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Solved Examples
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eee Does the equation x = 5y model direct variation, inverse variation, or neither?
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eee Find an equation that relates x and y inversely and y = 3 when x = 18.6.
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eee Find an equation that relates x and y inversely and y = 12 when x = 8.
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eee Find an equation that relates x and y inversely, such that y = 227 when x = 7.
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eee Charlie used the relation v = ir to calculate the resistance, r of a copper wire, where i is the current and v, the constant potential. Find the relationship between the current in the wire and the resistance of the wire. eee View Solution
eee Find an equation that relates x and y inversely and y = 5 when x = 3. eee View Solution
eee Find an equation that relates x and y inversely and y = 9 when x = 1.
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eee Find an equation that relates x and y inversely, assuming y = 10 when x = 14.
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eee Which variation does the equation xy = 4, model? eee View Solution
eee Which variation does the equation y = 4x2 - 7 model?
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eee According to Hooke's Law, the force needed to stretch a spring is proportional to the length to which the spring is stretched. If 40 pounds stretches a spring to 3 inches, then how much will the spring be stretched by a force of 96 pounds? eee View Solution
eee If y varies inversely with x and y = 0.5 when x = 2.5, then find the value of y when x = 5. eee View Solution
eee The number of hours h that it takes m men to cut x trees varies directly as the number of trees and inversely as the number of men. If 3 men cut 6 trees in 3 hours, then how many men are needed to cut 12 trees in 3 hours?
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eee The current in an electrical conductor varies inversely as the resistance of the conductor. What is the current when the resistance is 47 ohms, if the current is 7 amperes when the resistance is 235 ohms? eee View Solution
eee m varies inversely as the square of p. If m is 36 when p is 4, then find m when p is 6.
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eee A machine makes 186 copies in 9 hours. How many copies can it make in 78 hours, if number of hours and the number of copies vary directly? eee View Solution
eee Jimmy drives a distance of 280 km at a speed of 70 km/hr. With what speed should he drive so that he covers twice the distance in the same time? eee View Solution
eee Write an equation that relates x and y directly, when x = 5, y = 20. eee View Solution
eee An oil drilling company pumps 54 gallons of oil per minute into tankers. Find the time taken to pump 1836 gallons of oil into the tankers, if number of gallons of oil pumped is directly proportional to the time taken for pumping.
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eee Mr.Sunny, a salesman gets a commission of $2 on every $200 of the sales he makes. Write a direct variation model that relates his commission to his sales.
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eee Find an equation that relates x and y directly, if x = 5 when y = - 25. eee View Solution
eee The age of Matt (y) is 4 times the age of Rebecca (x). Find a direct variation model that relates the ages of Matt and Rebecca. eee View Solution
eee 6 people can do a job in 10 hours. How long will it take 9 people to do the same job? eee View Solution
eee A certain project can be completed by 6 workers in 27 days. In order to complete the project sooner, the company plans to hire additional workers. How many workers are needed to complete the project in 18 days?
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eee The volume of a gas varies inversely with the pressure of the gas on its container. If a pressure of 25 pounds per square inch corresponds to a volume of 68 cubic inches, What pressure is needed to correspond to a volume of 80 cubic inches? eee View Solution
eee The volume of a gas varies inversely with the pressure of the gas on its container. If a pressure of 38 kg per square meter corresponds to a volume of 280 cubic meters, What is the volume under a pressure of 56 kg per square meter? eee View Solution
eee A pump empties a swimming pool in 40 minutes at the rate of 1400 L/min. If the rate of pumping is 2000 L/min, how long does it take to empty the swimming pool? eee View Solution
eee Does the equation x = 6y model direct variation, inverse variation, or neither?
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eee Does the graph model direct variation, inverse variation, or neither? eee View Solution
eee Find an equation that relates x and y inversely and y = 6 when x = 4.
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eee Find an equation that relates x and y inversely, such that y = 3110 when x = 10.
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eee If L is a constant, then what type of variation does v = LT represent?
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eee Paul used the relation v = ir to calculate the resistance, r of a copper wire, where i is the current and v, the constant potential. Find the relationship between the current in the wire and the resistance of the wire. eee View Solution
eee Find an equation that relates x and y inversely and y = 5 when x = 4. eee View Solution
eee Find an equation that relates x and y inversely and y = 6 when x = 3.
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eee Find an equation that relates x and y inversely and y = 2 when x = 17.6.
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eee Which variation does the equation xy = 7, model? eee View Solution
eee Find an equation that relates x and y inversely, assuming y = 11 when x = 13.
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eee Which variation does the equation y = 4x2 - 11 model?
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eee Which variation does the graph model? eee View Solution
eee If R and T are constants, then what type of variation does PV = RT represent?
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eee According to Hooke's Law, the force needed to stretch a spring is proportional to the length to which the spring is stretched. If 46 pounds stretches a spring to 5 inches, then how much will the spring be stretched by a force of 62 pounds? eee View Solution
eee If y varies inversely with x and y = 0.2 when x = 3.5, then find the value of y when x = 2. eee View Solution
eee The number of hours h that it takes m men to cut x trees varies directly as the number of trees and inversely as the number of men. If 5 men cut 10 trees in 5 hours, then how many men are needed to cut 40 trees in 5 hours?
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eee The current in an electrical conductor varies inversely as the resistance of the conductor. What is the current when the resistance is 49 ohms, if the current is 6 amperes when the resistance is 196 ohms? eee View Solution
eee m varies inversely as the square of p. If m is 16 when p is 3, then find m when p is 4.
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eee A machine makes 365 copies in 25 hours. How many copies can it make in 95 hours, if number of hours and the number of copies vary directly? eee View Solution
eee George drives a distance of 80 km at a speed of 40 km/hr. With what speed should he drive so that he covers twice the distance in the same time? eee View Solution
eee Write an equation that relates x and y directly, when x = 6, y = 30. eee View Solution
eee Mr.Arthur, a salesman gets a commission of $2 on every $200 of the sales he makes. Write a direct variation model that relates his commission to his sales.
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eee An oil drilling company pumps 94 gallons of oil per minute into tankers. Find the time taken to pump 4136 gallons of oil into the tankers, if number of gallons of oil pumped is directly proportional to the time taken for pumping.
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eee Find an equation that relates x and y directly, if x = 2 when y = - 10. eee View Solution
eee The age of Sunny (y) is 4 times the age of Paula (x). Find a direct variation model that relates the ages of Sunny and Paula. eee View Solution
eee "The graph of a direct variation model is a line that always passes through the origin". State whether the above statement is true or false.
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eee The cost of producing pencils varies directly with the number of pencils produced. If the cost of producing 9,000 pencils is $630, then what will be the cost of production for 14,000 pencils? eee View Solution