How do you calculate the size of a rainbow? Q: Is it of any coincidence that mathematics is able to describe physical reality – given that both are inventions of the human mind? Q: Why do we (people) wave our arms when we fall? Q: How do you calculate 6/2(1+2) or 48/2(9+3)? Q: How do lenses that concentrate light not violate the second law of thermodynamics? Equations Inequalities System of Equations System of Inequalities Polynomials Rationales Coordinate Geometry Complex Numbers Polar/Cartesian Functions Arithmetic & … Is this not a paradox? It’s a work in progress. Q: How many samples do you need to take to know how big a set is? The two real solutions of this equation are 3 and –3. What is its relevance? Q: What’s the relationship between entropy in the information-theory sense and the thermodynamics sense? Q: How does the Oberth Effect work, and where does the extra energy come from? Q: How do velocities add? Q: If you could drill a tunnel through the whole planet and then jumped down this tunnel, how would you fall? For example, you can sum up Newton’s physics almost instantly. It's a collection of over fifty of my favorite articles, revised and updated. Q: Is it possible to write a big number using a small number? Is there an orbit where the effects cancel out? Q: If you were on the inside of the Sun falling in, the matter closer to the surface doesn’t affect your acceleration, but the matter closer to the core does. Perimeter = a + b + c + d. Circle: Perimeter = 2 × pi × r or Perimeter = pi × d. Area = pi × r 2 or Area = (pi × d 2 )/4. Q: What is the probability that two randomly chosen people will have been born on the same day? Q: Is it more efficient to keep keep a swimming pool warm or let it get cold and heat it up again? Do primes follow a pattern? I am in third grade. A Quantum Computation Course 4: Full Measure, A Quantum Computation Course 3: Rise of the Quanta, A Quantum Computation Course 2: Quantum Harder. Q: If a photon doesn’t experience time, then how can it travel? Use the Lasso Select tool to draw a circle around the equation. Q: How many times do you need to roll dice before you know they’re loaded? You may select the numbers to be represented with digits or in words. Q: How do I encrypt/hide/protect my email? Type your algebra problem into the text box. Q: What’s the point of going to the Moon? Q: How does Earth’s magnetic field protect us? If you want to chose a path that extremizes (either minimizes or maximizes) S, then you can do it by solving the Euler-Lagrange equations: This is called the Euler-Lagrange equations (plural) because this is actually several equations. Is the “brown note” possible? Q: If you were to break down an average human body into its individual atoms, and then laid the atoms out in a single straight line, how far would it stretch? Is there a limit to how much information can be compressed? complex-equation-calculator. Learn from detailed step-by-step explanations Get walked through each step of the solution to … Q: Who would win in a fight: Gödel or Feynman? Q: What’s up with that “bowling ball creates a dip in a sheet” analogy of spacetime? Why is light so special? Q: What’s the difference between anti-matter and negative-matter? 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: What are “delayed choice experiments”? Q: As a consequence of relativity, objects becomes more massive when they’re moving fast. If time were to speed up, slow down, or stop, what would you experience? The real root is 2, and the imaginary roots are 5i and –5i. What’s uncertain in the uncertainty principle? And if you want to describe the dynamics of a system, Lagrangians are an extremely compact way to do it. Why use approximations when the exact answer is known? Q: Are there an infinite number of prime numbers? Do any of you have a clue about what logic is? 2y + xi = 4 + x − i. sorry, but i don’t understand physics, I’m not even gonna try reading that sh*t Q: If you double your bet every time you lose, won’t you eventually win and come out ahead? Find all the roots, real and imaginary, of x4 + 12x2 – 64 = 0. Q: If you were shrunk to microscopic size would you be able to see normally? Once you’ve got the Lagrangian of a system, you can describe the behavior of that system by applying the “principle of least action“, which says that the behavior of a system (the orbit a planet takes, the path of light through materials, etc.) Mathematical equations aren't just useful — many are quite beautiful. Does that mean we’re all a little inbred? Q: Is there an equation that determines whether a question gets answered on ask a mathematician/physicist? Are atoms, people, stars, and everything else getting bigger too? 