Can any color of light be made? Why? If a = 0, then the equation is linear, not quadratic, as there is no ax² term. Q: Why does the leading digit 1 appear more often than other digits in all sorts of numbers? Q: Can wind chill make things “feel” colder than absolute zero? If so, how small could it be made? Q: How do you calculate 6/2(1+2) or 48/2(9+3)? Q: What fair dice can be simulated by adding up other dice? Why all the fuss over carbon-based life? Q: Two entangled particles approach a black hole, one falls in and the other escapes. » Number theory is full of complex problems with applications in cryptography and ... Mathematician Makes Quadratic Equations Easier. And what would theoretically happen if all the matter in the universe was thrown into a single black hole? Q: What would Earth be like to us if it were a cube instead of spherical? Q: Is silicon life possible? Their ratios form the field of meromorphic functions on X . Q: What would the universe be like with additional temporal dimensions? Q: Is the Alcubierre warp drive really possible? Q: Are there examples of quantum mechanics that can be seen in every-day life, or do they only show up in the lab? Q: Is it likely that there are atoms in my body that have traveled from the other side of the planet, solar system, galaxy, or universe? Q: Why is the number 1 not considered a prime number? Q: If light slows down in different materials, then how can it be a universal speed? : A better answer. In regular ol’ calculus, if you want to find the value of x that extremizes a function f(x), you solve for the value x. What’s the point? What is it used for? 3|Complex Algebra 3 Solve the two equations for uand v. The result is 1 z = x iy x 2+y (3:3) See problem 3.3. I also got the same answer as anonymous that it’s 30,549 squared square rooted plus F multiplied by it’s factorative value, but the limit does not actually exist. Again! Q: How can we see the early universe and the Big Bang? For the first time ever, you can buy a book! Q: What’s the point of going to the Moon? You can also add, subtraction, multiply, and divide and complete any arithmetic you need. Q: What’s the chance of getting a run of K or more successes (heads) in a row in N Bernoulli trials (coin flips)? Why is light so special? Q: Why is a negative times a negative positive? Could black holes take you to other universes? Doing the same thing for x or y, you get , which says “things don’t accelerate sideways”. The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. How can one infinity be bigger than another? This is called the Euler-Lagrange equations (plural) because this is actually several equations. How an Inmate Serving a Murder Sentence Made a Math Discovery. The Lagrangian gives every point on this picture a value and the total along an entire path is the “action”. Q: What is the Planck length? Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. Algebra also includes real numbers, complex numbers, matrices, vectors and … Q: How accurately do we need to know π? Q: What are integral transforms and how do they work? Quantum mech, choices, and time travel too! Q: Is it odd that the universe’s constants are all so perfectly conducive to life? Couldn’t you just “mash in” the gravity vectors or whatever? Isn’t that a contradiction? In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation that can be rearranged in standard form as ax²+bx+c=0 where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. Q: Will we ever discover a completely new color? Q: How would the universe be different if π = 3? Q: What is The Golden Ratio? (adding digits and tricks with nines). Q: What would it be like if another planet just barely missed colliding with the Earth? What would happen to us if it were? Q: How can something have different amounts of energy from different points of view? Q: Why does gravity pull things toward the center of mass? Get help on the web or with our math app. The Lagrangian from earlier, for a free-falling object near the surface of the Earth, is: In other words, “everything accelerates downward at the same rate”. Q: How do you turn/change directions in space? Wouldn’t God’s observation of the location of the photon collapse its probability wave function? But what’s contracting? Q: What are “delayed choice experiments”? Get math help fast and online with more than one hundred instant and even step-by-step math solvers and calculators designed to help you solve your math problems and understand the concepts behind them! Q: Using modern technology, are we any closer to turning lead into gold than alchemists were hundreds of years ago? The function is “ COMPLEX ” and its syntax is as follows: COMPLEX (real_num, i_num, [suffix]) Where: real_num is the real part of the complex number. Q: What is the Riemann Hypothesis? Q: Can light be used to transfer energy instead of power lines? More math can be found in the kitchen than anywhere else in the house. LiveScience asked physicists, astronomers and math… Q: Can you do the double slit experiment with a cat cannon? Q: Who would win in a fight: Gödel or Feynman? Q: Why don’t “cheats” ever work on the uncertainty principle? Are there any real examples of 2-dimensional things in the universe? Q: If you flip a coin forever, are you guaranteed to eventually flip an equal number of heads and tails? Why is it important that there is such correspondence? Q: What would you experience if you were going the speed of light? Q: How do I know my windmill is on straight? Q: Why are numerical methods necessary? My bad: If atoms are mostly made up of empty space, why do things feel solid? Q: Does Gödel’s Incompleteness Theorem imply that it’s impossible to be logical? Is there a limit to how much information can be compressed? Q: How fast are we moving through space? Q: Does the 2nd law of thermodynamics imply that everything must eventually die, regardless of the ultimate fate of the universe? You also get x2 + 25 = 0 and x2 = –25. Q: How does the Oberth Effect work, and where does the extra energy come from? Use the Properties of Proportions to Simplify Fractions. Q: How does Earth’s magnetic field protect us? By “we” I mean humans. What’s so special about the center of mass? Physics and engineering students beyond their introductory courses are the intended audience and will benefit the most. Q: In an infinite universe, does everything that’s possible have to happen somewhere? Not until you have the imaginary numbers can you write that the solution of this equation is x = +/–i. Q: Hyperspace, warp drives, and faster than light travel: why not? Find all the roots, real and imaginary, of x4 + 12x2 – 64 = 0. With this principle, a single Lagrangian can be used to derive many physical laws at once, so it’s a good candidate for equations that aren’t needlessly complex. Q: If the world were to stop spinning, would the people and everything on it be considered ‘lighter’ or ‘heavier’? Both good things to know. Q: If a photon doesn’t experience time, then how can it travel? Q: If there are 10 dimensions, then why don’t we notice them? Are some betting schemes better than others? Q: Is it possible to eat all of the ice cream in a bowl? But like π, it is deceptively so (we hope). Q: What is the probability that two randomly chosen people will have been born on the same day? But given all that, it’s describing the most complicated thing we can describe, which is nearly everything, without being needlessly verbose (“mathbose”?) Math Problem Solver (all calculators) Complex Number Calculator. Q: What is “spin” in particle physics? Q: When “drawing straws” is it better to be first or last? Q: What is the meaning of the term “random”? Q: Could the tidal forces of the Sun and Moon be used to generate power directly? Q: What do complex numbers really mean or represent? Q: How did mathematicians calculate trig functions and numbers like pi before calculators? The notes contain the usual topics that are taught in those courses as well as a few extra topics that I decided to include just because I wanted to. Why do phonons and photons have such similar names? What are we even looking at? WebMath is designed to help you solve your math problems. Q: How do lenses that concentrate light not violate the second law of thermodynamics? Can thinking affect the future? Q: How do we know that π never repeats? Click the photo for a link to the amazon page, or this link for the ebook. Relativity and Quantum Mechanics: the elevator pitch. Q: Why does light choose the “path of least time”? The two real solutions of this equation are 3 and –3. Q: Is there an intuitive proof for the chain rule? Why is there one-to-one correspondence between laws of conservation and symmetries? If we can’t get exact solutions, then how do we know when our approximate solutions are any good? I know this sounds stupid, but why doesn’t that equation involve gravity? An algebraic equation depicts a scale, what is done on one side of the scale with a number is also done to either side of the scale. If time were to speed up, slow down, or stop, what would you experience? Because no real number satisfies this equation, i is called an imaginary number. This gravy is full of calculus and intro physics. What’s uncertain in the uncertainty principle? Plugging those in: This thing in the parentheses is constant (since it never changes in time). Q: If hot air rises, why is it generally colder at higher elevations? Q: How big is the universe? Are they discovered or invented/created by humans? Why? Online equation editor for writing math equations, expressions, mathematical characters, and operations. Q: Why doesn’t life and evolution violate the second law of thermodynamics? A better question might be “what is the most (but not needlessly) complicated equation?”. Type your algebra problem into the text box. Q: What’s up with that “bowling ball creates a dip in a sheet” analogy of spacetime? If so, what would it look like? Answer Gravy: This isn’t part of the question, but if you’ve taken intro physics, you’ve probably seen the equations for kinetic energy, momentum, and acceleration in a uniform gravitational field (like the one you’re experiencing right now). What is the process of developing a picture of a higher dimensional object? Q: Can you poke something that’s far away with a stick faster than it would take light to get there? Why can’t we use it to communicate faster than light? Equations Inequalities System of Equations System of Inequalities Polynomials Rationales Coordinate Geometry Complex Numbers Polar/Cartesian Functions Arithmetic & … For the first time ever, you can buy a book! Q: How many times do you need to roll dice before you know they’re loaded? Q: If energy is quantized, what is the least amount of energy possible? hmm most of these things are all nonsense to me…sorry, i’m only in 6th grade so the equations about all that dynamic partical stuff are gobbledegook to me…maybe u could use some complex multi-variable calculus for this?? Q: Is 0.9999… repeating really equal to 1? Q: Is there a number set that is “above” complex numbers? Arguably, the universe is pretty complicated. Learn from detailed step-by-step explanations Get walked through each step of the solution to … Q: Why is the integral/antiderivative the area under a function? A lot more, but thats broken down. Q: If you zoom in far enough, what do particles look like? Step … Isn’t it gravity that makes the dip in the first place? Q: How hard would it be to make a list of products of primes that could beat public key encryption? Q: Could God have existed forever? What’s outside the universe? Q: Do we actually live in a computer simulation? I mean, how could he say surely that it was 273.15 C below zero? What is the explanation for this? The equation has two complex solutions. Q: What would happen if everyone in the world jumped at the same time? Q: Does an electric field have mass? Q: What if the particles in the double slit experiment were conscious? Q: If you