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.
To solve for this, we need to use Pythagorean Theorum.
Pythagorean Theorum is when we add the squares of the legs (A & B) to solve for the hypotenuse (C) or the side that's across from the 90 degree angle.
The formula for Pythagorean Theorum is A^2 + B^2 = C^2.
We have our two leg lengths, 15 and 36 (A & B).
Square 15 and 36.
15^2 = 225
36^2 = 1,296
Now that we have our side lengths, let's add them up.
225 + 1,296 = 1,521.
Now, to solve for C, we need to square root our sum.
The square root of 1,521 is 39.
Your hypotenuse is 39.
Your answer is C.) 39.
I hope this helps!
The EXPONENTIAL REGRESSION equation obtained by fitting the data is 
To obtain the exponential regression equation which models the data, we could use technology, we involves Inputting the data into an EXPONENTIAL REGRESSION CALCULATOR or EXCEL
Using an exponential regression calculator :
The regression equation obtained is :
The general function of an exponential regression function is : 
A = 58.031 = Initial value ; B = Decay factor
Hence, the EXPONENTIAL REGRESSION EQUATION obtained using technology is :
Learn more :
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