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AP Calculus BC Tuesday, 23 September 2014

AP Calculus BC Tuesday, 23 September 2014. OBJECTIVE TSW implicit differentiation to solve related rates applications. Checkerboard, Please. You will be given 20 minutes to complete Part II (no calculator) of the test. NOTE: A normal line is perpendicular. TOMORROW/THURSDAY

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AP Calculus BC Tuesday, 23 September 2014

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  1. AP Calculus BCTuesday, 23 September 2014 • OBJECTIVETSW implicit differentiation to solve related rates applications. Checkerboard, Please. • You will be given 20 minutes to complete Part II (no calculator) of the test. • NOTE: A normal line is perpendicular. • TOMORROW/THURSDAY • ASSESSMENT: Derivatives • I choose the partners.

  2. Related Rates Area formulas for common shapes (these should be memorized!): Rectangle Equilateral Triangle Square (one side is s) Hexagon Circle Ellipse Trapezoid General Triangle

  3. Related Rates Volume formulas for common shapes (these should be memorized!): Rectanglar Prism Right Cylinder Cube (one side is s) Cone Sphere

  4. Related Rates Pythagorean Theorem (c the length of the hypotenuse): Regardless of the type of related rates application – circles, spheres, triangles, etc. – proper units and correct labels must always be used.

  5. Related Ratesapplications deal with the rate at which one quantity changes with respect to another quantity, usually time. So, instead of using what we have been, dy/dx, which gives the rate at which y changes with respect to x, we’ll now use other variables to see how things change wrt(with respect to)time. Ex:dA/dt rate of change of area wrt time dT/dt rate of change of Temp wrt time dx/dt rate of change of xwrt time Remember: A rate of change is a derivative!!!

  6. Ex:The radius of a circle is increasing at a rate of two inches per minute. Find the rate of change of the area when the radius is six inches. We need the area formula for a circle: What is the rate of change of area wrt time? (That is, what is dA/dt)? We want dA/dt when r = 6 in. This is called the general differential equation.

  7. Assignment • Related Rates Packet #1: • #1 – 9 all • Use a separate sheet of notebook paper. • Show all work. • Due on Friday, 26 September 2014. • TOMORROW/THURSDAY • ASSESSMENT: Derivatives • I choose the partners.

  8. AP Calculus BCWednesday, 24 September 2014 • OBJECTIVE TSW (1) take an assessment on derivatives, and (2) continue working with related rates. PARTNERS • Robyn Yeh & Sara Preza • Anna Ly & Trang Lam • Nhat Dam Tang & Thomas Nguyen • Kevin Le & James Cody • ArvanhPchan, Jacob Egliht, & Zach Stachowiak • Jade Harrison & Jennifer Vu • Enoc Balderas & Ryan Haney You will have 50 minutes to finish the assessment. You may use a calculator but no notes. Turn in to me when you finish.

  9. RELATED RATES Examples:Circles and Spheres 2) 3) 4) 5)

  10. Related Rates: Triangles & Cones • For triangles and cones (and light poles, shown Friday), labeled pictures are required (even if no directions require them).

  11. Pythagorean Theorem Application Ex:A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of two feet per second. How fast is the top moving down the wall when the base is seven feet from the wall?

  12. Ex:A small balloon is released at a point 150 feet away from an observer, who is on level ground. If the balloon goes straight up at a rate of 8 feet per second, how fast is the distance from the observer to the balloon increasing when the balloon is 50 feet high?

  13. Cones Application Ex:At a sand-and-gravel plant, sand is falling off a conveyor and onto a conical pile at the rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when it is 15 feet high?

  14. Ex:Water is pouring into a conical cistern at the rate of 8 cubic feet per minute. If the height of the cistern is 12 feet and the radius of its circular opening is six feet, how fast is the water level rising when the water is four feet deep?

  15. Assignment • Related Rates Packet #1: • Use a separate sheet of notebook paper. • Show all work. • #1 – 9 all • Due on Friday, 26 September 2014. • #11 – 25 odd • Due on Monday, 29 September 2014.

  16. Light Poles Application Ex:A man six feet tall walks at a rate of five feet per second away from a light that is fifteen feet above the ground. When he is ten feet from the base of the light, a) at what rate is the tip of his shadow changing? b) at what rate is the length of his shadow changing?

  17. Light Poles Application Ex:A light is at the top of a 16-foot pole. A girl 5 feet tall walks away from the pole at a rate of 4 feet per second. a) At what rate is the tip of her shadow moving when she is 18 feet from the pole? b) At what rate is the length of her shadow increasing?

  18. Assignment • Related Rates Packet #1: • #27 – 37 all • Use a separate sheet of notebook paper. • Show all work. • Due Tuesday, 30 September 2014.

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