Question Solved1 Answer The motion of a parachutist free-falling from rest from a stationary helicopter is given by the differential equation dy v=9.8 -0.002v2 dx where x m is her distance below the helicopter and v ms' is her velocity. Solve the differential equation to show that y= = 70(1-e e 0.004x))/2 [6]

3.4-15. Oxbridge University maintains a powerful mainframe computer for research use by its faculty, Ph.D. students, and research associates. During all working hours, an operator must be available to operate and maintain the computer, as well as to per- form some programming services. Beryl Ingram, the director of the computer facility, oversees the operation. It is now the beginning of the fall semester, and Beryl is con- fronted with the problem of assigning different working hours to her operators. Because all the operators are currently enrolled in the university, they are available to work only a limited number of hours each day, as shown in the following table. Maximum Hours of Availability Operators Wage Rate Mon. Tue. Wed. Thurs. Fri. 6 K. C. D. H. H. B. S. C. K. S. N. K. $25/hour $26/hour $24/hour $23/hour $28/hour $30/hour 6 0 4 5 3 Oo oo ao 8 5 4 5 3 0 6 0 0 8 6 Joao There are six operators (four undergraduate students and two graduate students). They all have different wage rates because of differences in their experience with computers and in their pro- gramming ability. The above table shows their wage rates, along with the maximum number of hours that each can work each day. Each operator is guaranteed a certain minimum number of hours per week that will maintain an adequate knowledge of the operation. This level is set arbitrarily at 8 hours per week for the undergraduate students (K. C., D. H., H. B., and S. C.) and 7 hours per week for the graduate students (K. S. and N. K.). The computer facility is to be open for operation from 8 A.M. to 10 P.M. Monday through Friday with exactly one operator on duty during these hours. On Saturdays and Sundays, the computer is to be operated by other staff. Because of a tight budget, Beryl has to minimize cost. She wishes to determine the number of hours she should assign to each operator on each day. (a) Formulate a linear programming model for this problem.

Identify each variable as quantitative or qualitative.a) ethnic origin of a candidate for public officeb) score (0-100) on a placement examinationc) fast-food establishment preferred by a student(McDonald's, Burger King, or Carl's Jr.)d) mercury concentration in a sample of tuna

•• An infinite slab of charge of thickness 2zo lies in the xy-plane between z = -zo and 46. z = +z0. The volume charge density p (C/m³) is a constant. a. Use Gauss's law to find an expression for the electric field strength inside the slab (-zo zo). c. Draw a graph of E from z = 0 to z = 3z0.

Exercise 5 : Two particles in a potential well Consider two noninteracting particles, both of mass m, in a quadratic potential well (i.e. har- monic oscillator potential). For the case with one particle in the single-particle state [n) and the other in state k) (n + k), calculate the expectation value of the squared interparticle spacing ((21 – 222) assuming: 5.1 The particles are distinguishable 5.2 The particles are identical spin-o bosons 5.3 The particles are identical spin-1/2 fermions in a spin triplet state. Hint: use bra-ket notation as much as possible. Remember that for the harmonic oscillator it is easiest to use, whenever possible, raising and lowering operators to evaluate expectation values (i.e. to evaluate integrals).

Problem 4 A new test is developed for cancer detection with sensitivity 0.80 and specificity 0.91. Assume this cancer affects 6% of the population. (a) Sketch the probability tree for this test and label each branch appropriately. (b) Calculate the Bayes probability that an individual has cancer if their test result is posi- tive. (c) Calculate the Bayes probability that an individual does not have cancer if their test result is negative. (d) Compute a naive Bayes estimate for either b or c. Your choice! Then, briefly explain why is this referred to as "naive".

Activity #2 6. Using the chart provided in Lecture Module 2/Slide 71, what star would have been the North Star in 1000 BC? pts 7. (a) Bailey's beads occur during what type of eclipse? (Hint: There are 3 types of solar eclipses and 3 types of lunar eclipses. or these 6 types of eclipses, Bailey's beads can be seen only during 1 of them.] Part 10 pts (b) What Activity #2 6. Using the chart provided in Lecture Module 2/Slide 71, what star would have been the North Star in 1000 BC? pts 7. (a) Bailey's beads occur during what type of eclipse? (Hint: There are 3 types of solar eclipses and 3 types of lunar eclipses. or these 6 types of eclipses, Bailey's beads can be seen only during 1 of them.] Part 10 pts (b) What causes Bailey's beads to form? Part b = 10 pts 8. During an annular eclipse of the Sun, we see a bright annulus or "ring of fire." During a total solar eclipse we see the corona during totality. In both events, the Moon is directly in line with the Sun and Earth. What differentiates these two types of solar eclipses? That is what aspect of the eclipse geometry has changed to create an annular eclipse rather than a total eclipse? 115 pts