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Where HA is an acid which dissociates in the conjugate base of the acid nd a hydrogen ion that combines with water to form the hydronium ion H 3 O When the concentrations of HA, A, and H 3 O no longer change over time, the reaction is at equilibrium and the dissociation constant may be calculatedThe Formula is given below (a b c)³ = a³ b³ c³ 3 (a b) (b c) (a c) Explanation Let us just start with (abc)² = a² b² c²2ab2bc2ca =a² b² c²2 (abbcca) now (abc)² (abc)= (a b c)³= a² b² c²2 (abbcca) (abc) =a ² abc b² abcc² abc 2 (abbcca) abcThe magnitude of the equilibrium constant for an ionization reaction can be used to determine the relative strengths of acids and bases For example, the general equation for the ionization of a weak acid in water, where HA is the parent acid and A− is its conjugate base, is as follows
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A + b + c ka formula-Example Solve 8a 3 27b 3 125c 3 30abc Solution This proceeds as Given polynomial (8a 3 27b 3 125c 3 30abc) can be written as (2a) 3 (3b) 3 (5c) 3 (2a)(3b)(5c) And this represents identity a 3 b 3 c 3 3abc = (a b c)(a 2 b 2 c 2 ab bc ca) Where a = 2a, b = 3b and c = 5c Now apply values of a, b and c on the LHS of identity ie a 3 b 3 c 3 3abcLearn about Algebra Formula, Equations and List of Basic Algebraic Formulas & Expression in Math Algebra includes real numbers, complex numbers, matrices, vectors and many other topics
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Relationship between Ka of a weak acid and Kb for its conjugate base Equations for converting between Ka and Kb, and converting between pKa and pKb If you're seeing this message, it means we're having trouble loading external resources on our websiteAs stated in the title, I'm supposed to show that $(abc)^3 = a^3 b^3 c^3 (abc)(abacbc)$ My reasoning $$(a b c)^3 = (a b) c^3 = (a b)^3 3(a b)^2c 3(a b)c^2 c^3 Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careersIntroduction to a plus b whole cube formula with example problems with proofs to learn how to derive ab whole cube identity in mathematics
What Is The Formula For Math A B C 3 Math Quora What Is The Formula Of Math A 3 B 3 Math Quora What Are Various Forms To Write A B C A Whole Cube Quora If A B C Are In Continued Proportion Prove That A 3 B 3 C 3 A 2 B 2 C 2 1 A 3 1 B 3 1 C 3 Mathematics Topperlearning Com 8p157uuuLet me help you with this formula in detail (a b c)³ = a³ b³ c³ 3 (a b) (b c) (a c) Proof (a b c)³ = a³ b³ c³ 3 (a b) (b c) (a c)History The formula is credited to Heron (or Hero) of Alexandria, and a proof can be found in his book, Metrica, written c CE 60 It has been suggested that Archimedes knew the formula over two centuries earlier, and since Metrica is a collection of the mathematical knowledge available in the ancient world, it is possible that the formula predates the reference given in that work
The formula is matha^2 b^2 c^2 2ab 2bc 2ca/math PROOF math(abc)^2/math can be written as math(abc)*(abc)/math, Therefore, math(abcExample 2 Solve (8x 4y 7z) 2 Solution This proceeds as Given polynomial (8x 4y 7z) 2 represents identity first ie (a b c) 2 Where a = 8x, b = 4y and c = 7z Now apply values of a, b and c on the identity ie (a b c) 2 = a 2 b 2 c 2 2ab 2bc 2ca and we get (8x 4y 7z) 2 = (8x) 2 (4y) 2 (7z) 2 2(8x)(4y) 2(4y)(7z) 2(7z)(8x) Expand the exponential forms andSolution (2x 3)3 is in the form of (a b)3 Comparing (a b)3 and (2x 3)3, we get a = 2x b = 3 Write the formula / expansion for (a b)3 (a b) 3 = a 3 3a 2 b 3ab 2 b 3 Substitute 2x for a and 3 for b (2x 3) 3 = (2x) 3 3 (2x) 2 (3) 3 (2x) (3 2) 3 3
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A3 b3 c3 = (a b c) (a2 b2 c2 – ab – bc – ca) 3abcRules Pyaar Ka Superhit Formula 03 https//yunrilboshkelcom/?pietTriangle given a,b,c = s(sa)(sb)(sc) when s = (abc)/2 (Heron's formula) regular polygon = (1/2) n sin(360°/n) S 2 when n = # of sides and S = length from center to a corner Units Area is measured in "square" units The area of a figure is the number of squares required to cover it completely, like tiles on a floor
