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Question Number 147187 Answers: 1 Comments: 2

if (xyz^(−) )^2 = (x+y+z)^5 then find: x^3 +y^3 +z^3 −∣(x+y+z)+(x^2 +y^2 +z^2 )∣

$${if}\:\:\left(\overline {{xyz}}\right)^{\mathrm{2}} \:=\:\left({x}+{y}+{z}\right)^{\mathrm{5}} \:\:{then}\:{find}: \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} −\mid\left({x}+{y}+{z}\right)+\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)\mid \\ $$

Question Number 147183 Answers: 1 Comments: 0

prove that e^((√2) + (√3)) > ((13 + 2(√6))/2)

$${prove}\:{that} \\ $$$$\boldsymbol{{e}}^{\sqrt{\mathrm{2}}\:+\:\sqrt{\mathrm{3}}} \:>\:\frac{\mathrm{13}\:+\:\mathrm{2}\sqrt{\mathrm{6}}}{\mathrm{2}} \\ $$

Question Number 147176 Answers: 1 Comments: 0

Question Number 147175 Answers: 0 Comments: 0

Question Number 147169 Answers: 1 Comments: 4

lim_(x→0) (((3^x + 5^x + 6^x )/3))^(1/x) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\left(\frac{\mathrm{3}^{\boldsymbol{{x}}} \:+\:\mathrm{5}^{\boldsymbol{{x}}} \:+\:\mathrm{6}^{\boldsymbol{{x}}} }{\mathrm{3}}\right)^{\frac{\mathrm{1}}{\boldsymbol{{x}}}} =\:? \\ $$

Question Number 147166 Answers: 2 Comments: 0

∫_R e^(ixt) e^(−t^2 ) dt..

$$\int_{\mathbb{R}} \mathrm{e}^{\mathrm{ixt}} \mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt}.. \\ $$

Question Number 147163 Answers: 0 Comments: 0

Question Number 147162 Answers: 1 Comments: 0

Question Number 147158 Answers: 2 Comments: 0

Question Number 147157 Answers: 0 Comments: 1

proof that tan∅+sesin c∅/tan∅+sec∅ = 1+sin∅/cos∅

$${proof}\:{that}\:{tan}\emptyset+\mathrm{sesin}\:\mathrm{c}\emptyset/{tan}\emptyset+{sec}\emptyset\:=\:\mathrm{1}+{sin}\emptyset/{cos}\emptyset \\ $$

Question Number 147149 Answers: 1 Comments: 0

Two concurrent forces F_1 = 12N and F_2 = 30N are 150° apart. Calculate the angle between F_2 and the resultant force.

$$\:\mathrm{Two}\:\mathrm{concurrent}\:\mathrm{forces}\:\boldsymbol{{F}}_{\mathrm{1}} \:=\:\mathrm{12N}\:\mathrm{and} \\ $$$$\:\boldsymbol{{F}}_{\mathrm{2}} \:=\:\mathrm{30N}\:\mathrm{are}\:\mathrm{150}°\:\mathrm{apart}.\:\mathrm{Calculate}\: \\ $$$$\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\boldsymbol{{F}}_{\mathrm{2}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{resultant} \\ $$$$\:\mathrm{force}. \\ $$

Question Number 147146 Answers: 2 Comments: 0

Question Number 147147 Answers: 0 Comments: 0

One end of an inextensible string is fixed to a ceiling and the other end is tied to a wooden block. The block is pulled aside by a horizontal force P, such that the string now makes an angle of 45° with the downward vertical. When the force P is raised through an angle of 30°, it decreases by 8N to keep the system in equilibrium without shifting the string. Find the (a) value of P. (b) mass of the block.

$$\:\mathrm{One}\:\mathrm{end}\:\mathrm{of}\:\mathrm{an}\:\mathrm{inextensible}\:\mathrm{string}\:\mathrm{is} \\ $$$$\:\mathrm{fixed}\:\mathrm{to}\:\mathrm{a}\:\mathrm{ceiling}\:\mathrm{and}\:\mathrm{the}\:\mathrm{other}\:\mathrm{end}\:\mathrm{is} \\ $$$$\:\mathrm{tied}\:\mathrm{to}\:\mathrm{a}\:\mathrm{wooden}\:\mathrm{block}.\:\mathrm{The}\:\mathrm{block}\:\mathrm{is} \\ $$$$\:\mathrm{pulled}\:\mathrm{aside}\:\mathrm{by}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{force}\:\boldsymbol{{P}}, \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{string}\:\mathrm{now}\:\mathrm{makes}\:\mathrm{an} \\ $$$$\:\mathrm{angle}\:\mathrm{of}\:\mathrm{45}°\:\mathrm{with}\:\mathrm{the}\:\mathrm{downward}\: \\ $$$$\:\mathrm{vertical}.\:\mathrm{When}\:\mathrm{the}\:\mathrm{force}\:\boldsymbol{{P}}\:\:\mathrm{is}\:\mathrm{raised} \\ $$$$\:\mathrm{through}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{30}°,\:\mathrm{it}\:\mathrm{decreases}\:\mathrm{by} \\ $$$$\:\mathrm{8N}\:\mathrm{to}\:\mathrm{keep}\:\mathrm{the}\:\mathrm{system}\:\mathrm{in}\:\mathrm{equilibrium} \\ $$$$\:\mathrm{without}\:\mathrm{shifting}\:\mathrm{the}\:\mathrm{string}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\left({a}\right)\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{{P}}. \\ $$$$\:\:\:\:\:\:\:\:\:\left({b}\right)\:\mathrm{mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{block}. \\ $$

