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:
After travelling 360 miles, 15 litres of petrol will be left.
Step-by-step explanation:
If a car can travel 480 miles with a full tank of 60 liters of petrol, it could be said that each liter of petrol allows to travel 8 miles (480/60 = 8). Therefore, since the driver has driven his car for 360 miles, his tank has spent 45 liters of petrol (360/8 = 45). In conclusion, given that the tank has a capacity of 60 liters and that it was full at the time of departure, having spent 45 liters, 15 liters remain in the tank.
Answer:
X ≥ 59.50
Step-by-step explanation:
So to begin, your equation would need to solve for x. X has to be greater than or equal to the minimum amount each player needs to raise for the uniforms. To find how much money they need to raise subtract $224.36 from $759.84 to get $535.48. Divided $535.48 by 9 players to see the minimum amount they each need to contribute. You should get $59.50 roughly. So each player would need to raise greater than or equal to $59.50.
Hope this helps!
Answer: aA 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years = (0.163,0.189)
Step-by-step explanation:
Let p = population proportion of adults in the U.S. who have donated blood in the past two years.
Given: A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years.
Sample size: n= 2322
Sample proportion 
Critical z-value for 90% confidence level : z*=1.645
The confidence interval for population proportion:
A 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years:
Hence,
Answer:
113°
Step-by-step explanation:
When parallel, opposite sides are equal
