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Prove by induction that f(n) = 2^(k + 2) + 3^(3k + 1) is divisible by 7 for all positive n.

First we establish our base case: f(0) = 22 + 31 = 4 + 3 = 7, so clearly f(0) is divisible by 7.Now. by the inductive hypothesis. we assume that f(k) is divisible by 7, and attempt t...

Answered by William P. Further Mathematics tutor
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How do you define a class in python

Here's a simple example of a class:class Animal: def init(self, name, noise): self.name = name self.noise = noise def make_noise(self): print(self.noise) here init

Answered by William P. Python tutor
1332 Views

how do I solve the equation x^2 + 7x + 11 = 0, to 3dp?


This is a quadratic equation and there are three ways to solve one. This question specifies that the answer should be left to three decimal places. This tells you that you can not factorise, as your...

Answered by Jamie D. Maths tutor
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Let f (x) = 5x and g(x) = x2 + 1 , for x ∈  . (a) Find f-1(x) . (b) Find ( f ° g) (7) .

a,y=5xfinding the inverse: x=5y - dividing by 5 (1/5)x=y f-1(x)=(1/5)x
b,5x(72+1)=250

Answered by Maths tutor
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Differentiate f = ln(x^2 + 1) / (x ^ 2 + 1).

We'll apply the quotient rule using "u = ln(x2 + 1)" and "v = x2 + 1". First we'll need to calculate u' and v'.Using normal differentiation rules, we can see &quo...

Answered by William P. Maths tutor
9575 Views

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