VIEWS: 128 PAGES: 19 POSTED ON: 8/15/2010
Direct and Inverse Variation Take notes when you see this animated pencil. Take Notes Objectives • Understand the specialized vocabulary • Know the basic algebraic equations that represent direct and inverse variation • Apply techniques for classifying the types of variation Direct Proportion Direct Variation Directly Proportional • A relationship between two variables in which one is a “constant multiple” of the other. When one variable changes the “other changes in proportion” to the first. • If y is directly proportional to x, the equation is of the form y = kx (where k is a constant). Example of Direct Variation • Equation: y = 3x x y y/x • Variable y is directly 0 3 0 proportional to x. 1 3 3/1=3 • Tripling x causes y to triple. 2 3 6 6/2=3 3 9 9/3=3 4 12 12/4=3 5 15 15/5=3 Graph of Direct Variation y = 3x y x Inverse Variation Inverse Proportion Inversely Proportional • A relationship where the “product of two variables is a constant”. When one variable increases the other decreases in proportion so that the “product is unchanged”. • If y is inversely proportional to x, the equation is of the form y = k/x (where k is a constant). Example of Inverse Variation • Equation: y = 48/x x y xy • Variable y is inversely 1 48 48 proportional to x. 3 2 24 1/3 48 • Tripling x causes y to one third. The product 3 16 48 of x and y is always 48. 4 12 48 6 8 48 8 6 48 Graph of Inverse Variation y 20 18 y = 48/x 16 14 12 10 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18 20 x Do the following Qs 1. If all the HKIS items in the Dragon Shop are on sale for 85%, what will be the new cost for the following: a) a T-shirt that costs $70 originally b) a windbreaker jacket that cost $130 originally Do the following Qs 2. If the scale on a map reads 0.25 in. : 4 mi, calculate the following: a) find the actual distance from Metropolis to Smallville which has a measured map distance of 9.25 in. b) find the map distance from Smallville to Roswell which has an actual distance of 268 mi. Do the following Qs 3. If model yachts are built to 1 in / 9 ft of the actual size, calculate the following: a) find the model length of a Blue Tooth yacht which is 120 ft long. b) find the actual length of a K2 yacht which has a model length of 9.5 in. Do the following Qs 4. Circle the correct terminology to make true statements. a) Knowing that the distance is equal to speed times time (d = st), in a 100 meters sprint, any speed is directly or inversely proportional to time? b) If the speed is constant, then any distance is directly or inversely proportional to time? Do the following Qs 5. Given that length and width are inversely proportional to a constant area of 90 m2, calculate the following: a) If the length is 15 m, what is the width? b) If you want to create a box with an area of 90 m2 that wraps around the Earth’s equator, you require a width of 38 million meters. What is the length of the box? Do the following Qs 6. Given that pressure (P) and volume (V) are inversely proportional to each other when temperature is constant, use P1V1 = P2V2 to calculate the following. a) If P1 = 1 atm and V1 = 4.5 Liters, find P2, if V2 = 1.5 L? b) If P1 = 0.5 atm and V1 = 4.5 Liters, find V2, if P2 = 1.0 atm? Do the following Qs 7. Circle the correct terminology to make true statements. In science, power (P) is defined by the work (W) done in a certain amount of time. P = W/t. a) If the work done is constant, then pressure is directly or inversely proportional to time? b) If the power is constant, then any work done is directly or inversely proportional to time? Do the following Qs 8. In order to have objects balanced on a double pan scale, the massleft times the distanceleft must equal to massright times the distanceright (mldl = mrdr). 50 g 20 g 15 cm Distance ? Calculate the distance needed away from the fulcrum (pivot) so that the 50g object will balance the left hand side. Do the following Qs 9. In order to have objects balanced on a double pan scale, the massleft times the distanceleft must equal to massright times the distanceright (mldl = mrdr). 5g Mass ? 25 g 15 cm 20 cm Calculate the mass needed to be placed 15 cm away from the fulcrum (pivot) so that it will balance the right hand side. Do the following Qs 10. In order to have objects balanced on a double pan scale, the massleft times the distanceleft must equal to massright times the distanceright (mldl = mrdr). 50 g 20 g 20 g 5 cm 5 cm Distance ? Calculate the distance needed away from the fulcrum (pivot) so that the scale is balance.