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Question Number 173273 Answers: 1 Comments: 1

Question Number 173254 Answers: 3 Comments: 4

solve for x,y,z ∈R x+y+z=(√3) xy+yz+zx=1

$${solve}\:{for}\:{x},{y},{z}\:\in{R} \\ $$$${x}+{y}+{z}=\sqrt{\mathrm{3}} \\ $$$${xy}+{yz}+{zx}=\mathrm{1} \\ $$

Question Number 173250 Answers: 1 Comments: 0

Solve for real numbers: ∫_0 ^( x) (t^2 /((t ∙ sinh t − cosh t)^2 )) dt = 0

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\int_{\mathrm{0}} ^{\:\boldsymbol{\mathrm{x}}} \:\frac{\mathrm{t}^{\mathrm{2}} }{\left(\mathrm{t}\:\centerdot\:\mathrm{sinh}\:\mathrm{t}\:−\:\mathrm{cosh}\:\mathrm{t}\right)^{\mathrm{2}} }\:\mathrm{dt}\:=\:\mathrm{0} \\ $$

Question Number 173245 Answers: 1 Comments: 0

The ends X and Y of an inextensible strings 27m long are fixed at two points on the same horizontal line which are 20 m apart. A particle of mass 7.5 kg is suspended from a point P on the string 12 m from X. (a) Illustrate this information in a diagram. (b) calculate, correct to two decimal places, <YXP and <XYP. (c) Find, correct to the nearest hundredth, the magnitudes of the tensions in the string. [take g=10 ms^(−2) ]

$$\mathrm{The}\:\mathrm{ends}\:\boldsymbol{\mathrm{X}}\:\mathrm{and}\:\boldsymbol{\mathrm{Y}}\:\mathrm{of}\:\mathrm{an}\:\mathrm{inextensible}\:\mathrm{strings}\:\mathrm{27m} \\ $$$$\mathrm{long}\:\mathrm{are}\:\mathrm{fixed}\:\mathrm{at}\:\mathrm{two}\:\mathrm{points}\:\mathrm{on}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{horizontal}\:\mathrm{line}\:\mathrm{which}\:\mathrm{are}\:\mathrm{20}\:\mathrm{m}\:\mathrm{apart}. \\ $$$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{7}.\mathrm{5}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{suspended} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\boldsymbol{\mathrm{P}}\:\mathrm{on}\:\mathrm{the}\:\mathrm{string}\:\mathrm{12}\:\mathrm{m}\:\mathrm{from}\:\boldsymbol{\mathrm{X}}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Illustrate}\:\mathrm{this}\:\mathrm{information}\:\mathrm{in}\:\mathrm{a}\:\mathrm{diagram}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{calculate},\:\mathrm{correct}\:\mathrm{to}\:\boldsymbol{\mathrm{two}}\:\mathrm{decimal} \\ $$$$\mathrm{places},\:<\mathrm{YXP}\:\mathrm{and}\:<\mathrm{XYP}. \\ $$$$\left(\mathrm{c}\right)\:\mathrm{Find},\:\mathrm{correct}\:\mathrm{to}\:\mathrm{the}\:\boldsymbol{\mathrm{nearest}}\:\mathrm{hundredth}, \\ $$$$\mathrm{the}\:\mathrm{magnitudes}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tensions}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{string}.\:\:\left[\mathrm{take}\:\boldsymbol{\mathrm{g}}=\mathrm{10}\:\mathrm{ms}^{−\mathrm{2}} \right] \\ $$

Question Number 173242 Answers: 2 Comments: 1

Question Number 173240 Answers: 1 Comments: 2

Question Number 173233 Answers: 0 Comments: 0

Question Number 173231 Answers: 0 Comments: 0

Question Number 173236 Answers: 2 Comments: 0

lim_(x→∞) ((x/(1+x)))^x =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{x}}{\mathrm{1}+{x}}\right)^{{x}} =? \\ $$

Question Number 173216 Answers: 0 Comments: 0

O-circumcenter , I-incenter, R-circumradii, r-radii, a,b,c,d-sides in a bicenteric quadrilateral. Prove that: 20I^2 + r Σ_(cyc) (√(4R^2 − a^2 )) = 2(R^2 + 2r^2 )

$$\mathrm{O}-\mathrm{circumcenter}\:,\:\mathrm{I}-\mathrm{incenter},\:\mathrm{R}-\mathrm{circumradii}, \\ $$$$\mathrm{r}-\mathrm{radii},\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}-\mathrm{sides}\:\mathrm{in}\:\mathrm{a}\:\mathrm{bicenteric} \\ $$$$\mathrm{quadrilateral}.\:\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{20I}^{\mathrm{2}} \:+\:\mathrm{r}\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\sqrt{\mathrm{4R}^{\mathrm{2}} \:−\:\mathrm{a}^{\mathrm{2}} }\:=\:\mathrm{2}\left(\mathrm{R}^{\mathrm{2}} \:+\:\mathrm{2r}^{\mathrm{2}} \right) \\ $$

