Question

the mass is 500 grams and the volume is 40 cubic centimeters. d = \frac{500}{40}
the mass is 125 grams and the volume is v cubic centimeters. d = \frac{125}{v}
the volume is 1.4 cubic centimeters and the density is 80 grams per cubic centimeter. (let m equal mass in grams) 80 = \frac{m}{1.4}
the mass is m grams and the volume is v cubic centimeters. d = \frac{m}{v}
write an equation to represent the relationship between the three quantities (density, mass, and volume) in each situation. let the density, d, be measured in grams/cubic centimeters (or g/cm3).
d = \frac{m}{v}
🔥 equation 1 is correct!
🔥 equation 2 is correct!
🙁 not quite. think about what m represents and how 80 and 1.4 relate to the variable.
try again

Explanation:

Step1: Recall density formula

The formula for density $D$ is $D=\frac{m}{v}$, where $m$ is mass and $v$ is volume.

Step2: Analyze first - case

Given mass $m = 500$ grams and volume $v=40$ cubic centimeters. Substituting into the formula, we get $D=\frac{500}{40}$.

Step3: Analyze second - case

Given mass $m = 125$ grams and volume $v$ (variable). Substituting into the formula, we get $D=\frac{125}{v}$.

Step4: Analyze third - case

Given volume $v = 1.4$ cubic centimeters and density $D = 80$ grams per cubic centimeter. Using the formula $D=\frac{m}{v}$, we can rewrite it as $80=\frac{m}{1.4}$ to solve for mass $m$.

Step5: Analyze fourth - case

Given mass $m$ (variable) and volume $v$ (variable). Substituting into the formula, we get $D=\frac{m}{v}$.

Answer:

The equations $D=\frac{500}{40}$, $D=\frac{125}{v}$, $80=\frac{m}{1.4}$, $D=\frac{m}{v}$ correctly represent the relationships between density, mass, and volume for the respective situations.