Question

The speed, v, of a wave is inversely proportional to the square root of the

depth, d, of the water. When v= 30 then d = 400.
Find y when d=25.

Answer 1

The speed of a wave is inversely proportional to the square root of the depth of the water. Using this relationship, we can find the value of y when d=25.

Step-by-step explanation:

In this problem, we are given that the speed, v, of a wave is inversely proportional to the square root of the depth, d, of the water. We are also given that when v = 30, d = 400.

To find y when d = 25, we can set up a proportion using the inverse proportionality relationship. Since v is inversely proportional to the square root of d, we can write:

v = k/sqrt(d)

where k is the constant of proportionality.

Plugging in the values we know, we have:

30 = k/sqrt(400)

Solving for k, we find that k = 30 * sqrt(400) = 30 * 20 = 600.

Now we can find y using the proportion:

30 = 600/sqrt(25)

Simplifying, we have:

30 = 600/5

Finally, solving for y, we find that y = 600/5 = 120.

Answer 2

v = 120

Step-by-step explanation:

If v is inversely proportional to square root of d, then we can write

`v √(d)` = k

If v = 30 and d = 400, then

30(
`√(400)`) = k

k = 30(20) = 600

Now
`v √(d)` = 600

If d = 25, then v
`√(25)` = 600

5v = 600

v = 120