Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that
<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>
<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>
where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.
Then the sum is
<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>
and its magnitude is
||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)
… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))
… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))
… = √(16 + 16 cos(135° - 45°) + 4)
… = √(20 + 16 cos(90°))
… = √20 = 2√5
Answer:
y = (-1)x
Step-by-step explanation:
What you are to do here is to "rewrite -y - x = 0 in the slope-intercept form y = mx + b."
Start by solving -y - x = 0 for y: -y = x or y = -x.
Rewrite this by inserting the coefficient 1 and representing b by 0:
y = (-1)x + 0
which is equivalent to y = (-1)x
Answer:
The expression for the other number is (n-1)
Step-by-step explanation:
we know that
The difference between two consecutive number is equal to 1
Let
x ----> the smaller of two consecutive number
n ----> the larger of two consecutive numbers
we have that
Solve for x
therefore
The expression for the other number is (n-1)
Answer:
X= -19
Step-by-step explanation:
If you add $300 and $600 and you spent 1,300. you would have 2,200 dollars left in all.
