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AllQuestion and Answers: Page 208

Question Number 200048 Answers: 0 Comments: 2

Question Number 200041 Answers: 3 Comments: 0

By strong induction prove that any natural number equal to or bigger than 8 can be written as 3a+5b where a and b are non−negative integers.

$${By}\:{strong}\:{induction}\:{prove}\:{that}\:{any} \\ $$$${natural}\:{number}\:{equal}\:{to}\:{or}\:{bigger}\:{than} \\ $$$$\mathrm{8}\:{can}\:{be}\:{written}\:{as}\:\mathrm{3}{a}+\mathrm{5}{b}\:{where}\:{a}\:{and}\:{b} \\ $$$${are}\:{non}−{negative}\:{integers}. \\ $$

Question Number 200040 Answers: 2 Comments: 0

Q: If , tan((π/4) −α )= (1/2) ⇒Find the value of , tan(4α)=?

$$ \\ $$$$\:\:\:\:\:{Q}:\:\:{If}\:\:,\:\:{tan}\left(\frac{\pi}{\mathrm{4}}\:−\alpha\:\right)=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\Rightarrow{Find}\:{the}\:{value}\:{of}\:,\:{tan}\left(\mathrm{4}\alpha\right)=? \\ $$$$ \\ $$

Question Number 200035 Answers: 1 Comments: 2

Question Number 200025 Answers: 3 Comments: 0

Question Number 200022 Answers: 0 Comments: 0

solve the associated legendre equation λ=l (l+1)η^2 ;l=0,1,2... and m^2 ≤ l(l+1) which requires −l≤m≤l using power series

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{associated}\:\mathrm{legendre}\:\mathrm{equation} \\ $$$$\lambda={l}\:\left({l}+\mathrm{1}\right)\eta^{\mathrm{2}} \:;{l}=\mathrm{0},\mathrm{1},\mathrm{2}...\:\:\:{and}\:{m}^{\mathrm{2}} \leqslant\:{l}\left({l}+\mathrm{1}\right)\: \\ $$$${which}\:{requires}\:−{l}\leqslant{m}\leqslant{l}\:\mathrm{using}\:\mathrm{power}\:\mathrm{series} \\ $$

Question Number 200019 Answers: 1 Comments: 0

Question Number 200013 Answers: 0 Comments: 3

Question Number 200012 Answers: 0 Comments: 0

Question Number 200053 Answers: 0 Comments: 1

Question Number 200061 Answers: 1 Comments: 0

∫_(−∞) ^(+∞) ((xsinx )/((x^2 +1)(x^2 +4)))dx = ??

$$\:\:\:\:\int_{−\infty} ^{+\infty} \frac{{x}\mathrm{sin}{x}\:}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{dx}\:\:=\:\:\:?? \\ $$

Question Number 200060 Answers: 2 Comments: 0

Question Number 200005 Answers: 3 Comments: 0

Question Number 200004 Answers: 1 Comments: 0

Question Number 199987 Answers: 1 Comments: 0

Use mathematical induction to prove that the statement a+(a+d)+(a+2d)+...+(a+(n−1)d)=(n/2)[2a+(n−1)d] is true for all natural numbers Any help please

$$\:\boldsymbol{{Use}}\:\boldsymbol{{mathematical}}\:\boldsymbol{{induction}} \\ $$$$\:\boldsymbol{{to}}\:\boldsymbol{{prove}}\:\boldsymbol{{that}}\:\boldsymbol{{the}}\:\boldsymbol{{statement}} \\ $$$$\:\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{d}}\right)+\left(\boldsymbol{\mathrm{a}}+\mathrm{2}\boldsymbol{\mathrm{d}}\right)+...+\left(\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\boldsymbol{\mathrm{d}}\right)=\frac{\boldsymbol{\mathrm{n}}}{\mathrm{2}}\left[\mathrm{2}\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\boldsymbol{\mathrm{d}}\right] \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{true}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{natural}}\:\boldsymbol{\mathrm{numbers}} \\ $$$$\boldsymbol{\mathrm{A}{ny}}\:\boldsymbol{{help}}\:\boldsymbol{{please}} \\ $$

Question Number 199986 Answers: 2 Comments: 0

How do I solve this please? Show that if the sides of a right triangle are in an arithmetic sequence, then their ratio is 3:4:5.

$$ \\ $$How do I solve this please? Show that if the sides of a right triangle are in an arithmetic sequence, then their ratio is 3:4:5.

