Introduction This experiment focuses on two concepts. These concepts are Proportionality and Superposition theorems. Proportionality is a way to relate two quantities together. This means that when more input is supplied‚ you get more output which is proportional to the input. The Proportionality Theorem states that the response in a circuit is proportional to the source acting in the circuit. This is also known as Linearity. The proportionality constant (K) relates the input voltage to the
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should get the answer. (√3 – i)-10 We are using De Moivre’s Theorem to solve this problem. De Moivre’s Theorem: If z=r(cosθ + i sinθ)‚ then for any integer n‚ zn=rn(cos(nθ) + i sin(nθ)). So ‚ we have z = √3 – i‚ and we would like to evaluate z-10 = (√3 – i)-10. First‚ we need to express z = (√3 – i) into polar form. r = √(〖(√3)〗^2+1^2 )=2 tanθ = -1/√3 θ = 5π/6 So‚ z=2(cos(5π/6) + i sin(5π/6)) Apply De Moivre’s Theorem‚ z-10 = (√3 – i)-10 =2-10 (cos(10*5π/6) + i sin(10*5π/6)) = .
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------------------------------------------------- Spiral of Theodorus In geometry‚ the spiral of Theodorus (also called square root spiral‚ Einstein spiral or Pythagorean spiral)[1] is a spiral composed of contiguous right triangles. It was first constructed by Theodorus of Cyrene. ------------------------------------------------- ------------------------------------------------- [edit]Construction The spiral is started with an isosceles right triangle‚ with each leg having a length of 1
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using trigonometry tan equation. Tan ɵ = Tan 69 = If I subtract 4m from the above‚ this will give me the length of ½ the border as each side of the border is equal. I will then work out the base of the 2nd triangle marked B using Pythagoras theorem (the square of the hyp) = (the sum of the other 2 sides). hyp² = x² + 4² I will then work out the area of the two triangles with the equation A = ½ x base x perpendicular height A = ½ ͯ b ͯ h By adding the two areas of the triangle together
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sum of the area of squares of its adjacent and opposite sides.) Then let’s look at the famous Pythagoras theorem: “The square on the hypotenuse of a right angled triangle is equal to the sum of squares of its sides” The Sulba sutra was written on 12th century B.C. but the Pythagoras theorem was introduced on 6th century B.C‚ 600 years after Sulba sutra. That is‚ most of the works‚ theorems and concepts of mathematics existed in India on its own form even before in other countries. Let’s look at
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laws of logic. A falsehood must therefore be any statement or claim that cannot be sustained by a valid logical process with the given assumptions. Let’s take the example of Pythagoras‚ whose famous theorem is ubiquitous to this day. Pythagoras assumed a Euclidean plane system and used past theorems to prove his own. It is not his proof that will be the focus of this essay‚ but the process. Pythagoras developed his proof through the method of abstraction‚ that is‚
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MATHS-SA1-TEST1 Q1) Use the following information to answer the next question. The steps for finding the H.C.F. of 2940 and 12348 by Euclid’s division lemma are as follows. 12348 = a × 4 + b a = b × 5 + 0 What are the respective values of a and b? A. 2352 and 588 B. 2940 and 588 C. 2352 and 468 D. 2940 and 468 Answer The steps to find the H.C.F. of 12348 and 2940 are as follows. 12348 = 2940 × 4 + 588 2940 = 588 × 5 + 0 Comparing with the given steps‚ we obtain a =
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When it comes to Euclidean Geometry‚ Spherical Geometry and Hyperbolic Geometry there are many similarities and differences among them. For example‚ what may be true for Euclidean Geometry may not be true for Spherical or Hyperbolic Geometry. Many instances exist where something is true for one or two geometries but not the other geometry. However‚ sometimes a property is true for all three geometries. These points bring us to the purpose of this paper. This paper is an opportunity for me to
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observe which is why trig plays such a big role. With trig we can start to calculate distances between matter and the angles at which they are facing the earth. This is how the Greeks started with the Pythagoras theorem (seen on the right). Although nowadays we mostly use the trig laws and theorems‚ SIN ( finding the rise O/H)‚ COS( finding the run A/H) and TAN( finding the slope O/A). With these functions many immeasurable distances can be found by knowing two distances or a distance and an angle. Astronomers
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topics of Napoleon’s Theorem‚ the first thing that struck my mind was that it was somehow related to the French leader‚ Napoleon Bonaparte. But then a thought struck me: Napoleon was supposed to good at only politics and the art of warfare. Mathematics was never related to him. On surfing the internet to learn about the theorem‚ I came to know that this theorem was in fact named after the same Napoleon as he was good at Maths too (other than waging wars and killing people). The theorem was discovered in
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