Warm-up 8-7 HW 99, #9 HW 99, #18.

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Warm-up 8-7 HW 99, #9 HW 99, #18

Lesson 8-7 Quadratic Variation Objectives: Students will: Be able to find equations of direct, inverse, and joint quadratic variation Solving problems involving quadratic variation

Quadratic Variation 3 possibilities 1) Direct → y = kx2 “y varies directly with the square of x” 2) Inverse → “y varies inversely with the square of x” 3) Joint → y = kxz “y varies jointly with x and z”

Writing Variation Equations Choose equation Decide x, y (and z) Write general equation Plug in values Solve for k Re-write equation with k-value

Example 1 Find the equation of variation where y varies inversely as the square of x, and y = 2 when x = 3. Example 2 Find an equation of variation where y varies jointly as x and z, and y = 2, when x = 3, and z = 4.

Example 3 The intensity I of the light from a lamp varies directly as the wattage W of the lamp and inversely as the square of the distance D from the lamp. The intensity is 10 units when a 100-watt bulb is used at a distance of 20 feet. What is the intensity if a 75-watt bulb is used at 25 feet. Example 4 The force of attraction F between two magnets varies inversely as the square of the distance D between them. The force is 5 newtons when the magnets are 2 cm apart. What is the force when the magnets are 5 cm apart?

HW 100