Question

The temperature of water in a certain lake on a day in October can be determined by using the model y=15.2-0.537x where x is the number of feet down from the surface of the lake and y is the Celsius temperature of the water at that depth. Based on this model, how deep in the lake is the water 9 degrees?

Answer 1

Set y (temperature in degrees Celsius) equal to 9 in the equation y=15.2-0.537x, and solve for x (depth in feet). The solution reveals that the lake's water becomes 9 degrees Celsius at a depth of about 11.54 feet.

Step-by-step explanation:

To determine the depth in the lake where the water is 9 degrees Celsius, we need to set y in the given equation y=15.2-0.537x equal to 9 and solve for x.

So, we have 9 = 15.2 - 0.537x. This can be rearranged as 0.537x = 15.2 - 9, which simplifies down to 0.537x = 6.2. Dividing both sides by 0.537, we get x = 6.2 / 0.537.

Therefore, when you calculate x, you'll find that it equals approximately 11.54. This means that the water is 9 degrees Celsius at a depth of approximately 11.54 feet beneath the surface of the lake, according to the given model.

Learn more about Solving Linear Equations