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 700 meters, the water temperature is 8° celsius. what is the water temperature at a depth of 200 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 200 meters. the water temperature will be ° celsius. (if needed, round answer to 2 decimal places.) question help: video

Explanation:

Step1: Write the inverse - variation formula

The inverse - variation formula is $T=\frac{k}{d}$, where $T$ is the water temperature, $d$ is the depth, and $k$ is the constant of proportionality. We know that when $d = 700$ meters, $T = 8^{\circ}C$. Substitute these values into the formula: $8=\frac{k}{700}$.

Step2: Solve for $k$

Multiply both sides of the equation $8=\frac{k}{700}$ by 700 to isolate $k$. So, $k=8\times700 = 5600$.

Step3: Find the temperature at a new depth

Now we want to find the temperature $T$ when $d = 200$ meters. Use the formula $T=\frac{k}{d}$ with $k = 5600$ and $d = 200$. Then $T=\frac{5600}{200}=28$.

Answer:

The constant of proportionality $k = 5600$ and the water temperature at a depth of 200 meters is $28^{\circ}C$.