Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)a = 5, 4,    b = 3, −1

To find the angle between two vectors, we can use the dot product formula. The dot product of two vectors a and b is given by the formula:

a · b = |a| |b| cos(theta)

where |a| and |b| are the magnitudes of vectors a and b, and theta is the angle between them.

First, let's calculate the magnitudes of vectors a and b:

|a| = sqrt(5^2 + 4^2) = sqrt(25 + 16) = sqrt(41) |b| = sqrt(3^2 + (-1)^2) = sqrt(9 + 1) = sqrt(10)

Next, let's calculate the dot product of vectors a and b:

a · b = 5 * 3 + 4 * (-1) = 15 - 4 = 11

Now, we can rearrange the dot product formula to solve for cos(theta):

cos(theta) = (a · b) / (|a| |b|)

cos(theta) = 11 / (sqrt(41) * sqrt(10))

cos(theta) = 11 / (sqrt(410))

Using a calculator, we can approximate the value of cos(theta) to be approximately 0.5303.

Finally, we can find the angle theta by taking the inverse cosine (arccos) of cos(theta):

theta = arccos(0.5303)

Using a calculator, we find that theta is approximately 57.4 degrees.

Therefore, the angle between vectors a and b is approximately 57.4 degrees.