# Varies directly proportional relationship

### BBC - Standard Grade Bitesize Maths I - Direct variation : Revision

If money earned is proportional to the days on which the shop is open, then the The specific questions you will be expected to answer will vary depending 'x' is directly proportional to another variable 'y', their relationship can be written as. Example 1: The circumference of a circle is directly proportional to its diameter, and the constant of Example 2: An object's weight on earth varies directly to its weight on the moon. Next, consider the relationship between time and rate. to vary directly as x, or to be directly proportional to x. Direct Variation graph of this equation is shown in Figure D 1. y varies directly as the nth power of x.

## Finding the variation formula

Everything You'll Have Covered Direct variation is a type of proportionality relation between two varying quantities. Two quantities are proportional if they are constant multiples of each other.

The constant k is called the constant of variation. Examples of direct variation: The cost of gasoline varies directly with the number of gallons purchased.

The relationship between circumference and diameter of a general circle is given by. Therefore, circumference and diameter vary directly.

### Proportion – Algebraic Problems

The constant of proportionality is equal to The length of an object, measured in feet, varies directly with its length, measured in inches. The variation equation is because there are 12 inches to a foot. Directly varying quantities are commonly represented by statements, graphs, or tables. The form of each representation is given below.

### Directly Proportional and Inversely Proportional

For example, given that x and y vary directly, the following statement provides enough information to find the constant of proportionality: The distance, d, an object in free fall drops varies directly with the square of the time, t, that it has been falling. If an object in free fall drops 36 feet in 1. The constant of variation is called the spring constant.

If a hanging spring is stretched 3 centimeters when a 2-kilogram weight is attached to it, then determine the spring constant. If a hanging spring is stretched 6 centimeters when a 4-kilogram weight is attached to it, then how far will it stretch with a 2-kilogram weight attached?

The breaking distance of an automobile is directly proportional to the square of its speed. If it takes 36 feet to stop a particular automobile moving at a speed of 30 miles per hour, then how much breaking distance is required if the speed is 35 miles per hour? After an accident, it was determined that it took a driver 80 feet to stop his car. In an experiment under similar conditions, it takes 45 feet to stop the car moving at a speed of 30 miles per hour.

Estimate how fast the driver was moving before the accident. A balloon is filled to a volume of cubic inches on a diving boat under 1 atmosphere of pressure. If the balloon is taken underwater approximately 33 feet, where the pressure measures 2 atmospheres, then what is the volume of the balloon?

If a balloon is filled to cubic inches under a pressure of 3 atmospheres at a depth of 66 feet, then what would the volume be at the surface, where the pressure is 1 atmosphere?

To balance a seesaw, the distance from the fulcrum that a person must sit is inversely proportional to his weight.

If a pound boy is sitting 3 feet from the fulcrum, then how far from the fulcrum must a pound boy sit to balance the seesaw? The current, I, in an electrical conductor is inversely proportional to its resistance, R.

The number of men, represented by y, needed to lay a cobblestone driveway is directly proportional to the area, A, of the driveway and inversely proportional to the amount of time, t, allowed to complete the job. Typically, 3 men can lay 1, square feet of cobblestone in 4 hours. How many men will be required to lay 2, square feet of cobblestone given 6 hours? The volume of a right circular cylinder varies jointly as the square of its radius and its height.

Find a formula for the volume of a right circular cylinder in terms of its radius and height.