Question

The water temperature in the ocean varies inversely with the depth of the water. The deeper a person dives, the colder the water becomes. At a depth of 1,000 meters, the water temperature is 9° Celsius. What is the water temperature at a depth of 800 meters? Find the constant of proportionality k. k= (If needed, round answer to 2 decimal places.) Using the k from above find the water temperature in degrees Celsius at a depth of 800 meters. The water temperature will be ° Celsius. (If needed, round answer to 2 decimal places.)

Answer 1

The relation between the water temperature and depth of the water is inversely proportional.

Let water temperature be t and depth of water is d.

The relation is written as

$t.d=k$

here k is the constant of proportionality .

For the depth of water 1000 m , the temperature is 9° Celsius.

$1000.9=k$$k=9000.$

Thus the value of constant of proportionality k is 9000.

For depth of 800 meters , the temperature of water is

$t.800=9000$$t=\frac{9000}{800}$$t=11.25^{\circ}C$

Therefore, the temperature of water with depth of 800 meters is 11.25 degree Celsius.