Question Number 147144 Answers: 1 Comments: 0

prove that equation of a circle passing through the points of intersection of a circle S=0 and a line L=0 can be taken as S+λL=0 where λ is a parameter

$${prove}\:{that}\: \\ $$$${equation}\:{of}\:{a}\:{circle}\:{passing}\:{through} \\ $$$${the}\:{points}\:{of}\:{intersection}\:{of}\:{a}\:{circle} \\ $$$${S}=\mathrm{0}\:{and}\:{a}\:{line}\:{L}=\mathrm{0}\:{can}\:{be}\:{taken}\:{as} \\ $$$${S}+\lambda{L}=\mathrm{0}\:{where}\:\lambda\:{is}\:{a}\:{parameter} \\ $$

Question Number 147137 Answers: 1 Comments: 0

Question Number 147135 Answers: 3 Comments: 0

Question Number 147134 Answers: 0 Comments: 2

(√(2sin(x)−1)) ∙ sin(x) > 0

$$\sqrt{\mathrm{2}{sin}\left({x}\right)−\mathrm{1}}\:\centerdot\:{sin}\left({x}\right)\:>\:\mathrm{0} \\ $$

Question Number 147130 Answers: 1 Comments: 2

Question Number 147115 Answers: 0 Comments: 0

pleaae there is challenge to this question as to whether the answer is ((43)/6) OR −((1187)/(42)) please help Question simplify 37(1/2) ÷ (5/9) of ((4/7)+(1/5))−80(1/3). the same question but different answer from different books

$$\mathrm{pleaae}\:\mathrm{there}\:\mathrm{is}\:\mathrm{challenge}\:\mathrm{to}\:\mathrm{this}\: \\ $$$$\mathrm{question}\:\mathrm{as}\:\mathrm{to}\:\mathrm{whether}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is} \\ $$$$\:\:\:\:\:\frac{\mathrm{43}}{\mathrm{6}}\:\:\:\mathrm{OR}\:\:\:−\frac{\mathrm{1187}}{\mathrm{42}}\:\:\mathrm{please}\:\mathrm{help} \\ $$$$\mathrm{Question}\: \\ $$$$\mathrm{simplify}\:\:\mathrm{37}\frac{\mathrm{1}}{\mathrm{2}}\:\boldsymbol{\div}\:\frac{\mathrm{5}}{\mathrm{9}}\:\mathrm{of}\:\left(\frac{\mathrm{4}}{\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{5}}\right)−\mathrm{80}\frac{\mathrm{1}}{\mathrm{3}}. \\ $$$$\:\mathrm{the}\:\mathrm{same}\:\mathrm{question}\:\mathrm{but}\:\mathrm{different}\: \\ $$$$\mathrm{answer}\:\mathrm{from}\:\mathrm{different}\:\mathrm{books} \\ $$

Question Number 147122 Answers: 1 Comments: 0

lim_(n→∞) Σ_(k=1) ^n 2^k ∙((2)^(1/2^k ) −1)^2 = ?

$$\underset{\boldsymbol{{n}}\rightarrow\infty} {{lim}}\:\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\mathrm{2}^{\boldsymbol{{k}}} \centerdot\left(\sqrt[{\mathrm{2}^{\boldsymbol{{k}}} }]{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}} \:=\:?\: \\ $$

Question Number 147344 Answers: 1 Comments: 0

lim_(n→∞) ∫_( 0) ^( 1) log (((1+sin^n x)/(1+x+x^n )))dx = ?

$$\underset{{n}\rightarrow\infty} {{lim}}\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:{log}\:\left(\frac{\mathrm{1}+{sin}^{\boldsymbol{{n}}} \boldsymbol{{x}}}{\mathrm{1}+{x}+{x}^{\boldsymbol{{n}}} }\right){dx}\:=\:? \\ $$

Question Number 147119 Answers: 2 Comments: 0

if x>−1 , q≥2 then: (1+x)^q ≥ 1+qx+(q−1)x^2

$${if}\:\:\:{x}>−\mathrm{1}\:,\:{q}\geqslant\mathrm{2}\:\:\:{then}: \\ $$$$\left(\mathrm{1}+{x}\right)^{\boldsymbol{{q}}} \:\geqslant\:\mathrm{1}+{qx}+\left({q}−\mathrm{1}\right){x}^{\mathrm{2}} \\ $$

Question Number 147118 Answers: 1 Comments: 0