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This is the formula for direct variation
y= kx
This is the formula for inverse variation
y = k/x
On a map, distance in km and distance in cm varies directly, and 25 km are represented by 2cm. If two cities are 7cm apart on the map, what is the actual distance between them?
87.5 km
If y varies directly as x, and y = 3 when x = 9, find x when y = 5.
x=15.
Y varies inversely as x and y = 2 when x = 8. Find y when x = 32
y= 1/2
The electric current I, is amperes, in a circuit varies directly as the voltage V. When 12 volts are applied, the current is 4 amperes. What is the current when 18 volts are applied?
6 amperes
y varies inversely with x. If y = 7 when x = -4, find y when x = 5.
y= -5.6
y varies directly with x. If y = 15 when x = -18, find y when x = 1.6.
y=-4/3
Hooke’s law states that the distance d that a spring is stretched by a hanging object varies directly as the mass m of the object. If the distance is 20 cm when the mass is 3 kg, what is the distance when the mass is 8 kg?
distance= 160/3 = 53.3 cm
If y varies inversely as x, and y = 34 when x = 3, find y when x =5.
y= 20.4
Y varies directly as x and y = 0.225 when x =4. Find y when x = 12.
y=0.675
The frequency of a vibrating string varies inversely as its length. A string 3 feet long vibrates 175 cycles per second. Find the frequency of a 5 foot string.
105 cycles per second
Two variables x and y are related such that 'x' varies inversely as the square of 'y'. Write an equation in x, y and k to describe the variation.
Calculate the value of k knowing that when x=3, then y=2.
y2=k X 1/x OR y2=k/x
k=12
In planning a trip, the time it takes to make the trip varies inversely with the rate of the car. If I take Route A and average 40 mph, it will take 9.5 hours to complete the trip. If I go by Route B and average 50 mph, how long will the trip take?
7.6 hours