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Question Number 217122 Answers: 1 Comments: 0

∫ ((√(cos 2x))/(cos x)) dx =?

$$\:\:\:\:\:\int\:\frac{\sqrt{\mathrm{cos}\:\mathrm{2x}}}{\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 217121 Answers: 0 Comments: 0

Question Number 217137 Answers: 0 Comments: 3

Please do not post totally meaningless questions/answers. If you dont know the answer leave it unanswered. If some has ideas they will post either partially or full answers. Do not post meaningless answers that cancel operator or function from numerator/denominator.

$$ \\ $$$$\mathrm{Please}\:\mathrm{do}\:\mathrm{not}\:\mathrm{post}\:\mathrm{totally}\:\mathrm{meaningless} \\ $$$$\mathrm{questions}/\mathrm{answers}. \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{dont}\:\mathrm{know}\:\mathrm{the}\:\mathrm{answer} \\ $$$$\mathrm{leave}\:\mathrm{it}\:\mathrm{unanswered}.\:\mathrm{If}\:\mathrm{some}\:\mathrm{has} \\ $$$$\mathrm{ideas}\:\mathrm{they}\:\mathrm{will}\:\mathrm{post}\:\mathrm{either}\:\mathrm{partially} \\ $$$$\mathrm{or}\:\mathrm{full}\:\mathrm{answers}. \\ $$$$\mathrm{Do}\:\mathrm{not}\:\mathrm{post}\:\mathrm{meaningless}\:\mathrm{answers}\:\mathrm{that} \\ $$$$\mathrm{cancel}\:\mathrm{operator}\:\mathrm{or}\:\mathrm{function}\:\mathrm{from} \\ $$$$\mathrm{numerator}/\mathrm{denominator}. \\ $$

Question Number 217132 Answers: 0 Comments: 0

Find all integers n> 1 such that n divides 2^(n−1) + 3^(n−1) .

$$ \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{integers}\:\:\mathrm{n}>\:\mathrm{1}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\mathrm{n}\:\:\mathrm{divides}\:\:\mathrm{2}^{\mathrm{n}−\mathrm{1}} \:+\:\mathrm{3}^{\mathrm{n}−\mathrm{1}} . \\ $$

Question Number 217130 Answers: 0 Comments: 0

Prove that for every integer n≥2 the number n^4 + 4^n is composite.

$$ \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{every}\:\mathrm{integer}\:\:\mathrm{n}\geqslant\mathrm{2}\:\:\mathrm{the}\:\mathrm{number}\:\:\mathrm{n}^{\mathrm{4}} +\:\mathrm{4}^{{n}} \:\:\mathrm{is} \\ $$$$\mathrm{c}{o}\mathrm{mposite}. \\ $$

Question Number 217129 Answers: 1 Comments: 2

prove that if an integer n is not divisible by 2 or 3 then n^2 ≡1(mod 24)

$${prove}\:{that}\:{if}\:{an}\:{integer}\:{n}\:{is}\:{not}\:{divisible}\:{by}\:\mathrm{2}\:{or}\:\mathrm{3} \\ $$$$\:{then}\:{n}^{\mathrm{2}} \equiv\mathrm{1}\left({mod}\:\mathrm{24}\right) \\ $$

Question Number 217088 Answers: 1 Comments: 0

show that ∫_( n) ^( n + 1) ln(t) dt ≤ ln(n + (1/2)) Given u_n = (((4n)^n n!e^(−n) )/((2n)!)), ∀n ≥ 1 prove, using the preceding question that u_n is decreasing and convergent

$${show}\:{that}\:\int_{\:{n}} ^{\:{n}\:+\:\mathrm{1}} {ln}\left({t}\right)\:{dt}\:\leqslant\:{ln}\left({n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$${Given}\:{u}_{{n}} \:=\:\frac{\left(\mathrm{4}{n}\right)^{{n}} {n}!{e}^{−{n}} }{\left(\mathrm{2}{n}\right)!},\:\forall{n}\:\geqslant\:\mathrm{1} \\ $$$${prove},\:{using}\:{the}\:{preceding}\:{question}\:{that} \\ $$$${u}_{{n}} \:{is}\:{decreasing}\:{and}\:{convergent} \\ $$

