SHOW ALL YOUR WORK AND ALL STEPS USING THE PREVIOUS CLASS NOTES
5 MINUTES PER QUESTION (Similar Questions will be on the test)
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1. If 𝑧 varies jointly as 𝑥 and 𝑦, and 𝑧 = 3 and when 𝑥 = 3 𝑎𝑛𝑑 𝑦 = 6, 𝑓𝑖𝑛𝑑 𝑧 𝑤ℎ𝑒𝑛 𝑥 =
22 𝑎𝑛𝑑 𝑦 = 10.
2. If 𝑝 varies jointly as square of 𝑥 and the fourth root of 𝑦, and 𝑃 = 24 and when
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𝑥 = 12 𝑎𝑛𝑑 𝑦 = 81, 𝑓𝑖𝑛𝑑 𝑝 𝑤ℎ𝑒𝑛 𝑥 = 1200 𝑎𝑛𝑑 𝑦 = 16 .
3. Ohm’s law states that the current I in a direct-current circuit varies inversely as the
resistance R. If a resistance of 12 ohms produces a current of 3.5 amperes, find the
current when resistance is 2.4 ohms.
4. The pressure of wind on a wall varies jointly as the area A of the wall and square of the
velocity 𝑣 of the wind. If 𝑃 = 100 𝑝𝑜𝑢𝑛𝑑𝑠 𝑤ℎ𝑒𝑛 𝐴 = 80 𝑠𝑞𝑢𝑎𝑟𝑒 𝑓𝑒𝑒𝑡 𝑎𝑛𝑑 𝑣 =
40 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 , 𝑓𝑖𝑛𝑑 𝑖𝑓 𝐴 = 120 𝑠𝑞𝑢𝑎𝑟𝑒 𝑓𝑒𝑒𝑡 𝑎𝑛𝑑 𝑣 = 50 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟.
5. The weight w of an object on or above the surface of the earth varies inversely as the
square of the distance d of the object from the center of the earth. If an astronaut
weighs 120 pounds at the surface of the earth, how much would she weigh in a satellite
400 miles above the surface? (Radius of the earth 4000 miles).
6. The volume V of a given mass gas varies directly as the temperature T and inversely as
the pressure P. If a gas has volume 16 cubic inches when the temperature is 320 degree
Kelvin and the pressure is 300 pounds per square inch, find the volume when the
temperature is 350 degree Kelvin and the pressure is 280 pounds per inch.
7. The strength W of a rectangular beam of wood varies jointly as the width w and the
square of the depth d, and inversely as the length L of the beam. What would be the
effect on W of doubling w and d while decreasing L by a factor of 20%?
8. If u varies inversely as the cube root of x, and u = 56 when x= -8, find u when x= 1000.
9. If I is inversely proportional to the square of t, and I =100 when t=20, find I when t=12.
10. If y varies directly as the square of x, what is the effect on y of doubling x? (Hint: K
remains constant).