Question

15. The average speed that a tsunami (a large tidal wave) travels is represented

by the function s = (2002)1/2, where s is the speed (in miles per hour) that

the tsunami is traveling and d is the average depth (in feet) of the wave.

a. Find the inverse of the function.

b. Find the average depth of the tsunami when the recorded speed of the

wave is 250 miles per hour.

Answer 1

a) the inverse function is
`(s^2)/(200)`

b) when s = 250, then d= 312.5

Explanation:

a)The function is
`s=(200d)^1/2`. To find the inverse, we will try to solve for d. Then, by raising up to 2 in both sides we get

`s^2 = 200d`

Dividing by 200 both sides we get

`(s^2)/(200)=d`.

Thus, the inverse function in this case is
`d= g(s) = (s^2)/(200)`

b)In this case, we are given that s = 250,

then
`d = (250^2)/(200) = 312.5`

Answer 2

Correct question :

The average speed that a tsunami (a large tidal wave) travels is represented

by the function
`s = (200d)^1^/^2` where s is the speed (in miles per hour) that the tsunami is traveling and d is the average depth (in feet) of the wave.

a. Find the inverse of the function.

b. Find the average depth of the tsunami when the recorded speed of the wave is 250 miles per hour.

Answer:

a)
`d = (s^2)/(200)`

b) 312.5 ft

Explanation:

Given:

Average speeds,
`s = (200d)^1^/^2`

a) To find the inverse of the function.

`s = (200d)^1^/^2`

s² = 200d

200d = s²

`d = (s^2)/(200)`

Therefore, inverse of the function =

`d = (s^2)/(200)`

b) average depth when speed is 250 miles per hour.

Average depth = d

Therefore, let's use the formula :

`d = (s^2)/(200)`

`= (250^2)/(200)`

`= (62500)/(200)`

d = 312.5 feet

The average depth when speed is 250 miles per hour is 312.5 ft