5.5 App. of rational/radical functions (variation)

Let [math]x, y, z[/math] be three variables. [math]x[/math] and [math]y[/math] have inverse variation and [math]x[/math] and [math]z[/math] have direct variation. If [math]x=6[/math], then [math]y=z=3[/math]. Find [math]x^2y[/math] when [math]z=4[/math].

Let [math]x, y[/math] be variables. Suppose [math]x-a[/math] and [math]y-a[/math] have inverse variation. If [math]x=3[/math], then [math]y=-4[/math]; if [math]x=1[/math], then [math]y=8[/math]. Find [math]a[/math].

According to the formula of kinetic energy, the mass of an object [math]m[/math] varies inversely with the square of the velocity [math]v[/math] and directly with the energy [math]E[/math]. Which of the following equations best represents the relation of [math]E, m[/math], and [math]v[/math]?

According to the Ohm’s theorem, the resistance [math]R[/math] varies inversely with Ampare [math]I[/math] and directly with Voltage [math]V[/math]. Which of the following equations best represents the relation of [math]R, V[/math], and [math]I[/math]?

Let [math]x, y[/math] be two variables satisfying the equation [math]y=ax+b[/math] where [math]a, b[/math] are nonzero constants. Which statements is/are true?

According to the Gas law, the volume [math]V[/math] of a trapped gas varies inversely with pressure [math]P[/math] and directly with temperature [math]T[/math]. ?Which of the following equation is true?

According to Newton’s Law of Gravitation, the gravitation force between two planets is directly proportional to the product of their masses, and inversely propertional to the square of the distance separating them. Consider three planets; Planets [math]Mu[/math] and [math]Alpha[/math] have equal masses, while Planet [math]Theta[/math] has twice the mass of Planet [math]Mu[/math]. For which arrangements below will the gravitational force be the greatest?

Which of the following is an example of an inverse relation?

[math]y[/math] varies directly with the square of [math]x[/math] and inversely with the square root of [math]z[/math], If [math]y=2[/math], when [math]x=\dfrac{1}{6}[/math] and [math]z=\dfrac{1}{4}[/math]. What is the value of [math]y[/math] when [math]x=\dfrac{3}{8}[/math] and [math]z=\dfrac{1}{9}[/math]?

The load [math]P[/math] (in kilograms) that can safely be supported by a horizontal beam varies directly with the beams’ width [math]W[/math] and the cube of its depth [math]D[/math], and inversely with its unsupported length [math]L[/math]. Show your algebraic work that leads to the answers for the following questions:

If [math]P[/math] does not change, just write “1”.

The Kinetic Energy, [math]E[/math] of an object varies jointly with the mass of the object(m) and the square of its velocity. If the mass of the object double while the velocity of the object is quatered, find how the kinetic energy changes.

(Calculator) One group of students can set up all 300 desks in the gym in 35 minutes. A second group of students can complete the same task in 45 minutes. Working together, how long will it take the students to set up all 300 desks in the gym? Round to the nearest minute.

(Calculator) Ryan is training for a race. He runs from his house, 5km down the hill, then turns back around and runs 5 km back to his house. Because the return trip is uphill, and he is tired, Ryan’s speed on his return trip is only 80% of his downhill speed. If it takes him a total of 55 minutes to run 10 km, what is Ryan’ s speed, in km/min, going uphill? Round to the nearest 2 decimals.

(Calculator) Jack can assemble five cabinet from Ikea in 3 hours, Jill can assemble the same five cabinets in 4 hours. Working together, how long (in hours and minutes) will it take them to assemble the five cabinets?

(Calculator) Jean rows a boat 6 km downstream, and then turns around and rows the same distance home. The effect of the current on Jean’s boat is 3 km/hr. She spent 4.5 hours in total rowing. What is the speed, in km/hr, of the boat in still water? Round to the nearest hundredth.