Question

Assignment 5: Introduction to MATLAB Calculations & Plotting 1. The surface to volume ratio of the earth is 7.5753 x 10 diameter for the earth. miles. Determine an approximate 2. The length L of a belt that traverses two pulley wheels, one of radius R and one of radius r and whose centers are distance S apart is given by L 2Scose+ T(R + r) + 20(R-r) where 0 = sin (R-r)/S) Determine L when R 30 cm, r -12 cm, and S -50 cm. (Remember MATLAB likes angles in radians). 3. A geometric series is defined as the sequence 1, x, x', x... in which the powers of x range over the integers from 0 to infinity. The sum of the terms in a geometric series converges to the limiting value of 1/ (1-x) if |x| < 1; otherwise the terms diverge. For x 0.63, compute the sum of the first 11 terms in the series, and compare the result a with the limiting value. Repeat for 51 and 101 terms. Do this by generating a vector of integers to use as the exponent of x; then use the sum function. I Repeat part (a) using x= -0.63. b. A water tank consists of a cylindrical part of radius r and height h, and a hemispherical top. The 4. tank is to be constructed to hold 500 m of fluid when filled. The surface area of the cylindrical part is 2rrh, and its volume is trth. The surface area of the hemispherical top is given by 2Tur and its volume is given by 2Ttr/3. The cost to construct the cylindrical part of the tank is $300.00/m2 surface area; the hemispherical part costs $400.00/m2. Plot the cost versus r for the interval 2 m <r< 10 m, and determine the radius that results in the least cost. Compute the corresponding height, h. At Edsel Automotive, the management team is planning to expand one of its plants by adding a 5. new assembly line for sport utility vehicles (SUVS). The cost of setting up the new SUV assembly line is estimated at $7 million. The cost of manufacturing (raw materials, labor, etc.) an SUV is $36,000 and the company is planning to sell each SUV for $38,500. Industrial engineers at Edsel say that the new assembly line will roll off nine SUVS a day. How many days will it take for the company to be at the break-even point? First solve this problem algebraically, and then make a graph of cost vs. quantity and revenue vs. quantity (on the same graph). Verify the algebraic answer using the graph.

Answer 1

Let the be a earth Then rjfau tphane arua Volume sphere 3 uhers Hadies aphee Auafaue New -4 7-5753 xlo aula y tanth miles Volume eavrth 7-5753 xIo 3 -4 3 7-5753 x1o 7-5753 x lo d diameteu where eark 7-5753110 miles 7-9205 x10