Answer:
Angle between the two vectors is 135°
u•v = -12
Step-by-step explanation:
Given two vectors u = (4,0) and v = (-3,-3).
To find the angle between the two vectors we will use the formula for calculating the angle between two vectors as shown;
u•v = |u||v|cos theta
cos theta = u•v/|u||v|
theta = arccos (u•v/|u||v|)
u•v = (4,0)•(-3,-3)
u•v = 4(-3)+0(-3)
u•v = -12
For |u| and |v|
|u| = √4²+0²
|u| = √16 = 4
|v| = √(-3)²+(-3)²
|v| = √9+9
|v| = √18
|v| = 3√2
|u||v| = 4×3√2 = 12√2
theta = arccos(-12/12√2)
theta = arccos(- 1/√2)
theta = -45°
Since cos is negative in the second quadrant, theta = 180-45°
theta = 135°
To get u•v using the formula u•v = |u||v|cos theta
Given |u||v| = 12√2 and theta = 135°
u•v = 12√2cos 135°
u•v = 12√2× -1/√2
u•v = -12√2/√2
u•v = -12
For the diagram of the vectors, find it in the attachment below.
Answer:
...
Step-by-step explanation:
1. B
angle A is 63 since 27+90= 117, 180-117= 63 (since a straight line is 180°)
2. 7x + 10 = 150 (since they are vertical angles)
7x = 140
x = 20
now plug in 7(20) +10
140+10=150
Answer:
x = 1.23529
Step-by-step explanation:
Step 1: Write equation
3/17 = x/7
Step 2: Solve for <em>x</em>
- Cross multiply: 21 = 17x
- Divide both sides by 17: 21/17 = x
- Rewrite: x = 21/17
- Convert to decimal: x = 1.23529
Answer:
yes
Step-by-step explanation:
To figure out if a point works with it's equation, you should replace the x and y with the point you got
-8 > 3(-5)+6
-8 > -15 +6
-8 > -9
Since -8 is bigger than -9, point (-5,-8) is true to the equation.
and as seen in the graph I have attached, the point does infact reside in the shaded in area. If you haven't learned how to graph this type of equation, you may disregard the graph :)
If you have any questions at all, don't be afraid to ask :)
