Algebra – Page 706

For-each-positive-integer-n-consider-the-highest-common-factor-h-n-of-the-two-numbers-n-1-and-n-1-For-n-lt-100-find-the-largest-value-of-h-n-

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Question Number 21230 by Tinkutara last updated on 16/Sep/17 $For each positive integer n, consider$ $the highest common factor h_{n} of the two$ $numbers n! + 1 and (n + 1)! . For n < 100,$ $find the largest value of h_{n} .$ Answered by dioph last updated…

A-If-w-2-then-the-set-of-points-z-w-1-w-is-contained-in-or-equal-to-B-If-w-1-then-the-set-of-points-z-w-1-w-is-contained-in-or-equal-to-Options-for-both-A-and-B-p-An-ellip

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Question Number 21219 by Tinkutara last updated on 16/Sep/17 $(A) If ∣ w ∣ = 2, then the set of points$ $z = w - \frac{1}{w} is contained in or equal to$ $(B) If ∣ w ∣ = 1, then the set of points$ $z = w + \frac{1}{w} is contained in or equal to$ $Options for both A and B :$ $(p) An ellipse with eccentricity \frac{4}{5}$ $(q) The set of points z satisfying Im z$ $$=\:\mathrm{0} \…

Find-a-triple-of-rational-numbers-a-b-c-such-that-2-1-3-1-1-3-a-1-3-b-1-3-c-1-3-

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Question Number 152281 by john_santu last updated on 27/Aug/21 $Find a triple of rational$ $numbers (a, b, c) such that$ $\sqrt[3]{\sqrt[3]{2} - 1} = \sqrt[3]{a} + \sqrt[3]{b} + \sqrt[3]{c}$ Answered by puissant last updated on 27/Aug/21 $${t}=\sqrt[{\mathrm{3}}]{\mathrm{2}}\:\Rightarrow\:{t}^{\mathrm{3}} =\mathrm{2}\:\rightarrow\:{t}^{\mathrm{3}}…

x-10y-50z-500-x-y-z-100-find-x-y-z-

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Question Number 86741 by M±th+et£s last updated on 30/Mar/20 ${\begin{cases} x + 10 y + 50 z = 500 \\ x + y + z = 100 \end{cases}$ $f i n d x, y, z$ Commented by mr W last updated on 30/Mar/20 $${x},{y},{z}\in{N}\:?…

prove-that-1-cos2x-cosx-1-sin-5x-2-2sin-x-2-1-2-2-cos-x-isin-x-1-cos-x-isin-x-1-i-tan-x-3-cos-5x-isin-5x-1-cos-5x-isin-x-1-cos-5x-isin-5x-

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Question Number 86737 by M±th+et£s last updated on 30/Mar/20 $p r o v e t h a t$ $1 / c o s 2 x + c o s x + 1 = \frac{s i n \frac{5 x}{2}}{2 s i n \frac{x}{2}} + \frac{1}{2}$ $2 / \frac{c o s (x) + i s i n (x) - 1}{c o s (x) + i s i n (x) + 1} = - i t a n (x)$ $3 / \frac{c o s (5 x) + i s i n (5 x) + 1}{c o s (5 x) - i s i n (x) + 1} = c o s (5 x) + i s i n (5 x)$ Commented by som(math1967) last updated…

Suppose-an-integer-x-a-natural-number-n-and-a-prime-number-p-satisfy-the-equation-7x-2-44x-12-p-n-Find-the-largest-value-of-p-

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Question Number 21200 by Tinkutara last updated on 15/Sep/17 $Suppose an integer x, a natural$ $number n and a prime number p$ $satisfy the equation 7 x^{2} - 44 x + 12 = p^{n} .$ $Find the largest value of p .$ Commented by mrW1 last updated…

k-1-n-sin-1-k-k-1-k-k-1-

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Question Number 152265 by mathdanisur last updated on 26/Aug/21 $\underset{k = 1}{\sum^{n}} \sin^{- 1} (\frac{\sqrt{k} - \sqrt{k - 1}}{\sqrt{k (k + 1}}) = ?$ Answered by mindispower last updated on 27/Aug/21 $${sin}^{−} \left({a}\right)−{sin}^{−} \left({b}\right)={sin}^{−}…

Question-152266

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Question Number 152266 by mathdanisur last updated on 26/Aug/21 Answered by qaz last updated on 27/Aug/21 $\int_{0}^{1} {Li}_{2} (x) \ln (1 + x) dx$ $$=\left[\left(\mathrm{1}+\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)−\left(\mathrm{1}+\mathrm{x}\right)\right]\mathrm{Li}_{\mathrm{2}} \left(\mathrm{x}\right)\mid_{\mathrm{0}} ^{\mathrm{1}} +\int_{\mathrm{0}}…

Question-86723

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Question Number 86723 by A8;15: last updated on 30/Mar/20 Commented by jagoll last updated on 30/Mar/20 $\cos^{2} x - \sin^{2} x = \tan x \times \cot x$ $\cos 2 x = 1 \Rightarrow {\begin{cases} x = 0 \\ x = π \end{cases}$ Terms of…

Let-f-x-x-1-x-2-x-3-then-find-the-value-of-k-for-which-f-x-k-has-1-no-solution-2-only-one-solution-3-two-solutions-of-same-sign-4-two-solutions-of-opposite-sign-

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Question Number 21168 by Tinkutara last updated on 15/Sep/17 $Let f (x) = ∣ x - 1 ∣ + ∣ x - 2 ∣ + ∣ x - 3 ∣,$ $then find the value of k for which f (x)$ $= k has$ $1 . no solution$ $2 . only one solution$ $3 . two solutions of same sign$ $4 . two solutions of opposite sign$ Answered…

Category: Algebra