Question Number 173213 Answers: 0 Comments: 0

Question Number 173212 Answers: 1 Comments: 0

Question Number 173224 Answers: 1 Comments: 0

Question Number 173228 Answers: 1 Comments: 0

Question Number 173227 Answers: 1 Comments: 1

Question Number 173226 Answers: 0 Comments: 2

Factorize the following equation: (1/4) (a + b)^2 − (9/(16)) (2a − b)^2

$$\:\:\:\:\boldsymbol{\mathrm{Factorize}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\frac{\mathrm{1}}{\mathrm{4}}\:\left({a}\:+\:{b}\right)^{\mathrm{2}} \:−\:\frac{\mathrm{9}}{\mathrm{16}}\:\left(\mathrm{2}{a}\:−\:{b}\right)^{\mathrm{2}} \\ $$

Question Number 173225 Answers: 1 Comments: 0

lim_(x→0) ((tan x+4tan 2x−3tan 3x)/(x^2 tan x)) =?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:{x}+\mathrm{4tan}\:\mathrm{2}{x}−\mathrm{3tan}\:\mathrm{3}{x}}{{x}^{\mathrm{2}} \:\mathrm{tan}\:{x}}\:=?\: \\ $$

Question Number 173196 Answers: 1 Comments: 1

What is the value of ((y^2 + yz + z^2 )/((x − y)(x − z)))+((z^2 + zx + x^2 )/((y − z)(z − y)))+((x^2 + xy + y^2 )/((z − x)(z−y)))

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{{y}^{\mathrm{2}} \:+\:{yz}\:+\:{z}^{\mathrm{2}} }{\left({x}\:−\:{y}\right)\left({x}\:−\:{z}\right)}+\frac{{z}^{\mathrm{2}} \:+\:{zx}\:+\:{x}^{\mathrm{2}} }{\left({y}\:−\:{z}\right)\left({z}\:−\:{y}\right)}+\frac{{x}^{\mathrm{2}} \:+\:{xy}\:+\:{y}^{\mathrm{2}} }{\left({z}\:−\:{x}\right)\left({z}−{y}\right)} \\ $$

Question Number 173192 Answers: 1 Comments: 0

lim_(n→∞) n^2 (√((1−cos(1/n))(√((1−cos(1/n))(√((1−cos(1/n))......∞))))))=?

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}^{\mathrm{2}} \sqrt{\left(\mathrm{1}−{cos}\frac{\mathrm{1}}{{n}}\right)\sqrt{\left(\mathrm{1}−{cos}\frac{\mathrm{1}}{{n}}\right)\sqrt{\left(\mathrm{1}−{cos}\frac{\mathrm{1}}{{n}}\right)......\infty}}}=? \\ $$

Question Number 173190 Answers: 2 Comments: 0

lim_(x→0) ((ln(2−e^x ))/(x+lnx))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{ln}\left(\mathrm{2}−{e}^{{x}} \right)}{{x}+{lnx}}=? \\ $$

Question Number 173188 Answers: 1 Comments: 0

Question Number 173184 Answers: 1 Comments: 0

Solve for real numbers: 2 ∫_0 ^( x) ((x^2 ∙ e^(arctan(x)) )/( (√(1 + x^2 )))) dx = 1

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{2}\:\int_{\mathrm{0}} ^{\:\boldsymbol{\mathrm{x}}} \:\frac{\mathrm{x}^{\mathrm{2}} \:\centerdot\:\mathrm{e}^{\boldsymbol{\mathrm{arctan}}\left(\boldsymbol{\mathrm{x}}\right)} }{\:\sqrt{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=\:\mathrm{1} \\ $$

Question Number 181404 Answers: 2 Comments: 5

Dterminer la valeur de x

$${Dterminer}\:{la}\:{valeur}\:{de}\:\:\boldsymbol{{x}} \\ $$

Question Number 173178 Answers: 0 Comments: 0

When the terms of a Geometric Progression (G.P.) with r=2 is added to the corresponding terms of an arithmetic progression (A.P.), a new sequence is formed. If the first terms of the GP and AP are the same and the first three termsof the new sequence are 3, 7 and 11 respectively, find the nth term of the new sequence

Question Number 181415 Answers: 1 Comments: 3

solve for x x^x^x =36

$$\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{solve}}\:\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} } =\mathrm{36} \\ $$$$ \\ $$

Question Number 173172 Answers: 0 Comments: 0

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