Question

consider the following. d = 85t, where d is the distance traveled in miles when driving for t hours; t = 2.5 and d = 212.5. (a) are the given values of the variables a solution to the equation? o yes o no (b) explain what the values mean in this situation. (include units in your answers. more information.) these values represent that a distance of x dimensionally incorrect. please check the type or dimension of your unit. is traveled when driving for x dimensionally incorrect. please check the type or dimension of your unit.

Explanation:

Step1: Substitute the values into the equation

Given the equation \(d = 85t\), substitute \(t = 2.5\) into the equation.
\(d=85\times2.5\)

Step2: Calculate the value of \(d\)

\(85\times2.5=(80 + 5)\times2.5=80\times2.5+5\times2.5=200 + 12.5 = 212.5\)

Answer:

(a) Yes
(b) The equation \(d = 85t\) represents a relationship where \(d\) (distance in miles) is a function of \(t\) (time in hours). When we substitute \(t = 2.5\) into the equation \(d=85t\), we are using the formula for distance \(d=v\times t\) (where \(v = 85\) miles per hour is the speed). The units of \(d\) (miles) and \(t\) (hours) are consistent with the formula \(d = v\times t\) (since \(v\) has units of miles per hour). So the value \(d = 212.5\) (miles) when \(t=2.5\) (hours) is a valid solution as it follows the formula for distance - rate - time relationship.