5/5 which would reduce to 1 meaning your slope equals 1
with your slope now you should use the point slope formula y-y1=m(x-x1)
i’m going to use the point (-1,2) so the equation would be
y-2=1(x-(-1))
simplifying that you would get
y-2=1x+1
then put it in y=mx+b form and get
y=x+3
