Question 10 (3 marks) Attempt 3 The three cubic roots of 10 rexp(ayme), rexp(agne), rexp(azmi) where...
Please use Python
Problem 2: 10 pts - Here is a cubic polynomial with three closely spaced real roots: p(x) = 580x4-2320x3-1 160x2 + 6960-1740 What are the exact roots of p? . Plot p(x) for -2 x 3 4. And plot the location of the four roots on the graph. Starting with xo2, what does Newton's method do? . Starting with 0.3 and xi0.9, what does the secant method do? Starting with the interval [0.5, 2.9, what does bisection...
The purpose of this question is to calculate the three cubic roots of a complex number. A complex number is of the form a + ib where i is v-1. The magnitude r of a complex number is Vab. The complex number a + ib can be written as r(cos θ + i sin θ). Therefore a -r cose and b rsin0 and b/a (r sin0)/(r cos0) - tane e- arctan(b/a). The 3 cubic roots of a complex number are...
Question 3.1 (10 marks) Consider the two complex numbers-V3+i and 2 3 cis(-/3) a) Write 1V3+i in polar form, in terms of its principal argument. b) Use your answer in a) to evaluate z1/21 in polar form, and then convert that into cartesian form. c) Using their polar forms, determine z122 and z2/句in terms of their principal argument. d) Determine (22)2 in polar form, in terms of its principal argument. e) Determine all distinct values of (22)1/3 in polar form,...
Question 10 (2 marks) Attempt 1 Use Green's theorem in the plane to evaluate '(17cy-3x)d3sy2 dy K anti-clockwise around the closed path C given by the curves: y=0, 1 sxs 3, r 3, 0 s0 s T, y 0, -3 sxs-1, r 1, TT2 0 2 0. Evaluate the line integral as a double integral using polar coordinates. Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression For example: 10.13906368...
[10 marks] Question 2: A cylindrical specimen of a ceramic material is loaded using the three-point bending mode. Calculate () the minimum possible radius (in mm) of the specimen without fracture; (ii) the flexural modulus where the deflection of the sample is 0.45 mm, assuming that no plastic deformation occurs. Given that the applied load is 460 N, the flexural strength is 113 MPa, and the separation between load points is 50 mm. a) If cupric oxide (CuO) is exposed...
Question 2 Consider the system shown in Figure Q2, where Wis a unit step disturbance and R is a unit step input. 0.4 s+ 1 10 Figure Q2 (5 marks) (3 marks) (c) Find the value for K so that the steady state error due to w(t) is less than 0.01; 6 marks) (d) In order to eliminate the steady state error, show whether a PI controller can be successful 6 marks) (a) Find the expression of E(s)-R(s)-Y(s) in terms...
Question 2 Consider the system shown in Figure Q2, where Wis a unit step disturbance and R is a unit step input. 0.4 s+ 1 10 Figure Q2 (5 marks) (3 marks) (c) Find the value for K so that the steady state error due to w(t) is less than 0.01; 6 marks) (d) In order to eliminate the steady state error, show whether a PI controller can be successful 6 marks) (a) Find the expression of E(s)-R(s)-Y(s) in terms...
Question 3 [10 marks] The Beetle Manufacturing Company produces the following three products: Screwdrivers Saws Hammers R40 R28 R16 Selling price per unit Variable costs per unit Contribution per unit R50 R12 R30 R12 R4 R20 Fixed costs are R76,000 per year. 50% of all sales in units are hammers, 30% are screwdrivers, and 20% are saws. Required: Calculate the following values: A. break-even point in total units. B. Number of hammers that will be sold at break-even. Total sales...
QUESTION 3 10 marks You are considering the purchase of a new automated CNC machining centre for your company's manufacturing division. The required capital is $3,300,000. The planned life of this machine is estimated at 1 years, after which the salvage value will be $450,000. You have calculated that this machining centre will enable the machining of precision components 24 hours per day (thus increasing gross revenue by $650,000 annually) and more efficiently (by reducing annual labor costs by $180,000)....
Question 3 A 10 m square and 7.5 m deep pit is to be excavated in a soil with a unit weight of 20 kN/m2. What is the stress relief at 2 m. 5 m and 10 m below the centre point of the bottom of the excavation? b. The circular flexible area is uniformly loaded (q 320 kN/m2). Determine the change in vertical stress: i. at point A At a point 2 m below point A 4 m A...