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. Q: Why do nuclear weapons cause EMPs (electromagnetic pulses)? Q: Could a simple cup of coffee be heated by a hand held device designed to not only mix but heat the water through friction, and is that more efficient than heating on a stove and then mixing? Take the square root of each side. Q: What is quantum supremacy? Like could there be a (other letter) orbital beyond that? Q: What would the universe be like with additional temporal dimensions? Q: What is “spin” in particle physics? Q: How is the “Weak nuclear force” a force? Using the Euler-Lagrange equations is philosophically similar: to find the path that extremizes S, you solve for the path . The “action”, , is a function of the path a system takes, . Place value. Q: How do I find the love of my life? Q: Should we be worried about artificial intelligence? Q: How big is the universe? In practice this is absurd (there are a few hundred billion stars in the Milky Way, but we can’t see most of them because there’s a galaxy in the way), but the equation you would use is pretty straight forward. What is “pure energy” like? Wow! Q: What is the meaning of the term “random”? But like π, it is deceptively so (we hope). If a = 0, then the equation is linear, not quadratic, as there is no ax² term. : A better answer. Q: How can we have any idea what a 4D hypercube or any n-D object “looks like”? Q: What did Einstein mean by: “Do not worry about your difficulties in Mathematics. The Standard Form of a Quadratic Equation looks like this: 1. a, b and c are known values. 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. Q: Can resonance be used to destroy anything? Q: What is the connection between quantum physics and consciousness? This gravy is full of calculus and intro physics. If so, then did time begin in that universe at the inception of the black hole? Q: What is the Riemann Hypothesis? Q: In base ten 1=0.999…, but what about in other bases? x − 2i2 + 6i = yi + 3xi3. the Earth orbiting the Sun) just an arbitrary reference frame decision, and no more true than the Earth being at the center? Q: What is a “measurement” in quantum mechanics? Evidently, if you want an equation that genuinely needs to be complicated, you don’t need a complicated situation, you need complicated dynamics. Q: What is the universe expanding into? Q: What the heck are imaginary numbers, how are they useful, and do they really exist? Q: What are Feynman diagrams, how are they used (theoretically & practically), and are there alternative/competing diagrams to Feynman’s? Q: How can wormholes be used for time travel? Q: If we meet aliens, will they have the same math and physics that we do? Q: Given two points on the globe, how do you figure out the direction and distance to each other? For the complex number a + bi, a is called the real part, and b is called the imaginary part. Q: If you could hear through space as though it were filled with air, what would you hear? Notably, it doesn’t cover gravity, but be cool. Q: If the number of ancestors you have doubles with each generation going back, you quickly get to a number bigger than the population of Earth. Q: Is the quantum zeno effect a real thing? Q: Is there a formula for finding primes? If so, how small could it be made? Q: How do you answer a question scientifically? 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. The two complex solutions are 3i and –3i. 3x + ( 3x − y) i = 4 − 6i. Not until you have the imaginary numbers can you write that the solution of this equation is x = +/–i. Q: What is The Golden Ratio? If you were to continuously throw galaxies worth of matter into a black hole, would it ever fill up? A complex equation is an equation that involves complex numbers when solving it. Q: Would it be possible for humans to terraform mars? Q: What is Bayes’ rule and how do I use it to improve my life? Q: If gravity suddenly increased would airplanes fall out of the sky, or would it compress the air in such a way that airplanes could keep flying? If matter formed from energy (as in the Big Bang expansion), where did the energy come from? A complex number is a number that has both a real part and an imaginary part. Q: “i” had to be made up to solve the square root of negative one. Q: What would Earth be like if it didn’t turn? Q: Do virtual particles violate the laws that energy can be created or destroyed? Q: How can we prove that 2+2 always equals 4. Find all the roots, real and imaginary, of 5x2 + 6x + 3 = 0. For example,   This equation goes on forever, but it’s fairly straight forward: every term you flip the sign and increase the denominator from one odd number to the next. Q: If you could see through the Earth, how big would Australia look from the other side? This is the basic idea behind “Kolmogorov Complexity“; the length of the shortest possible set of written instructions that can produce a given result (never mind how long it takes to actually compute it). Algebra II: What Is the Binomial Theorem? Q: Hyperspace, warp drives, and faster than light travel: why not? Q: Is the Alcubierre warp drive really possible? 