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The 3D reference style Conveniently referencing multiple worksheets If you want to analyze data in the same cell or range of cells on multiple worksheets within a workbook, use a 3D reference A 3D reference includes the cell or range reference, preceded by a range of worksheet namesJesip bought 3 boxes of cereal for $249 each, 1 pounds of meat for $456, 5 apples for $067 ech, and 5 yogurts for $6 How much did he spend at theShare with your friends Share 444
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Factorisea^3 b^3 C^3 3abc Get the answer to this question by visiting BYJU'S Q&A ForumWhat Is The Expansion Of A B C 3 Quora For more information and source, see on this link https//wwwquoracom/Whatistheexpansionofabc3Heron's Formula Area of a Triangle from Sides You can calculate the area of a triangle if you know the lengths of all three sides, using a formula that has been known for nearly 00 years It is called "Heron's Formula" after Hero of Alexandria (see below) Just use this two step process
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A 3 b 3 c 3 − 3abc = (a b c) (a 2 b 2 c 2 − ab − bc − ac) If (a b c) = 0, a 3 b 3 c 3 = 3abc Some not so Common FormulasAB = AC ⇒ B = C (left cancellation law) BA = CA ⇒B = C (right cancellation law) 6 AB = 0, does not necessarily imply that A = 0 or B = 0 or both A and B = 0 Important Points to be Remembered (i) If A and B are square matrices of the same order, say n, then both the product AB and BA are defined and each is a square matrix of order nQuadratic Formula For an equation of the form \(ax^2bxc=0\), you can solve for x using the Quadratic Formula $$ x = \frac{b \pm \sqrt{b^24ac}}{2a} $$ Binomial Theorem \((ab)^1= a b\) \((ab)^2=a^22abb^2\) \((ab)^3=a^33a^2b3ab^2b^3\) \((ab)^4=a^44a^3b6a^2b^24ab^3b^4\) Difference of Squares \(a^2b^2=(ab)(ab)\) Rules of Zero
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3a 2b = c subtract the 3a 2b = c 3a divide the 2 b = c 3a/2 (the 2 is under c3a) So from the looks of it, the third one(a – b) 3 = a 3 – 3a 2 b 3ab 2 – b 3 (a b – c) 2 = a 2 b 2 c 2 2ab – 2bc – 2ca (a – b c) 2 = a 2 b 2 c 2 – 2ab – 2bc 2caCase c) In this case we substitute x = a 2, y = b 2 and z = c 2, where a, b and c are non negative integers and x, y and z are greater than or equal to 2 So putting value of x, y and z in equation x y z = 50 we get a b c = 44 where n = 44 and r =3
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The answer is (ab)^3=a^33a^2b3ab^2b^3 It's easy to prove (ab)^3= =(ab)(ab)(ab)= =(a^2ababb^2)(ab)= =(a^22abb^2)(ab)= =a^3a^2b2a^2b2ab^2ab^2b^3Here a = 3x, b = 2y and c = z 3x (2y) (z) 2 = (3x) 2 (2y) 2 (z) 2 2 (3x) (2y) 2 (2y) (z) 2 (z) (3x) = 9x 2 4y 2 z 2 – 12xy 4yz – 6zx 2 Simplify a b c = 25 and ab bc ca = 59 Find the value of a 2 b 2 c 2 Solution According to the question, a b c = 25Example 2 Solve (8x 4y 7z) 2 Solution This proceeds as Given polynomial (8x 4y 7z) 2 represents identity first ie (a b c) 2 Where a = 8x, b = 4y and c = 7z Now apply values of a, b and c on the identity ie (a b c) 2 = a 2 b 2 c 2 2ab 2bc 2ca and we get (8x 4y 7z) 2 = (8x) 2 (4y) 2 (7z) 2 2(8x)(4y) 2(4y)(7z) 2(7z)(8x) Expand the exponential forms and
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Proof Formula \((abc)^3 = \\a^3 b^3 c^3 6abc \\ 3ab (ab) 3ac (ac) 3bc (bc) \) Summary (abc)^3 If you have any issues in the (abc)^3 formulas, please let me know through social media and mailFactorisea^3 b^3 C^3 3abc Get the answer to this question by visiting BYJU'S Q&A ForumAnother reason for using the generic acid formula of HA is that this avoids the need to constantly write a somewhat complex formula for the anion portion of the weak acid In fact, as I do this problem, I will write Ur¯ for the anion portion of uric acid (the C 5 H 3 N 4 O 3 ¯) Solution a) H = 10¯ pH = 10¯ 239 = x 10¯ 3 M
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Definition binomial A binomial is an algebraic expression containing 2 terms For example, (x y) is a binomial We sometimes need to expand binomials as follows (a b) 0 = 1(a b) 1 = a b(a b) 2 = a 2 2ab b 2(a b) 3 = a 3 3a 2 b 3ab 2 b 3(a b) 4 = a 4 4a 3 b 6a 2 b 2 4ab 3 b 4(a b) 5 = a 5 5a 4 b 10a 3 b 2 10a 2 b 3 5ab 4 b 5Clearly, doing this byPH ≈ − logH Ka, the acid ionization constant, is the equilibrium constant for chemical reactions involving weak acids in aqueous solution The numerical value of Ka is used to predict the extent of acid dissociationA 3 b 3 c 3 – 3abc = (a b If a b c = 0, then the above identity reduces to a 3 b 3 c 3 = 3abc;
