Question

what variables show a direct relationship? check all that apply.
the speed of a car and the distance traveled
the elevation above sea level and the air temperature
the number of students in a cafeteria and the amount of food consumed
the mass of an icicle and the time it takes to melt
the distance a planet is from the sun and that planets temperature
the mass of a space shuttle and its acceleration through space

Explanation:

• For the speed of a car and the distance traveled: Using the formula \(d = vt\) (where \(d\) is distance, \(v\) is speed, and \(t\) is time, assuming time is constant), as speed increases, distance traveled increases.
• For the elevation above sea level and the air temperature: As elevation increases, air temperature generally decreases (inverse relationship).
• For the number of students in a cafeteria and the amount of food consumed: More students usually mean more food is eaten (direct relationship).
• For the mass of an icicle and the time it takes to melt: A larger - mass icicle (more substance to melt) will take more time to melt (direct relationship).
• For the distance a planet is from the Sun and that planet's temperature: As a planet gets farther from the Sun (distance increases), its temperature generally decreases (inverse relationship).
• For the mass of a space shuttle and its acceleration through space: Using \(F=ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration, assuming force is constant), as mass increases, acceleration decreases (inverse relationship).

Answer:

• the speed of a car and the distance traveled
• the number of students in a cafeteria and the amount of food consumed
• the mass of an icicle and the time it takes to melt