Question

what is the meaning of each constant of proportionality, 1.6 and 0.625, in priyas cooler filling situation? how are the constants of proportionality, 1.6 and 0.625, related? recall that it takes priya five minutes to fill eight gallons. you can start your response with: the constants of proportionality, 1.6 and 0.625 represent... the relationship between 1.6 and 0.625 is... press the record button under “start audio recording.” say your answer. press the pause button and save your recording. listen to your recording. if you need to make changes, delete it, and record your response again.

Explanation:

Step1: Calculate gallons - per - minute constant

The rate of filling in gallons per minute is found by dividing the number of gallons by the number of minutes. Given 8 gallons in 5 minutes, the rate is $\frac{8}{5}=1.6$ gallons per minute. So, 1.6 represents the number of gallons filled per minute.

Step2: Calculate minutes - per - gallon constant

The rate of filling in minutes per gallon is found by dividing the number of minutes by the number of gallons. Given 5 minutes for 8 gallons, the rate is $\frac{5}{8}=0.625$ minutes per gallon. So, 0.625 represents the number of minutes it takes to fill one gallon.

Step3: Determine the relationship

The two constants 1.6 and 0.625 are reciprocals of each other since $1.6=\frac{8}{5}$ and $0.625 = \frac{5}{8}$, and $\frac{8}{5}\times\frac{5}{8}=1$.

Answer:

• The constants of proportionality, 1.6 and 0.625 represent: 1.6 represents the number of gallons filled per minute and 0.625 represents the number of minutes it takes to fill one gallon.
• The relationship between 1.6 and 0.625 is that they are reciprocals of each other.