Suppose the constant of variation, k, is positive.
If y varies directly with x, describe how y changes as x increases and decreases.
If y varies inversely with x, describe how y changes as x increases and decreases.
State whether the following equations represent direct or inverse variation:
The period of a pendulum varies directly with the square root of its length. If the length is quadrupled, what happens to the period?
State whether the following are examples of direct or inverse variation:
The variation relating the distance between two locations on a map and the actual distance between the two locations.
The variation relating the number of workers hired to build a house and the time required to build the house.
Rhe variation relating the time it takes an ice cube to melt in water and the temperature of the water.
In the equation y = 3 x, y varies directly as x.
Find the value of y when x = 10.
Find the value of y when x = 5.
For these two ordered pairs, what is the result when the y value is divided by the x value?
Find the equation relating p and q given the table of values:
| p | 3 | 6 | 9 | 12 |
|---|---|---|---|---|
| q | \dfrac{2}{9} | \dfrac{1}{18} | \dfrac{2}{81} | \dfrac{1}{72} |
Find the equation relating t and s given the table of values:
| s | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| t | 48 | 24 | 16 | 12 |
If d = \dfrac{1}{5} s, where d is the approximate distance (in miles) from a storm, and s is the number of seconds between seeing lightning and hearing thunder, describe the relationship between the distance and the number of seconds.
If r = \dfrac{d}{t}, where r is the speed when d kilometres in t hours, describe the relationship between the speed and the kilometres.
If f = \dfrac{m v^{2}}{r}, where f is the centripetal force of an object of mass m moving along a circle of radius r at velocity v, describe the relationship between the centripetal force and the mass.
The mass in grams, M, of a cube of cork varies directly with the cube of the side length in centimetres, x. If a cubic centimetre of cork has a mass of 0.29:
Find the constant of variation, k.
Express M in terms of x.
Find the mass of a cube of cork with a side length of 8 centimetres correct to two decimal places.
The surface area, A, of a regular tetrahedron varies directly with the square of its side length, s. A particular tetrahedron with a side length of 2 cm has a surface area of 6.93.
Find the constant of variation, k, to two decimal places.
Using the rounded value of k, express A in terms of s.
Find the surface area of a tetrahedron with a side length of 3 cm to two decimal places.
The area, A, of an equilateral triangle varies directly with the square of its side length, s. An equilateral triangle with a side length of 7 cm has an area of 21.22.
Find the constant of variation, k, to two decimal places.
Express A in terms of s.
Find the area of an equilateral triangle with a side length of 2 cm to two decimal places.
The number of eggs, n, used in a recipe for a particular cake varies directly with the square of the diameter of the tin, d, for tins with constant depth. 2 eggs are used in a recipe for a tin with a diameter of 17 cm.
Find the exact value of the constant of variation, k.
How many eggs, n, would be used for a tin with a diameter of 39 cm?