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Applications of RAM

Applications of RAM. Section 5.1b. The “Do Now” – p.255: #10. Time (sec). Velocity (in/sec). 20. 0 1 2 3 4 5 6 7 8 9 10. 0 12 22 10 5 13 11 6 2 6 0. 15. Velocity (in/sec). 10. 5. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Time (sec).

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Applications of RAM

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  1. Applicationsof RAM Section 5.1b

  2. The “Do Now” – p.255: #10 Time (sec) Velocity (in/sec) 20 0 1 2 3 4 5 6 7 8 9 10 0 12 22 10 5 13 11 6 2 6 0 15 Velocity (in/sec) 10 5 1 2 3 4 5 6 7 8 9 10 Time (sec) (a) Estimate distance with LRAM: 1(0 + 12 + 22 + 10 + 5 + 13 + 11 + 6 + 2 + 6) = 87 in = 7.25 ft

  3. The “Do Now” – p.255: #10 Time (sec) Velocity (in/sec) 20 0 1 2 3 4 5 6 7 8 9 10 0 12 22 10 5 13 11 6 2 6 0 15 Velocity (in/sec) 10 5 1 2 3 4 5 6 7 8 9 10 Time (sec) (a) Estimate distance with RRAM: 1(12 + 22 + 10 + 5 + 13 + 11 + 6 + 2 + 6 + 0) = 87 in = 7.25 ft

  4. Now let’s work through #12 on the same page!!! 50 40 30 Velocity (ft/sec) 20 10 110 120 10 20 30 40 50 60 70 80 90 100 Time (sec) Estimate for road length using LRAM: 10(0 + 44 + 15 + … + 30) = 3490 ft

  5. Now let’s work through #12 on the same page!!! 50 40 30 Velocity (ft/sec) 20 10 110 120 10 20 30 40 50 60 70 80 90 100 Time (sec) Estimate for road length using RRAM: 10(44 + 15 + 35 + … + 35) = 3840 ft

  6. Now let’s work through #12 on the same page!!! 50 40 30 Velocity (ft/sec) 20 10 110 120 10 20 30 40 50 60 70 80 90 100 Time (sec) 3490 ft + 3840 ft Average = = 3665 ft 2

  7. Using RAM to Approximate Volume Estimate the volume of a solid sphere of radius 4. First, graph the function: Now, imagine the sphere as the revolution of this function about the x-axis…

  8. Using RAM to Approximate Volume Estimate the volume of a solid sphere of radius 4. We partition the function into 8 subintervals of equal length and slice the sphere with planes perpendicular to the x-axis at the partition points. Look at the diagrams on p.251…

  9. Using RAM to Approximate Volume Estimate the volume of a solid sphere of radius 4. Each slice can be approximated by a cylinder: Radius: Height: Volume of each cylinder:

  10. Using RAM to Approximate Volume Estimate the volume of a solid sphere of radius 4. Use the RAM program: Function: Interval: [– 4, 4] Number of Slices (n) MRAM n 10 269.42299 25 268.29704 50 268.13619 100 268.09598 Let’s work with this last value…

  11. Using RAM to Approximate Volume Estimate the volume of a solid sphere of radius 4. Approximated volume: 268.09598 How close is this to the actual volume?: The error percentage is only about 5 thousandths of a percent! As a percentage of V :

  12. Using RAM to Approximate Volume Let’s try #20 on p.256… Volume of each of the cylinders: Use LRAM with on the interval [0,5], n = 5:

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