The formula
R =−0.0026? + 4.0807
can be used to predict the world record, in minutes, for the 1500-m run t years after 1900. Determine (in terms of an inequality) those years for which the world record will be less than 3.8 min.
Is ? supposed in your equation to be t?
If so, you need to solve
3.8 < 4.0807 - 0.0026 t
It can be rewritten
0.0026 t > 0.2807
Solve for t and add that to 1900.
The equation is not at all accurate. The men's world record for this distance became 3.325 minutes in 2004.
Perhaps the equation applies to the WOMEN's world recdrod time.
Please state your questions more carefully
To determine the years for which the world record will be less than 3.8 minutes, we can substitute R < 3.8 into the given formula and solve for t.
The formula R = -0.0026t + 4.0807 represents the world record time in minutes for the 1500-m run t years after 1900.
Substituting R < 3.8 into the formula, we get:
-0.0026t + 4.0807 < 3.8
Next, we can rearrange the inequality to isolate the t variable:
-0.0026t < 3.8 - 4.0807
-0.0026t < -0.2807
To solve for t, we need to divide both sides of the inequality by -0.0026. Since we are dividing by a negative value, the inequality direction will flip:
t > (-0.2807) / (-0.0026)
t > 108.0385
Therefore, the years for which the world record will be less than 3.8 minutes are t > 108.0385 years after 1900.