the formula R= -0.75t +3.85 can be used to predict the world record in the 1500 meter run, t years after 1930. Determine an inequality that identifies the years in which the world record will be less than 2.8 minutes.
R<2.8
-.75t+3.85<2.8
-.75t<-1.05
t>1.05/.75
To determine an inequality that identifies the years in which the world record will be less than 2.8 minutes, we need to substitute R with 2.8 in the formula and solve for t.
The formula given is:
R = -0.75t + 3.85
Substituting R with 2.8:
2.8 = -0.75t + 3.85
To isolate -0.75t, we subtract 3.85 from both sides:
2.8 - 3.85 = -0.75t
-1.05 = -0.75t
Now, divide both sides of the equation by -0.75 to solve for t:
(-1.05)/(-0.75) = t
1.4 = t
So, the world record will be less than 2.8 minutes when t is less than 1.4 years after 1930.
In inequality format, this can be written as:
t < 1.4
To determine the inequality that identifies the years in which the world record will be less than 2.8 minutes, we need to substitute the value of R (world record time) into the given formula and solve it for t.
The formula is R = -0.75t + 3.85, where R represents the world record time in minutes, and t represents the number of years after 1930.
We want to find the values of t for which R is less than 2.8 minutes. Therefore, we substitute R = 2.8 into the formula and solve for t:
2.8 = -0.75t + 3.85
Rearrange the equation to isolate t:
0.75t = 3.85 - 2.8
0.75t = 1.05
Now, divide both sides by 0.75 to solve for t:
t = 1.05 / 0.75
t = 1.4
So, the inequality that identifies the years in which the world record will be less than 2.8 minutes is t < 1.4.
Therefore, the world record will be less than 2.8 minutes for any year t before 1.4 years after 1930.