Objectives In this learning activity, you are expected to: a. illustrate situations that involve direct variation; b. translate into variation statement a relationship involving direct variation between two quantities; and c. solve problems involving direct variations. Key Concepts: 1. Relate direct variation to real-life situations; 2. Translate a situation into a mathematical statement involving direct variation; 3. Apply the concept of direct variation in solving real-life problems. If two variables x and y are so related that the ratio y over x is a non-zero constant k, then y is said to vary directly as x. That is, y=kx →k= k is called the constant of variation or the constant of proportionality. Activity 1 Let Me Practice to Translate First! Directions: Translate each into a mathematical statement. Write your answer on a separate sheet of paper. Example 1. The variable x varies as the square of y. Answer: x=ky or k= Example 2. The area A of a circle varies directly as the square of its radius r. Answer: A=kr2 where: k=π Now try these: 1. The variable x varies as the square root of y. 2. The length L of an object is directly proportional to the width w of the object. 3. The perimeter P of a regular polygon varies directly as the length s of the side of the polygon. 4. The fare F of the passenger varies directly as the distance d of his destination. 5. The cost C of fish varies directly as its weight w in kilograms. 6. An employee’s salary S varies directly as the number of days d he has worked. 7. The length L of a person’s shadow at a given time varies directly as the height h of the person. 8. The distance D travelled by a car varies directly as its speed r. 9. The area A of a square varies directly as the square of its side s. 10.The cost of electricity C varies directly as the number of kilowatt-hour consumption.
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Answer:
10.The cost of electricity C varies directly as the number of kilowatt-hour consumption