Use the vectors u = 4, 4 and v = −8, 3 to find the indicated quantity. (u · v)v

The scalar product, or dot product, of two vectors is the sum of the products of corresponding coordinates.

... u·v = (4, 4)·(-8, 3) = 4(-8) + 4(3) = -20

Then the product of a scalar and a vector is a vector with each of the original coordinates multiplied by the scalar.

... (u·v)v = -20v = -20(-8, 3) = (160, -60)

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240