Make up a scheduling problem that would be of some interest to you, similar to what we did in Exercise 67. Use graph theory to develop a solution.
Assume that the registrar at your school is building a final exam schedule and because the following courses are known to be particularly difficult, the registrar does not want any student to take finals for two of them on the same day. The courses are Anth215, Bio325, Chem264, Mat311, Phy212, Fin323, and ComD265. The table indicates which courses have students in common and therefore should have their finals on different days. Assume that two courses are related if they have any students in common. Model this set of courses with a graph and use it to design a final exam schedule.
Course | Has students in common |
Anth215 | Bio325, Chem264, Mat311, Fin323, ComD265 |
Bio325 | Chem264, Fin323 |
Chem264 | Mat311, Phy212 |
Mat311 | Phy212, Fin323, ComD265 |
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Chapter 4 Solutions
MYLAB W/ETEXT FOR MATHEMATICS ALL AROUN
- Complete the table. Enter DNE if a quantity doesn't exist or NEI if not enough information is given. f(c) limx-->c- f(x) limx-->c+ f(x) limx -->c f(x) continuity at x=c 2 4arrow_forwardFind the indefinite integral. (Use C for the constant of integration.) 9x arcsin(x) dxarrow_forwardFind the indefinite integral using the substitution x = 5 sin(e). (Use C for the constant of integration.) 1 dx (25-x²)3/2arrow_forward
- Find the indefinite integral using the substitution x = 7 sec(0). (Use C for the constant of integration.) √ ׳ √x² - 49 dxarrow_forwardUse the Cauchy Riemann equations (polar form version). Also, describe what happens at the branch cut.arrow_forwardb. i. Show that the following matrix is orthogonal. A = ドードー ii Find the inverse of matrix A. Show all working in an organized/orderly manner. 2 3 -619 A = 42 3 1 5 B-1127) a. Given D = , decode the following message: 32, 24, 42, 28, 24, 40, 50, 60, 132, 96, 12, 24arrow_forward
- 2 Graph of h 6. The graph of the function h is given in the xy-plane. Which of the following statements is correct? , the graph of h is increasing at an increasing rate. (A) For (B) For (C) For 苏|4 K|4 π π , the graph of h is increasing at a decreasing rate. 2 0 and b>1 (B) a>0 and 01 (D) a<0 and 0arrow_forwardQUESTION 4 Peter says that the following expressions can be simplified into one trigonometric ratio without the use of a calculator. Prove that Peter is correct by simplifying the following expressions into one trigonometric ratio: 4.1 sin 43° + sin 17º (5)arrow_forward3. Consider the sequences of functions fn: [-T, π] → R, sin(n²x) n(2) n (i) Find a function f : [-T, π] R such that fnf pointwise as n∞. Further, show that f uniformly on [-T,π] as n→ ∞. [20 Marks] (ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7,π]? Justify your answer. [10 Marks]arrow_forwardAmong a student group 54% use Google Chrome, 20% Internet Explorer, 10% Firefox, 5% Mozilla, and the rest use Safari. What is the probability that you need to pick 7 students to find 2 students using Google Chrome? Report answer to 3 decimals.arrow_forwardQuestion 3 a. Using Laplace theorem, find the determinant of the following matrix. 3 5 2 4 1 3 7 6 A= 2 48 3 569 7arrow_forwardSamples of rejuvenated mitochondria are mutated (defective) with a probability 0.13. Find the probability that at most one sample is mutated in 10 samples. Report answer to 3 decimal places.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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