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.
Hi there! To measure the angles, it’s best to have a protractor at hand. In terms of angles, complementary angles equal 90 degrees and supplementary angles equal 180 degrees. I could do this for you, but the angles aren’t always drawn to scale and it’s best to measure the angles out first before you do the other steps.
Given: Given that a citizen have 97 silver coins.
To find : Here we need to find that how many bronze coins would it take to equal this amount.
Solution: We know, 1 silver coin=10 bronze coin
So, 97 silver coin=10×97 bronze coin
=970 bronze coin
Therefore, 970 bronze coins would it take to equal this amount.
Answer:
The radius of the cone is 
Step-by-step explanation:
we know that
The volume of a cone is equal to
In this problem we have
substitute in the formula and solve for r
Simplify
square root both sides
For 12 Pounds (= 12 * 16 = 192 Ounce), it costs = 18.75
So, for 1 Ounce, it would be: 18.75 / 192 = 0.097
In short, Your Answer would be: $0.097
Hope this helps!
