Find v x w if v=-9i+2j-3k and w=8i-3j+8k

The cross product satisfies

The cross product is anti-commutative, so that for any two vectors and , , and

It's also distributive, which means we have

Table below represents the displacement of a fish from its reef as a function of time:

Time

(hours)

(x)       Displacement  from reef

(feet)  (y)

0                        4

1                       64

2                      124

3                      184

4                      244

Part A

To find the y-intercept, put x=0 and find for y;

As you can see from the the table when x=0 , y=4 this means, that the fish started off 4 feet away from its reef

At 0 hours, the distance its away from its reef is, 4 feet

Part B

The average rate of change of the function calculates the slope of the line or a curve on a given range.

For any point the slope between the ordered pairs (1, 64) and (3, 184).

the formula of slope is given by:

Slope

The average rate of the change of function represented by the table between x=1 to x=3 hours is, 60.

The average rate represents the speed of the fish in feet\ hour.

Part C:

To find the domain of the function :

Now, we know the slope and the y-intercept we can easily find the equation of the line where m is the slope and b is the y-intercept.

∵ m =60 and b=4, we have ,

if the fish continued to swim at this rate until it traveled 724 feet from the reef.

⇒

On simplify we get;

∴the fish would take 12 hours to traveled 724 feet from the reef.

so, the domain of the function would be between 0 and 12.