Which anine i color Annie no link or bot

Mathematics

1 answer:

rusak2 [61]2 years ago

6 0

Letter B or π is an irrational number, therefore it's the answer.

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Let x,y \epsilon R. Use mathmatical induction to prove the identity.

mariarad [96]

Step-by-step explanation:

We will prove by mathematical induction that, for every natural n,

$(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=x^{n+1}-y^{n+1}$

We will prove our base case (when n=1) to be true:

Base case:

$(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=(x-y)(x^{1}+y^{1})=x^2-y^2=x^{1+1}-y^{1+1}$

Inductive hypothesis:

Given a natural n,

$x^{n+1}-y^{n+1}=(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})$

Now, we will assume the inductive hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

Observe that, for y=0 the conclusion is clear. Then we will assume that $y\neq 0.$

$(x-y)(x^{n+1}+x^{n}y+...+xy^{n}+y^{n+1})=(x-y)y(\frac{x^{n+1}}{y}+x^{n}+...+xy^{n-1}+y^{n})=(x-y)y(\frac{x^{n+1}}{y})+(x-y)y(x^{n}+...+xy^{n-1}+y^{n})=(x-y)y(\frac{x^{n+1}}{y})+y(x^{n+1}-y^{n+1})=(x-y)x^{n+1}+y(x^{n+1}-y^{n+1})=x^{n+2}-yx^{n+1}+yx^{n+1}-y^{n+2}=x^{n+2}-y^{n+2}\\$

With this we have proved our statement to be true for n+1.

In conlusion, for every natural n,

$(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=x^{n+1}-y^{n+1}$

8 0

3 years ago

4. What is the experimental probability of spinning orange?

9966 [12]

Answer:6/25

To get this you just add up all the spins which equals 50 so this then means 50 is your denominator
Then because it’s asking for the orange you need to look at the orange colom and it say 12 so this is then this is the numerator
So it would be 12/50 but you can make this smaller so you divide by 2 and get 6/25

Hope this helped!