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: Which is a better approach to quantum mechanics: Copenhagen or Many Worlds? We offer an algebra calculator to solve your algebra problems step by step, as well as lessons and practice to help you master algebra. Where can I find the source code of this? Q: If time is relative, then how can we talk about how old the universe is? Why is it so counter intuitive? Not much more complicated. These Algebra 1 Equations Worksheets will produce distance, rate, and time word problems with ten problems per worksheet. Could black holes take you to other universes? For example, enter 3x+2=14 into the text box to get a step-by-step explanation of how to solve 3x+2=14.. How are the atoms in living things any different from the atoms in dead things? Q: What is the “False Vacuum” and are we living in it? Q: Using modern technology, are we any closer to turning lead into gold than alchemists were hundreds of years ago? Works across all devices Use our algebra calculator at home with the MathPapa website, or on the go with MathPapa mobile app. lol, From the equation of everything, can we get the theory of everything then? Q: Satellites experience less time because they’re moving fast, but more time because they’re so high. Q: Why is the speed of light the fastest speed? Would any change take place? Q: When “drawing straws” is it better to be first or last? Q: Why do superconductors have to be cold? will always be such that the “chosen” path will have the minimum total Lagrangian along that path. 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? From this single formula, you get the conservation of energy, conservation of momentum (when moving sideways), as well as the acceleration due to gravity. There are lots of variables and things in the equations described above, so… the answer would depend on those variables:) most people make up weird equations on these kinds of forums. WebMath is designed to help you solve your math problems. Q: What role does Dark Matter play in the behavior of things inside the solar system? It is recommended that only those with some existing knowledge of linear and complex algebra, differential equations, and even complex analysis and algebra only use this book. Q: Will black holes ever release their energy and will we be able to tell what had gone into them? Why is there one-to-one correspondence between laws of conservation and symmetries? (adding digits and tricks with nines). Q: Does how you deal cards affect how random they are? Why all the fuss over carbon-based life? Both good things to know. Q: What does a measurement in quantum mechanics do? To solve for the complex solutions of an equation, you use factoring, the square root property for solving quadratics, and the quadratic formula. How can they be sure that all life uses water? For the first time ever, you can buy a book! a can't be 0. Q: Why is the area of a circle equal to πR. If something were moving fast enough, would it become a black hole? 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? Q: How plausible is it that the laws of physics may actually function differently in other parts of the universe? Are there any real examples of 2-dimensional things in the universe? If they do, is the future determined and what does that mean for quantum randomness? Find all the roots, real and imaginary, of the equation 5x2 – 8x + 5 = 0. x = 0.4 + 0.6i, 0.4 – 0.6i. Has anyone calculated it? When x2 + 16 = 0, you find that x2 = –16. The force on star k is: . Q: What are the Intersecting Chord and Power of a Point Theorems? Are they discovered or invented/created by humans? Q: What are “actual pictures” of atoms actually pictures of? All equations must have some context before they do anything or even mean anything. The numbers are constants. Q: What’s the difference between black holes and worm holes? 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”. With digits or in words slit experiment with a lens different from year year... In fourth Grade when our approximate solutions are any good no real satisfies... All a little inbred in its orbit, illuminating, engaging, and would... The optimum spectrum to visualize things with the Heaviside, Sign, absolute value, and to... Calculus and intro physics rates of time or space or is there an equation without enough real of! 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