Question Number 199983 Answers: 1 Comments: 0

find lim_(x→∞) sin (((πx)/(5+3x))) by sequeeze theorem

$$\:\:\:\mathrm{find}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\left(\frac{\pi\mathrm{x}}{\mathrm{5}+\mathrm{3x}}\right)\: \\ $$$$\:\:\mathrm{by}\:\mathrm{sequeeze}\:\mathrm{theorem} \\ $$

Question Number 199996 Answers: 0 Comments: 0

Calculate the first order energy correction for 1−dimensional non−degenerate anharmonic oscillator whose harmiltonian is written in form H^ =(h^2 /(2m)) (d^2 /dx^2 ) + (1/2)kx^(2 ) +(1/5)γx^3 +(1/(12))βx^4

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{first}\:\mathrm{order}\:\mathrm{energy}\:\mathrm{correction}\:\mathrm{for} \\ $$$$\mathrm{1}−\mathrm{dimensional}\:\mathrm{non}−\mathrm{degenerate}\:\mathrm{anharmonic} \\ $$$$\mathrm{oscillator}\:\mathrm{whose}\:\mathrm{harmiltonian}\:\mathrm{is} \:\mathrm{written}\:\mathrm{in}\:\mathrm{form} \\ $$$$\hat {\mathrm{H}}=\frac{\mathrm{h}^{\mathrm{2}} }{\mathrm{2m}}\:\frac{\mathrm{d}^{\mathrm{2}} }{\mathrm{dx}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{kx}^{\mathrm{2}\:} +\frac{\mathrm{1}}{\mathrm{5}}\gamma{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{12}}\beta{x}^{\mathrm{4}} \\ $$

Question Number 199968 Answers: 1 Comments: 1

determiner x ?

$$\mathrm{determiner}\:\boldsymbol{\mathrm{x}}\:\:? \\ $$

Question Number 199959 Answers: 0 Comments: 4

how do I calculate for 7.86! without calculator?

$$\:\boldsymbol{{how}}\:\boldsymbol{{do}}\:\boldsymbol{{I}}\:\boldsymbol{{calculate}}\:\boldsymbol{{for}} \\ $$$$\:\mathrm{7}.\mathrm{86}!\:\boldsymbol{{without}}\:\boldsymbol{{calculator}}? \\ $$

Question Number 199956 Answers: 1 Comments: 0

Question Number 199952 Answers: 1 Comments: 0

Question Number 199942 Answers: 1 Comments: 0

Question Number 199940 Answers: 2 Comments: 3

Question Number 199934 Answers: 2 Comments: 0

y=f(x), x≥0 f(3x)= 3f(x). If ∫_3 ^(27) f(x)dx= 10 than ∫_0 ^3 f(x) dx =?

$$\:\: \mathrm{y}=\mathrm{f}\left(\mathrm{x}\right),\:\mathrm{x}\geqslant\mathrm{0}\: \\ $$$$\: \mathrm{f}\left(\mathrm{3x}\right)=\:\mathrm{3f}\left(\mathrm{x}\right).\:\mathrm{If}\:\underset{\mathrm{3}} {\overset{\mathrm{27}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\:\mathrm{10} \\ $$$$\:\mathrm{than}\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=?\: \\ $$

Question Number 199932 Answers: 2 Comments: 0

1. If 3 ∙ ab^(−) + bc^(−) = 115 Find: max(a+b+c)=? 2. a,b,c∈N If (a/2) + (b/3) = (c/4) Find: min(a+b+c)=?

$$\mathrm{1}. \\ $$$$\mathrm{If}\:\:\:\mathrm{3}\:\centerdot\:\overline {\mathrm{ab}}\:+\:\overline {\mathrm{bc}}\:=\:\mathrm{115} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{max}\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)=? \\ $$$$ \\ $$$$\mathrm{2}. \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{N} \\ $$$$\mathrm{If}\:\:\:\frac{\mathrm{a}}{\mathrm{2}}\:\:+\:\:\frac{\mathrm{b}}{\mathrm{3}}\:\:=\:\:\frac{\mathrm{c}}{\mathrm{4}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{min}\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)=? \\ $$

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