World Records in the 1500-m Run. The formula R = -0.075t + 3.85 can be used to predict the world record in the 1500-m run t years after 1930. Determine (in terms of an inequality) those years for which the world record will be less than 3.5 min.
{ Y l Y > 1930 } ?
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To determine the years for which the world record will be less than 3.5 minutes, we need to substitute the value of 3.5 minutes (convert to seconds) into the inequality and solve for "t".
First, let's convert 3.5 minutes into seconds. Since 1 minute is equal to 60 seconds, 3.5 minutes is equal to 3.5 * 60 seconds = 210 seconds.
So, we have the inequality:
-0.075t + 3.85 < 210
Now, we can solve this inequality for "t".
Subtract 3.85 from both sides to isolate the term with "t":
-0.075t < 210 - 3.85
Simplifying:
-0.075t < 206.15
Finally, divide both sides of the inequality by -0.075 to solve for "t".
Remember, when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.
t > 206.15 / (-0.075)
t > -2748.67
Now, we have the inequality:
t > -2748.67
To determine the years for which the world record will be less than 3.5 minutes (or 210 seconds), we need to find the years that are greater than -2748.67. However, the expression "Y > 1930" specifies that we are interested in the years after 1930.
So, combining the two conditions, the years for which the world record will be less than 3.5 minutes (or 210 seconds) can be represented by the inequality:
Y > 1930 and t > -2748.67