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Makovka662 [10]
3 years ago
10

How can I prove Euler's formula graphically?

Mathematics
2 answers:
lawyer [7]3 years ago
5 0

Answer:

We can now prove Euler's formula (v − e + f = 2) works in general, for any connected simple planar graph. Proof: by induction on the number of edges in the graph. Base: If e = 0, the graph consists of a single vertex with a single region surrounding it. So we have 1 − 0 + 1 = 2 which is clearly right.

slamgirl [31]3 years ago
4 0
Don’t know sorry o don’t understand ur question
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Sergeu [11.5K]

Answer:

f)-2

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Answer:

I dont know

Step-by-step explanation:

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fgiga [73]

Answer:

A': (-1,3)

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Akimi4 [234]

Answer:

here you go mate. sorry I just calculated straight away since you needed it urgently.

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PLEASE HELP ASAP: TRIGONOMETRY
ratelena [41]

Recall that sine is the ratio of opposite over hypotenuse, so we say

sin(theta) = opposite/hypotenuse

If we have a triangle labeled as such in the diagram below, then we can use symbols to write sin(theta) = A/C

Similarly, cos(theta) = B/C since cosine is the ratio of adjacent over hypotenuse.

Then from here we use a bit of algebra to compute the left hand side of the given equation. The goal is to see if we can simplify it to 1.

\sin^2\left(\theta\right)+\cos^2\left(\theta\right)\\\\\left(\sin\left(\theta\right)\right)^2+\left(\cos\left(\theta\right)\right)^2\\\\\left(\frac{A}{C}\right)^2+\left(\frac{B}{C}\right)^2\\\\\frac{A^2}{C^2}+\frac{B^2}{C^2}\\\\\frac{A^2+B^2}{C^2}\\\\\frac{C^2}{C^2}\\\\1

So this shows that the left hand side is identically the same as the right hand side (both sides are 1), and it doesn't matter what you replace theta with. Theta can be any real number and the equation will always be true.

Note: if you're wondering how A^2+B^2 became C^2, it's because of the pythagorean theorem. So that's why this trig identity is often referred to as the pythagorean trig identity.

6 0
3 years ago
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