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The binomial theorem describes the algebraic expansion of powers of a binomial: that is, the expansion of an expression of the form (x + y)^n where x and y are variables and n is the power to which the binomial is raised. When first encountered, n is a positive integer, but the binomial theorem can be extended to cover values of n which are fractional or negative (or both).
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Limitations of work energy theorem?
it doesn't define direction of velocity
Why Central Limit Theorem rolling a dice once you will never have a bell shaped curve?
Rolling a die once will give one point. A single point does not even define a line, let alone a curve!
Can one formally define a division ring as a field that isn't necessarily commutative?
wedderburn's little theorem says all finite division rings are commutative so they are fields. So if it is a finite division ring, then the answer is NO But for an infinite division ring... I think you can!
Can the Pythagoras theorem be proven emperically?
ANSWERYes The Pythagorean Theorem Can Be Proven Empirically.HOW?First, Lets Define The Theorem:In simplest terms, the Pythagorean Theorem is essentially a Formula that is TRUE for ANY/ALL RIGHT TRIANGLES (ANY Triangle that has ONE 90o ANGLE). The formula States: A2 + B2 = C2 , WHERE C is Always The Longest Side (Called The Hypotenuse) and is Always OPPOSITE the 90o Angle. A and B are The Other two sides of the triangle (not the Hypotenuse), the sides adjacent to the 90o Angle. To Prove The Pythagorean Theorem Empirically:First off lets define Empirically; all that it means, in this instance, is Show or Prove that the Theorem works through experience/experiment. This is very easy, just do the following: Using a protractor make a 90o AngleDraw 2 lines (Sides A & B) that make up the 90o Angle you measured out in Step 1Draw Side A - 5 cm in lengthDraw Side B - 8 cm in lengthDraw Side C - the Hypotenuse (A line that Connects Sides A and B) - But Do NOT Measure This with your ruler YET.Now since we need to PROVE that the Theorem is Correct, We have to Plug the length of the Sides A and B into the Theorem's Formula.52 + 82 = C2 (WHERE C2 is the Length of Side C/The Hypotenuse Squared)So Now we have the Equation: C2 = 25 + 64 = 89Now we need to Find what C equals, we do this by taking the Square Root of 89, and Since we know C is a Positive Number (Since its the Length of Side C), we can ignore the Negative portion of the Square Root and So We Know:C = 9.434 cmLAST STEP, NOW You MEASURE - with your Ruler, the Hypotenuse (Side C), and you will see that it equals 9.434 cm; therefore we have just Proved Empirically that the Pythagorean Theorem is Correct.
What number is q for?
It can represent anything that you want - provided that you define it as such. Here are some examples:Algebra: it could represent a typical element in the set of rational numbers.Geometry: In the Cartesian plane (or space), it could represent the ordinate (second coordinate) of a point.Probability: It could represent the probability of the complement of a given event - particularly for the binomial distribution.
What is the define binomial?
A binomial is something with 2 numbers or compounds: 2+2 or (9x+2)(x-4)
Limitations of work energy theorem?
it doesn't define direction of velocity
What are the disadvantages of Pick's Theorem?
Pick's theorem can't use for non-convex polygons. It needs at least 3 terms to define an area of a polygon.
Define boolean theorem?
Boolean Theory is used to make Boolean Equations easier to perform. It offers theories for solving single and multiple variables.
What is the importance of work-energy theorem?
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. This theorem is important because it allows us to analyze and predict the motion of objects by considering the work done on them. It provides a powerful tool for understanding and solving problems in mechanics.
Which theorem is used to prove the AAS triangle congruence postulate theorem?
The first thing you prove about congruent triangles are triangles that have same side lines (SSS) is congruent. (some people DEFINE congruent that way). You just need to show AAS is equivalent or implies SSS and you are done. That's the first theorem I thought of, don't know if it works though, not a geometry major.
Why Central Limit Theorem rolling a dice once you will never have a bell shaped curve?
Rolling a die once will give one point. A single point does not even define a line, let alone a curve!
What is an example of the Thomas Theorem in Lord of the Flies?
The conch shell could be seen as an example, because it has no actual ability to let only one person speak, but "If men define situations as real, they are real in their consequencesIf men define situations as real, they are real in their consequences", so the conch shell becomes real in its consequence.
Can we define the cardinal number as the number of subsets of that set?
No. The number of subsets of that set is strictly greater than the cardinality of that set, by Cantor's theorem. Moreover, it's consistent with ZFC that there are two sets which have different cardinality, yet have the same number of subsets.
Can one formally define a division ring as a field that isn't necessarily commutative?
wedderburn's little theorem says all finite division rings are commutative so they are fields. So if it is a finite division ring, then the answer is NO But for an infinite division ring... I think you can!
What is the formula for the width of a 3-D shape?
There is no single formula for the width of any arbitrary shape. If however, you already have two points that define that width, then you can calculate the distance between them with simple Pythagorean theorem: w = [Δx2 + Δy2 + Δz2]1/2
Who was Carolus Linnaeous?
Carolus Linnaeus, also known as Carl Linnaeus, was an 18th-century Swedish botanist, zoologist, and physician. He is best known for his work in establishing the modern system of naming and classifying organisms through the development of binomial nomenclature. Linnaeus's system laid the groundwork for modern taxonomy and is still used today to categorize and define species.
