If we set the equation equal to 0, we can factor it to find its roots:
x² + 4x + 4 = 0
(x + 2)(x + 2) = 0
x = -2
This graph has one root, a double root, at -2. This means that a single point, which must be the vertex of the parabola, touches the x-axis at (-2, 0)
Answer:-7x+2y=2
Step-by-step explanation:
(-2x+y=8)-(5x-y=6)
(-2x+y=8)> this side change since it’s negative
(-2x+y=8) - (-5x+y=-6)
-7x+2y=2
I answered a similar question for someone else. The absolute value of a complex number is called the modulus. This represents the DISTANCE to the origin from the point on the imaginary + real plane.
the real horizontal distance is 5 and the imaginary vertical distance is in this case 4 (from -4i) the distance is 4. So to figure out this just use the Pythagorean theorem.
5^2 + (4)^2 = c^2
25 +16 = c^2
c^2 = 41c = 6.4 So option D.
Answer:
option (D) is the right answer
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).