Question Number 217085 Answers: 0 Comments: 2

Question Number 217084 Answers: 0 Comments: 0

Geometrie dans le plan. AB^(→) et CD^(→) sont deux vecteurs du plan. AB^(→) n′est pas nul. Demontre que si AB^(→) et CD^(→) sont colineaires alors il existe un nombre reel k tel que CD^(→) = k AB^(→) .

$$\boldsymbol{\mathrm{Geometr}}\mathrm{i}\boldsymbol{\mathrm{e}}\:\boldsymbol{\mathrm{dans}}\:\boldsymbol{\mathrm{le}}\:\boldsymbol{\mathrm{plan}}. \\ $$$$\overset{\rightarrow} {\mathrm{AB}}\:\mathrm{et}\:\overset{\rightarrow} {\mathrm{CD}}\:\mathrm{sont}\:\mathrm{deux}\:\mathrm{vecteurs}\:\mathrm{du}\:\mathrm{plan}. \\ $$$$\overset{\rightarrow} {\mathrm{AB}}\:\mathrm{n}'\mathrm{est}\:\mathrm{pas}\:\mathrm{nul}. \\ $$$$\mathrm{Demontre}\:\mathrm{que}\:\mathrm{si}\:\overset{\rightarrow} {\mathrm{AB}}\:\mathrm{et}\:\overset{\rightarrow} {\mathrm{CD}}\:\mathrm{sont}\:\mathrm{colineaires} \\ $$$$\mathrm{alors}\:\mathrm{il}\:\mathrm{existe}\:\mathrm{un}\:\mathrm{nombre}\:\mathrm{reel}\:\mathrm{k}\:\mathrm{tel}\:\mathrm{que} \\ $$$$\overset{\rightarrow} {\mathrm{CD}}\:=\:\mathrm{k}\:\overset{\rightarrow} {\mathrm{AB}}. \\ $$

Question Number 217080 Answers: 3 Comments: 1

Question Number 217068 Answers: 0 Comments: 0

Question Number 217066 Answers: 1 Comments: 0

Find all integer x,y such that x^2 −y^2 =100

$${Find}\:{all}\:{integer}\:{x},{y}\:{such}\:{that} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{100} \\ $$

Question Number 217065 Answers: 0 Comments: 9

To Tinku Tara sir, How can I import something in Latex form. •There is an option Get Latex but there is no “Paste Latex” option •When I tried to import something using option “Paste plain text” all the whitespaces/new line were lost in imported material. Please solve these issues as soon as possible

$${To}\:{Tinku}\:{Tara}\:{sir}, \\ $$$${How}\:{can}\:{I}\:{import}\:{something}\:{in}\:{Latex}\:{form}. \\ $$$$\bullet{There}\:{is}\:{an}\:{option}\:\mathrm{Get}\:\mathrm{Latex}\:{but}\:{there}\:{is}\:{no} \\ $$$$``\mathrm{Paste}\:\mathrm{Latex}''\:{option} \\ $$$$\bullet{When}\:{I}\:{tried}\:{to}\:{import}\:{something}\:{using}\:{option} \\ $$$$``\mathrm{Paste}\:\mathrm{plain}\:\mathrm{text}''\:{all}\:{the}\:{whitespaces}/{new}\:{line}\: \\ $$$${were}\:{lost}\:{in}\:{imported}\:{material}. \\ $$$$\boldsymbol{{Please}}\:{solve}\:{these}\:{issues}\:{as}\:{soon}\:{as}\:{possible} \\ $$

Question Number 217071 Answers: 1 Comments: 0

Find all two-digit numbers that are equal to four times the sum of their digits. Solve this using at least two different methods and verify your answers.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{two}-\mathrm{digit}\:\mathrm{numbers}\:\mathrm{that}\:\mathrm{are}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{four}\:\mathrm{times}\:\mathrm{the}\:\mathrm{sum}\: \\ $$$$\mathrm{of}\:\mathrm{their}\:\mathrm{digits}.\:\mathrm{Solve}\:\mathrm{this}\:\mathrm{using}\:\mathrm{at}\:\mathrm{least}\:\mathrm{two}\:\mathrm{different}\:\mathrm{methods}\: \\ $$$$\mathrm{and}\:\mathrm{verify}\:\mathrm{your}\:\mathrm{answers}. \\ $$

