1. Find the angle between the vectors, approximate your answer to the nearest tenth. v= (-4, -3) w= (2, 6)
Answer: 145.3 degrees
17. One type of data that is non linear in nature is the exponential function. -False?
19. Exponential data follows the equation y= ab^x. True?
#16.
cosθ = v•w / |v||w| = -26 / 5*√40
θ = 145.3°
#17. true - take a look at the graph of any exponential function of x. That look like a straight line?
#18. true
To find the angle between two vectors, you can use the dot product formula. The dot product of two vectors, denoted as v · w, is equal to the magnitude of the first vector (v) multiplied by the magnitude of the second vector (w) multiplied by the cosine of the angle between them.
Let's calculate the dot product of the given vectors:
v = (-4, -3)
w = (2, 6)
The dot product formula is:
v · w = v1 * w1 + v2 * w2
Substituting the values:
v · w = (-4 * 2) + (-3 * 6)
= -8 - 18
= -26
Next, find the magnitudes of the vectors:
|v| = √((-4)^2 + (-3)^2)
= √(16 + 9)
= √25
= 5
|w| = √(2^2 + 6^2)
= √(4 + 36)
= √40
= 2√10
Now, substitute the values into the dot product formula to find the cosine of the angle between the vectors:
cos(θ) = (v · w) / (|v| * |w|)
= (-26) / (5 * 2√10)
= (-26) / (10√10)
= -2.6 / √10
Finally, use the inverse cosine (arccos) function to find the angle in radians:
θ = arccos(-2.6 / √10)
θ ≈ 2.996 radians
To convert the angle to degrees, multiply it by 180 and divide by π:
θ° = (2.996 * 180) / π
θ° ≈ 171.8°
Approximating the answer to the nearest tenth:
θ° ≈ 171.8° ≈ 145.3° (to the nearest tenth)
Therefore, the angle between the vectors v and w is approximately 145.3 degrees.
As for the other questions:
17. One type of data that is non-linear in nature is the exponential function.
False. Exponential functions are actually a type of non-linear function.
19. Exponential data follows the equation y = ab^x.
True. The equation y = ab^x represents an exponential function, where 'a' and 'b' are constants and 'x' is the independent variable.