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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...

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2422 Views

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

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Answered by William P. Python tutor
1431 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...

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Answered by Jamie D. Maths tutor
4050 Views

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
1780 Views

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...

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Answered by William P. Maths tutor
10162 Views

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