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In Exercises 1–28, compute the products. Some of these may be undefined. Exercises marked should be done by using technology. The others should be done in two ways: by hand and by using technology where possible. [HINT: See Example 3.]
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Finite Mathematics
- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1arrow_forwardSection 31 #28 - Generalizing Exercise 27, show that if √a+√b ≠ 0, then ℚ(√a+√b ) = ℚ(√a,√b ) for all a and b in ℚ. [Hint: Compute (a - b) / ℚ(√a+√b ).] [Exercise 27 - Prove in detail that ℚ(√3+√7) = ℚ(√3,√7).] I have exercise 27 completed...how would I generalize this?arrow_forwardIn this question, pA(x) denotes the characteristic polynomial of an n × n matrix A and mA(x) denotes its minimal polynomial. (a) Working over R, find pA(x) and mA(x) for 0 2 4A= 4 2 0 0 0 3 , which is a 3x3 matrix (b) Can the matrix in part (a) be diagonalised over R? Justify your answer. (c) Repeat parts (a) and (b) with R replaced by F5arrow_forward
- Find a polynomial of degree n=4 that has the given zero(s) x = −4, −1arrow_forwardThe populations, P, of six towns at time t in years are given by(i) P=2,090(1.08)t(ii) P=560(1.12)t(iii) P=2,700(0.9)t(iv) P=1200(1.18)t(v) P=800(0.78)t(vi) P=2000(0.99)t (a) Which towns are growing in size? Which are shrinking? Select all that apply.Growing towns: (i) (ii) (iii) (iv) (v) (vi) Shrinking towns: (i) (ii) (iii) (iv) (v) (vi) (b) Which town is growing the fastest? What is the annual percent growth rate for that town?Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) is growing the fastest. It is growing at a rate of % per year. (c) Which town is shrinking the fastest? What is the annual percent decay rate for that town? Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) is shrinking the fastest. It is shrinking at a rate of % per year. (d) Which town has the largest initial population (at t=0)? Which town has the smallest?Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) has the largest…arrow_forward1. Write a formal proof of Theorem 2.13arrow_forward
- homogenous DE 3udv-vdv-udu-vdu=0arrow_forward25. The populations, P, of six towns with time t in years are given by (i) P = 1000(1.08)t (ii) P = 600(1.12)t (iii) P = 2500(0.9)t (iv) P = 1200(1.185)t (v) P = 800(0.78)t (vi) P = 2000(0.99)t (a) Which towns are growing in size? Which are shrinking?arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage