Worksheet: Combined Variation

In this worksheet, we will practice writing an equation to describe combined variation and using proportions to find other sets of values.

Q1:

We know that 𝑦 varies directly with 𝑥 and inversely with 𝑧 . Given that 𝑦 = 5 when 𝑥 = 6 and 𝑧 = 3 , find the value of 𝑦 when 𝑥 = 2 4 and 𝑧 = 1 5 .

Q2:

When one inflates a balloon, the pressure of gas inside the balloon varies directly with the quantity of gas injected inside (the unit for this is moles), and the pressure varies inversely with the volume of the balloon (which increases when the balloon expands). Assume that the temperature of the gas inside the balloon is constant.

Write an equation for the pressure of gas inside the balloon ( 𝑃 ) in terms of the quantity of gas inside the balloon ( 𝑛 ) and the volume of the balloon ( 𝑉 ). Let 𝑘 be a constant.

  • A 𝑃 = 𝑘 𝑛 𝑉
  • B 𝑃 = 𝑘 𝑉 𝑛
  • C 𝑃 = 𝑘 𝑛 𝑉
  • D 𝑃 = 𝑘 𝑛 𝑉
  • E 𝑃 = 𝑛 𝑉 𝑘

Given that the pressure inside the balloon is 1.1 bars with 0.089 moles of air inside the balloon of volume 2 dm3, find the pressure inside the balloon when there are 0.24 moles of air and its volume is 4 dm3. Round your answer to one decimal place.

Q3:

In an electric circuit, the current intensity 𝐼 going through a resistor varies directly with the voltage drop 𝑉 across the resistor and inversely with the resistance 𝑅 . Given that the current intensity is 2.5 A with a voltage drop of 5 V across a resistor of resistance 2 Ω, find the value of the current intensity when the voltage drop is 15 V and the resistance is 3 Ω.

Q4:

When a given substance is heated, the change in its temperature varies directly with the amount of energy transferred to the substance, and it varies inversely with the mass of the substance.

Write an equation for the change in temperature Δ 𝑇 in terms of the amount of energy transferred 𝐸 and the mass 𝑚 .

  • A Δ 𝑇 = 𝑘 𝐸 𝑚
  • B Δ 𝑇 = 𝑘 𝑚 𝐸
  • C Δ 𝑇 = 𝑘 𝐸 𝑚
  • D Δ 𝑇 = 𝑘 𝐸 𝑚
  • E Δ 𝑇 = 𝐸 𝑚 𝑘

The temperature of 25 g of olive oil increases by 1 1 . 5 C when it receives 575 J of energy. Find the temperature increase of 115 g of olive oil when it receives 460 J of energy.

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