ALGEBRA 2 WKST - Sault Ste. Marie Area Public Schools ...



AP Name ________________________________________hr 4

Worksheet

Section 5.1 Date ____/____/____ Score:________/ = ________%

1. A particle starts at x = 0 and moves along the x-axis with velocity [pic] for time [pic]. Where is the particle at t = 4?

2. A particle starts at x = 0 and moves along the x-axis with velocity [pic]for time [pic]. Where is the particle at t = 4?

3. A particle starts at x = 0 and moves along the x-axis with velocity [pic]for time[pic]. Where is the particle when t = 4? Approximate the area under the curve using four rectangles of equal width and heights determined by the midpoints of the intervals.

4. A particle starts at x = 0 and moves along the x-axis with velocity [pic]for time[pic]. Where is the particle when t = 5? Approximate the area under the curve using five rectangles of equal width and heights determined by the midpoints of the intervals.

For the following questions refer to the region R enclosed between the graph of the function [pic]and the x-axis for [pic].

5. (a) Sketch the region R.

(b) Partition [0,2] into 4 subintervals and show the four rectangles that LRAM uses to approximate the area of R.

Compute the LRAM sum without a calculator.

6. Repeat 5 (b) for RRAM and MRAM.

7. Make a conjecture about the area of region R.

8. Use RAM to estimate the area of the region enclosed by the graph of [pic]and the x-axis for [pic]where a = 1 and b=3.

9. The following table gives dye concentrations for a dye-concentration cardiac-output determination. The amount of dye injected in this patient was 5mg instead of 5.6mg. Use rectangles to estimate the area under the dye concentration curve and then go on to estimate the patient’s cardiac output.

|Seconds after injection |Dye Concentration |

|t |(adjusted for recirculation)|

| |c |

|2 |0 |

|4 |0.6 |

|6 |1.4 |

|8 |2.7 |

|10 |3.7 |

|12 |4.1 |

|14 |3.8 |

|16 |2.9 |

|18 |1.7 |

|20 |1.0 |

|22 |0.5 |

|24 |0 |

[pic]

10. You and a companion are driving along a twisty stretch of dirt road in a car whose speedometer works but whose odometer (mileage counter) is broken. To find out how long this particular stretch of road is, you record the car’s velocity at 10-sec intervals, with the results shown in the table below. (The velocity was converted from mi/h to ft/sec using 30mi/h = 44ft/sec.) Estimate the length of the road by averaging the LRAM and RRAM sums.

|Time (sec) |Velocity (ft/sec) |Time (sec) |Velocity (ft/sec) |

|0 |0 |70 |15 |

|10 |44 |80 |22 |

|20 |15 |90 |35 |

|30 |35 |100 |44 |

|40 |30 |110 |30 |

|50 |44 |120 |35 |

|60 |35 | | |

11. A reservoir shaped like a hemispherical bowl of radius 8m is filled with water to a depth of 4 m.

(a) Find an estimate S if the water’s volume by approximating the water with eight circumscribed solid cylinders.

(b) It can be shown that the water’s volume is [pic]. Find the error [pic]as a percentage of V to the nearest percent.

12. The nose “cone” of a rocket is a paraboloid obtained by revolving the curve [pic]about the x-axis , where x is measured in feet. Estimate the volume V if the nose cone by partitioning [0,5] into five subintervals of equal length, slicing the cone with planes perpendicular to the x-axis at the subintervals’ left endpoints, constructing cylinders of height 1 based on cross sections at these points, and finding the volumes of these cylinders. (See accompanying figure)

[pic]

13. Repeat problem 12 using cylinders based on cross sections at the midpoints of the subintervals.

14. Oil is leaking out of a tanker damaged at sea. The damage to the tanker is worsening as evidenced by the increased leakage each hour, recorded in the table below.

Time (h) |0 |1 |2 |3 |4 |5 |6 |7 |8 | |Leakage (gal/h) |50 |70 |97 |136 |190 |265 |369 |516 |720 | |(a) Give an upper and lower estimate of the total quantity of oil that has escaped after 5 hours.

(b) Repeat part (a) for the quantity of oil that has escaped after 8 hours.

(c)The tanker continues to leak 720 gal/h after the first 8 hours. If the tanker originally contained 25,000 gal of oil, approximately how many more hours will elapse in the worst case before all of the oil has leaked? In the best case?

15. The graph shows the sales record for a company over a 10-year period. If sales are measured in millions of units per year, explain what information can be obtained from the area of the region, and why.

[pic]

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