Question

Researchers collect data from a storm as it grows in strength and becomes a hurricane. They first monitor the storm when it has a maximum wind speed of 21 miles per hour, and the maximum wind speed increases by 1 mile per hour every hour. The linear equation is y=57 after 36 hours. Does this equation make sense for all possible values of x and y?

Answer 1

Answer:

y=x+21 makes sense for this specific scenario.

Step-by-step explanation:

Let's analyze the given information:

The linear equation given is

y=mx+b, where:

y is the maximum wind speed of the hurricane in miles per hour,

x is the number of hours the storm has been monitored,

m is the rate at which the maximum wind speed is increasing (1 mile per hour per hour, in this case),

b is the initial maximum wind speed when the monitoring started (21 miles per hour in this case).

So, the given equation is

y=x+21.

Now, we are given that after 36 hours (x=36), the maximum wind speed (y) is 57 miles per hour.

Let's substitute these values into the equation to see if it holds true:

57=36+21

57=57

The equation holds true for the given values, so the linear equation

y=x+21 makes sense for this specific scenario.

However, it's important to note that this equation may not be accurate for all possible values of x and y in other contexts. In this case, it's a specific linear model describing the relationship between the maximum wind speed and the time elapsed for this particular storm.