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- Rouché's theorem for p(z)=z^6−5z^4+z^3-2z ;|z|=13. using Jacobi Method, determine Y4if initial guess X1= 5, Y1= 4, Z1 = 3. 5. sing Jacobi Method, determine Z4if initial guess X1= 5, Y1= 4, Z1 = 3.A field is delimited to the north by the streets y= e^x and y= e^-2x, to the south by the street y=0, to the west by the road x= -ln2 and to the east by x = ln3. Find the area of this field, considering that the x and y variables are expressed in km.
- proof (1+||x+y||) ≤ (1+||x||)(1+||y||) for all x,y element of RThe product rate of an assembly line is given by: dr/dt=3t^2-10t+10 Where t is the time in hours and dr/dt is the production rate per hour. a.) Approximate the number of items produced during the first 8 hours by usinf LRAMwith n=4. Show all work including graph and rectangles. b.) Find the exact number of items produced during the first 8 hours by using the fundamental therom of calculus.Using Method of Undetermined Coefficients to find the complete solution of the ODE.
- max z = x1 + 3x2 s.t. x1 + 2x2 ≥ 6 2x1 + x2 ≤ 8 x1, x2 ≥ 0 For the LP above, which of the following is its standard form? max z = x1 + 3x2 s.t. x1 + 2x2 + s1 = 6 2x1 + x2 + s2 = 8 x1, x2, s1, s2 ≥ 0 max z = x1 + 3x2 s.t. x1 + 2x2 – e1 = 6 2x1 + x2 – e2 = 8 x1, x2, e1, e2 ≥ 0 max z = x1 + 3x2 s.t. x1 + 2x2 + s1 = 6 2x1 + x2 – e2 = 8 x1, x2, s1, e2 ≥ 0 max z = x1 + 3x2 s.t. x1 + 2x2 – e1 = 6 2x1 + x2 + s2 = 8 x1, x2, e1, s2 ≥ 0To find P(0 ≤ Z ≤ 1.37) using Appendix C-1, find the row containing ---- in the far left column. Then find the column containing ---- in the top row.With reference to the attached scenario: The 100 meter diameter wheel needs to be designed so that it rotates at a constant rate and every complete revolution takes 15 minutes. The wheel has been installed in a vertical plane and the lowest seat is 2m above the ground surface. Each ride consists of only one full rotation. 1) Using calculus, determine what the maximum horizontal and vertical speeds of the rider would be and at which points during the ride they occur. 2)State expressions for the acceleration of the rider in both horizontal and vertical directions and show that the resultant acceleration experienced by the rider is independent of where on the ride he/she might be.
- 1) show that a GP has a limiting sum if 0<1-r < 2 2) by calculating the common ratio show that there is no GP with 1st term 8 and limiting sum 2. 3) a GP has positive 1st term a and has a limiting sum Sinfinite , show that Sinfinite > (1/2 )a. 4) fjind the reange of values of the limiting sum of a GP with i) a = 6 , ii) a = -8, iii) a>0 iv) a<0a) Check that the functions e^x, e^-x,coshx are solutions of y'''-y'=0 b) show directly that W(e^x, e^-x,coshx)=0 and conclude that these functions do not form a fundamental set c)Find a fundamental set of solutions by inspection. Justify your answer by computing the wronskianThe ELISA test is used to screen donated blood for the AIDS virus. It is estimated that 0.5% of the population is infected by the AIDS virus. The accuracy of the test is 97.7%; that is, a sample with the AIDS virus is correctly identified to be carrying the virus 97.7% of the time [P(POSITIVE | AIDS) = 0.977]. The specificity of the test is 92.6%; a healthy blood sample is correctly diagnosed 92.6% of the time [P(NEGATIVE | NO AIDS) = 0.926]. Using BAYES THEOREM: Starting with a population of 1,000,000 bottles of donated blood, find the number of bottles in each of the following four categories: AIDS Infected which tested POSITIVE AIDS Infected that tested NEGATIVE NO AIDS Infected that tested POSITIVE NO AIDS Infected that tested NEGATIVE. Discuss the false positive and false negative results. Should ELISA’s credibility be questioned?