If the growth rate of the number of bacteria at any time t is proportional to the number present at t and doubles in 1 week, how many bacteria can be expected after 2 weeks?

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A: L.H.S. =sinθ2-cosθ22R.H.S. =1-sinθ

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A: 1)Residue of f(z) about z=a is, The coefficient of (z-a)-1 in the Laurent series of f(z) about z=a2)…

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Q: d) Find the twenty-first term. e) Compute the sum of the first twenty-one terms.

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Q: Prove that sin 0 COS 0 2 2 = 1 - sin 0.

A: 1. sin2θ+cos2θ=1 2. sin2θ=2sinθcosθ

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Q: V= 2r Sto si Si D (r² cos + +) dz dr d +

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Q: By Cramer's Rule of determinants we know that we can solve the system of equations -6x y = 9 -3x 5y…

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A: one needs to simplify it.

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Q: 7) Solve the following system of equations below by the matrix inverse method. Show your work. x + y…

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Q: How many different numbers can be formed by various arrangements of the six digits 1, 1, 1, 1, 2, 3

A: Please refer to the solution in next step.

Q: Use mathematical induction to prove that, for n ≥ 1, n³ – n is divisible by 3.

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