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AP Calculus AB Individual Project

AP Calculus AB Individual Project. FRQ 2005 #2 Rifatul Istiaque. Question. Giv e n. The equations for R(t) and S(t) R(t) represents how much sand is removed. S(t) represents how much sand is added by a pumping station. From 0 to 6 hours

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AP Calculus AB Individual Project

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  1. AP Calculus AB Individual Project FRQ 2005 #2 Rifatul Istiaque

  2. Question

  3. Given • The equations for R(t) and S(t) R(t) represents how much sand is removed. S(t) represents how much sand is added by a pumping station. • From 0 to 6 hours • At t = 0, there are 2500 cubic yards of sand on the beach.

  4. Part A First you need to set up an integral because R(t) is in cubic yards per hour and you need to find just cubic yards. This has to have a lower limit of 0 and upper limit of 6 to represent the 6-hour period. There are two ways to do this problem: Algebraically or using a Calculator.

  5. Algebraically Separation Substitution Method: u = dt du= dt du = dt 31.816

  6. 2. Click ENTER and put 0 for the lower limit and 6 for the upper limit and the equation of R(t). Calculator 1. Go to MATH  9 3. And then click enter once more to get your answer. Remember to include units in your answer.

  7. Part B This is asking for the total number of cubic yards. At the beginning, t=0,there are 2500 cubic yards. R(t) and S(t) have to be subtracted by each other in an anti-derivative from 0 to t because that gives the number of cubic yards from 0 to t.

  8. Part C First: Find the derivative of Y(t): Second: Plug in t=4 into the new equation. Y’(t) = () Y’(4) = () = -1.909

  9. 2. Enter the equation (), which is S(t) – R(t), into your calculator and click enter. Calculator 1. Make x equal to 4 by clicking 4  sto  x

  10. Part D In this derivative equation, you have to find the zero’s of the graph. For questions that ask you about the minimum and the maximum value, you have to find the derivative of the equation. You have to use the x-values where it goes to 0 on the derivative graph as well as the endpoints and plug it into the original equation to get the minimum value.

  11. 2. Find the zero(s) of the function. Go to 2nd Trace  2: zero. Move accordingly left and right to get the zero. Calculator 1. Graph S(t) – R(t) 3. Use this x value as well as your end points to determine where the smallest point is by plugging it into your original equation. X = 0 Y(0) = 2500 X = 6 Y(6) = 2493.2766 X = 5.1178653 Y(5.1178653) = 2492.3694 The amount of sand is at a minimum at x = 5.118 hours. The smallest value is 2492.3694.

  12. Citations • Collegeboard • TI 83 Flash Debugger • Snipping Tool • Google

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