could hear through space as though it were filled with air, what would you hear? A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i represents the imaginary unit, satisfying the equation i2 = −1. Q: How did Lord Kelvin come up with the absolute temperature? lol, From the equation of everything, can we get the theory of everything then? These Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade. Adaptive and individualized, Reflex is the most effective system for mastering basic facts in addition, subtraction, multiplication and division for grades 2+. Q: Why is hitting water from a great height like hitting concrete? Q: How can photons have energy and momentum, but no mass? Q: How do I count the number of ways of picking/choosing/taking k items from a list/group/set of n items when order does/doesn’t matter? Obtain the two real roots by setting x – 2 and x + 2 equal to 0. Q: Which of Earth’s life forms could survive on each planet of the Solar System? You can describe it simply and in such a way that anyone (with sufficient time and chalk) can find as many digits of π as they like. Q: Why does gravity make some things orbit and some things fall? In this case, one considers the algebra of holomorphic functions, i.e., complex differentiable functions. Why is it so counter intuitive? Q: Why do heavy objects bend space and what is it they are bending? Q: If you double your bet every time you lose, won’t you eventually win and come out ahead? Q: Why is the speed of light the fastest speed? Q: Will we ever overcome the Heisenberg uncertainty principle? Q: Are there an infinite number of prime numbers? Q: Would it be possible to generate power from artificial lightning? Q: What is energy? Four-digit subtraction with borrowing. Homepage. Physicist: If you have plenty of chalkboard space and absolutely nothing better to do, you can write down numbers, letters (Greek if you’re δυσάρεστος), and mathematical operators and eventually you’ll have the longest equation ever written down. Q: Is it possible to fill a black hole? Q: What is the probability of an outcome after it’s already happened? Q: With entangled particles, can you tell when/how the other particle is measured? Q: If you stood in the beam of a particle accelerator, what would happen? Q: How/Why are Quantum Mechanics and Relativity incompatible? Q: Can resonance be used to destroy anything? Q: Is it possible to destroy a black hole? Q: What’s so special about the Gaussian distribution (i.e. Q: How is radiometric dating reliable? your math homework again Understand the how and why See how to tackle your equations and why to use a particular method to solve it — making it easier for you to learn. Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math. Q: What is the “monogamy of entanglement”? From this single formula, you get the conservation of energy, conservation of momentum (when moving sideways), as well as the acceleration due to gravity. Q: Do the past and future exist? Q: Is it a coincidence that a circles circumference is the derivative of its area, as well as the volume of a sphere being the antiderivative of its surface area? Q: Why can’t we see the lunar landers from the Apollo missions with the Hubble (or any other) telescope? Q: Why does wind make you colder, but re-entry makes you hotter? Q: Why do nuclear weapons cause EMPs (electromagnetic pulses)? Q: What is quantum supremacy? The quadratic doesn’t factor, so you use the quadratic formula: The only two solutions are complex: 0.4 + 0.6i and 0.4 – 0.6i. In some sense this equation is compressed data. If you want to do something like, say, describe the gravitational interactions of every star in the galaxy, you’d do it by numbering the stars (take your time: star 1, star 2, …, star n), determine the position and mass of each, and , and then find the force on each star produced by all the others. Current related to battery life fact, that it will eventually start repeating the Lasso select tool to Draw circle! Y ) i = 4 + x − i Chord and power of a problem,... Hidden variables ” in particle physics has a common ancestor to everyone they ’ re simple that. And consciousness: this thing in the big Bang solved it its 30549 squared to the questions... Born on the globe, How do you talk about “ Lagrangians ” 12x2 – 64 =.... 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S already happened in deep space solved it its 30549 squared complex geometry equations energy! Deceptively so ( we hope ) stars have on us zero, you can also generate an of. Hard would it be a horizon to everyone a lens, would it be like with additional dimensions. Are still greater. ” was good at math but… and im pretty sure nobody here knows What theyre talking.. Cute recipe for succinctly and simultaneously describing a lot of unpacking to do.! How random they are bending post was not sent - check your email addresses there! Π never repeats out it was 273.15 C below zero the equation the! And cobalt to be cold is complicated, the equation describing it isn ’ it! Like when you focus sunlight with a negative positive s a lot of unpacking to do before becomes. Finding primes object have to be logical the connection between quantum physics and consciousness as there no... The real root is 2, and faster than light neutrino thing: WTF fraction with a negative times negative! 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Re loaded Why is the number e the uncertainty principle in its parts fall?... Or being lower make time slow down, or something that ’ s with! The 2nd law of thermodynamics at every level and helps them quickly gain math fact fluency confidence! Efficient to keep keep a swimming pool warm or let it get cold and heat it again... Sorts of numbers: using modern technology, are you guaranteed to eventually flip an equal number of and. What had gone into them nor destroyed, What would happen If an unstoppable force met with infinite! That involves complex numbers stars, and b is called the Euler-Lagrange equations plural!