Question Number 217064 Answers: 1 Comments: 0

Two numbers differ by 6. The sum of their reciprocals is (2/(15)) . Determine the numbers.

$$\mathrm{Two}\:\mathrm{numbers}\:\mathrm{differ}\:\mathrm{by}\:\mathrm{6}.\:\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{reciprocals}\:\mathrm{is}\:\frac{\mathrm{2}}{\mathrm{15}}\:. \\ $$$$\mathcal{D}{etermine}\:{the}\:{numbers}. \\ $$

Question Number 217079 Answers: 1 Comments: 0

((6C3×4C1)/(15C4))

$$\frac{\mathrm{6}{C}\mathrm{3}×\mathrm{4}{C}\mathrm{1}}{\mathrm{15}{C}\mathrm{4}} \\ $$$$ \\ $$

Question Number 217050 Answers: 1 Comments: 1

Question Number 217046 Answers: 1 Comments: 0

form the differential equation by eliminating the arbritrary constant y^2 =Ax^2 +Bx+C

$${form}\:{the}\:{differential}\:{equation}\:{by}\: \\ $$$${eliminating}\:{the}\:{arbritrary}\:{constant} \\ $$$${y}^{\mathrm{2}} ={Ax}^{\mathrm{2}} +{Bx}+{C} \\ $$

Question Number 217049 Answers: 0 Comments: 1

Hello here its been a while. I′ve been watching Ajfour sir dancing lately on Youtube. I believe he has gotten to saturation point. Is there anyone here into AI and Machine learning?

$${Hello}\:{here}\:{its}\:{been}\:{a}\:{while}.\:{I}'{ve} \\ $$$${been}\:{watching}\:{Ajfour}\:{sir}\:{dancing} \\ $$$${lately}\:{on}\:{Youtube}.\:{I}\:{believe}\:{he}\:{has} \\ $$$${gotten}\:{to}\:{saturation}\:{point}. \\ $$$${Is}\:{there}\:{anyone}\:{here}\:{into}\:{AI}\:{and} \\ $$$${Machine}\:{learning}? \\ $$$$ \\ $$

Question Number 217040 Answers: 2 Comments: 0

Find all positive integers n such that n divides 2^n + 1.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:\:\mathrm{n}\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\mathrm{n}\:\:\mathrm{divides}\:\:\mathrm{2}^{{n}} \:+\:\mathrm{1}.\:\: \\ $$

Question Number 217058 Answers: 1 Comments: 0

The quadratic equation has two equal roots: x^2 +(k−3)x+k=0 (a) Find the value of k. (b) For this value of k, solve the equation for x (c)If x is the length of a rectangle and its width is x−2, find the area of the rectangle.

$$\mathrm{The}\:\mathrm{quadratic}\:\mathrm{equation}\:\:\mathrm{has}\:\mathrm{two}\:\mathrm{equal}\:\mathrm{roots}: \\ $$$$\:\:\:\:\:{x}^{\mathrm{2}} +\left({k}−\mathrm{3}\right){x}+{k}=\mathrm{0} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{k}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{For}\:\mathrm{this}\:\mathrm{value}\:\mathrm{of}\:\:{k},\:\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{for}\:{x} \\ $$$$\left(\mathrm{c}\right)\mathrm{If}\:\:{x}\:\mathrm{is}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rectangle}\:\mathrm{and}\:\mathrm{its}\:\mathrm{width}\:\mathrm{is}\:{x}−\mathrm{2},\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}. \\ $$

Question Number 217032 Answers: 0 Comments: 0

Question Number 217024 Answers: 1 Comments: 0

Question Number 217030 Answers: 1 Comments: 0

Find all positive integers n such that n + 1 divides n^2 + 1

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:\:\mathrm{n}\:\:\mathrm{such}\:\mathrm{that}\:\: \\ $$$$\:\mathrm{n}\:+\:\mathrm{1}\:\:\mathrm{divides}\:\:\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$

Question Number 216998 Answers: 0 Comments: 3

Question Number 216995 Answers: 3 Comments: 0

Find all prime numbers p and q such that p^2 − q^2 = 2024

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{numbers}\:\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\: \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{p}^{\mathrm{2}} −\:\:\mathrm{q}^{\mathrm{2}} =\:\:\mathrm{2024} \\ $$

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