( EXERCISE 5.5 - LINEAR ALGEBRA )

1) Find uv, vu, and vv.

u = i + j,v = j k

(a)u v

(b)vu

(c)vv

2)

Find a unit vector orthogonal to both u and v.

u=3i 2j + 5k

v=1/2i 3/4j +1/10k

3) EXERCISE 5.4

a)

Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times, whereas an animal that is galloping has all four feet off the ground at some point in its stride. The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal. Use the table and the method of this example to find an equation that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute). Weight, x 25 35 50 75 500 1000

Galloping Speed, y 195.5 181.7 172.8 164.2 124.9 113.2

Take the natural logarithm of each coordinate to obtain points of the form (ln x, ln y).

(Round your answers to three decimal places.)

Weight, x 25 35 50 75 500 1000

Galloping Speed, y 195.5 181.7 172.8 164.2 124.9 113.2

ln x

ln y

Find the least squares regression line for the transformed points. (Round your answers to three decimal places.)

ln y = + ln x

Find an equation of the form y = ax^b

that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute). (Round your value for a to one decimal place and your value for b to three decimal places.)

y =