If f and g are functions of time, and at time t = 2, f equals 5 and is rising at a rate of 6 units per second, and g equals 7 and is rising at a rate of 9 units per second, then f/g equals and is changing at a rate of units per second. If f and g are functions of time, and at time t = 3, f equals 9 and is rising at a rate of 6 units per second, and g equals 8 and is rising at a rate of 9 units per second, then f/g equals and is changing at a rate of units per second.

a)

It is changing at a rate of  units per seconds

b)

It is changing at a rate of units per seconds

Step-by-step explanation:

A

Given that:

f and g are functions of time (t):

i.e  

f(t) =0

g(t) = 0

Now; at time (t) = 2 ; f equals 5 and is rising at a rate of 6 units per second.

Also; at time 2; g equals 7 and is rising at a rate of 9 units per second

This implies that:

f(2) = 5                   f' (2) = 6

g(2) = 7                  g' (2) = 9

Then can be directly  calculated from the  given values which is:

Using differentiation to determine the rate of changing ; we have

=

∴ It is changing at a rate of  units per seconds

B

Given that:

f and g are functions of time (t):

i.e  

f(t) =0

g(t) = 0

NOW; at time (t) = 3

f (3) = 9                                      f' (3) = 6

g (3) = 8                                     g' (3) = 9

Then can be directly  calculated from the  given values which is:

Using differentiation to determine the rate of changing ; we have

∴ It is changing at a rate of units per seconds

The negative signs means they are decreasing.

step-by-step explanation: it is d