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(a – b – c) 2 = a 2 b 2 c 2 – 2ab 2bc – 2ca (a b) 3 = a 3 3a 2 b 3ab 2 b 3;3(a b)3 = a3 b3 3ab(a b) 4 (a b) 3 = a3 b3 3ab(a b) 5(a b c)2 = a2 b2 c2 2ab2bc 2ca 6(a b c)3 = a3 b3 c33a2b3a2c 3b2c 3b2a 3c2a 3c2a6abc 7a2 b2 = (a b)(a – b ) 8a3 – b3 = (a – b) (a 2 ab b2 ) 9a3 b3 = (a b) (a 2 ab b2 ) 10(a b)2 (a b) 2 = 4ab 11(a b)2 (a b) 2 = 2(a 2 b2 )Triangle given a,b,c = s(sa)(sb)(sc) when s = (abc)/2 (Heron's formula) regular polygon = (1/2) n sin(360°/n) S 2 when n = # of sides and S = length from center to a corner Units Area is measured in "square" units The area of a figure is the number of squares required to cover it completely, like tiles on a floor
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It is no good to try to stop knowledge from going forward Ignorance is never better than knowledge Enrico Fermi Nothing is better than reading and gaining more and more knowledge Stephen William HawkingWhat is the formula of (ab) whole cube?Learn about Algebra Formula, Equations and List of Basic Algebraic Formulas & Expression in Math Algebra includes real numbers, complex numbers, matrices, vectors and many other topics
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In this section, you will learn the formula or expansion for (a 3 b 3)We already know the formula/expansion for (a b) 3 That is, (a b) 3 = a 3 b 3 3ab(a b) Case 1 (a b) 3 = a 3 b 3 3ab(a b) Subtract 3ab(a b) from each sideCalculator Use This online calculator is a quadratic equation solver that will solve a secondorder polynomial equation such as ax 2 bx c = 0 for x, where a ≠ 0, using the quadratic formula The calculator solution will show work using the quadratic formula to solve the entered equation for real and complex rootsThe Ka value of HCO_3^ is determined to be 50E10 Determine the value for the Kb and identify the conjugate base by writing the balanced chemical equation Based on the Kb value, is the anion a
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Few Other Mathematical Formula Here are all other math formulas which are also equally important for your exams Nice and Amazing questions but padne me achha lga enhe padne se hamare mind ka vikas hota or jab i enko soul krta$\implies$ $(ab)^2 \,=\, a^2b^22ab$ Simplification The subtraction of two times product of two terms from the sum of the squares of the terms is simplified as the square of difference of the termsA 4 – b 4 = (a – b)(a b)(a 2 b 2)
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A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 b 2 = c 2Such a triple is commonly written (a, b, c), and a wellknown example is (3, 4, 5)If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer kA primitive Pythagorean triple is one in which a, b and c are coprime (that is, they have no common divisor larger than 1)Agunaji1kiradebola agunaji1kiradebola Math Secondary School What's the formula for (abc) the whole cube 2 See answers sawakkincsem sawakkincsem Let me help you with this formula in detailA 1,1 ×b 1,1 a 1,2 ×b 2,1 a 1,3 ×b 3,1 = c 1,1 The dot product is performed for each row of A and each column of B until all combinations of the two are complete in order to find the value of the corresponding elements in matrix C For example, when you perform the dot product of row 1 of A and column 1 of B, the result will be c 1,1 of
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What's the formula for (abc) the whole cube Get the answers you need, now!A B C 3 Formula Source (s) https//shrinkurlim/badse DanielM Lv 4 1 decade ago This is just multiplying out and bookkeeping It's a^3 b^3 c^3 plus 3 of each term having one variable and(a b) 3 = a 3 b 3 3ab(a b) (a – b) 3 = a 3 – 3a 2 b 3ab 2 – b 3 = a 3 – b 3 – 3ab(a – b) a 3 – b 3 = (a – b)(a 2 ab b 2) a 3 b 3 = (a b)(a 2 – ab b 2) (a b) 4 = a 4 4a 3 b 6a 2 b 2 4ab 3 b 4 (a – b) 4 = a 4 – 4a 3 b 6a 2 b 2 – 4ab 3 b 4;
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