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SPECIALIST MATHS

SPECIALIST MATHS. Calculus Week 4 Related Rates. Related Rates. Related rate give relationship between two or more variables whose value are changing with time.

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SPECIALIST MATHS

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  1. SPECIALIST MATHS Calculus Week 4 Related Rates

  2. Related Rates • Related rate give relationship between two or more variables whose value are changing with time. • An example could be the relationship in the rate of change in the radius of a balloon to the rate of change in its volume as it is being blown up.

  3. RELATED RATES Problem Solving Techniques • Draw a large clear labeled diagram • Write down information • Distinguish between variables and constants • Write an equation connecting the variables • Differentiate the equation with respect to time • Solve for the given case

  4. Ideas for writing an equation between variables and constants • Pythagoras's theorem • Similar triangles • Right angled triangle trigonometry • Sine and Cosine rules

  5. Example 7 Car P leaves town A at 1:30pm moving north at 60 km/hr. At 2:30pm car Q leaves town A moving east at 80 km/hr. At what rate is the distance between cars P and Q changing at 3:30pm.?

  6. Solution to example 7 P A Q

  7. Continued

  8. Example 8 The surface area of a balloon is increasing at a rate of 8cm2/sec Find the rate that the air is being pumped into the balloon, ( ie the rate the volume of air in the balloon is increasing) the instant when the radius is 10 cm.

  9. Solution to Example 8

  10. Continued

  11. Example 9 (using trig) An observer watches a rocket being launched at a distance of 1000 km from the launch pad. At the instant when the angle of elevation of the rocket is 45o the angle is changing at a rate of 1 radian per second. Determine the vertical velocity of the rocket at this instant.

  12. Solution to Example 9

  13. Continued

  14. This Week • Text pages 226 to 232, and 247 t0 250. • Exercise 6F Q 1 – 12 • Exercise 7C Q 1 - 9

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