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Question Number 171990 Answers: 1 Comments: 0

solve: log_7 2 + log_(49) x =log_7 (√3)

$${solve}: \\ $$$${log}_{\mathrm{7}} \mathrm{2}\:+\:{log}_{\mathrm{49}} {x}\:={log}_{\mathrm{7}} \sqrt{\mathrm{3}} \\ $$

Question Number 171989 Answers: 1 Comments: 0

solve: A two digit number is such that 4 times the unit digit is 5 more than thrice the ten digit. when the digit are reversed the number is increase by nine, find the number

$${solve}:\:{A}\:{two}\:{digit}\:{number}\:{is}\:{such} \\ $$$${that}\:\mathrm{4}\:{times}\:{the}\:{unit}\:{digit}\:{is}\:\mathrm{5}\:{more}\: \\ $$$${than}\:{thrice}\:{the}\:{ten}\:{digit}.\:{when}\:{the} \\ $$$${digit}\:{are}\:{reversed}\:{the}\:{number}\:{is}\: \\ $$$${increase}\:{by}\:{nine},\:{find}\:{the}\:{number} \\ $$$$ \\ $$

Question Number 171988 Answers: 0 Comments: 0

solve: x^2 =16^x

$${solve}: \\ $$$${x}^{\mathrm{2}} =\mathrm{16}^{{x}} \\ $$

Question Number 171984 Answers: 0 Comments: 0

Question Number 171979 Answers: 1 Comments: 0

Question Number 171972 Answers: 1 Comments: 0

Question Number 171971 Answers: 2 Comments: 0

∫(x/(x^2 +4x+3)) dx=...

$$\int\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{3}}\:{dx}=... \\ $$

Question Number 171966 Answers: 0 Comments: 0

Question Number 171955 Answers: 2 Comments: 0

f(x)+ f((1/(1−x))) = 1+(1/(x(1−x))) f(x) = ??

$$\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)+\:\boldsymbol{{f}}\left(\frac{\mathrm{1}}{\mathrm{1}−\boldsymbol{{x}}}\right)\:=\:\mathrm{1}+\frac{\mathrm{1}}{\boldsymbol{{x}}\left(\mathrm{1}−\boldsymbol{{x}}\right)} \\ $$$$\:\:\:\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:=\:\:??\:\:\:\:\:\:\:\:\: \\ $$

Question Number 171954 Answers: 0 Comments: 0

Find without softs: ∫_(1/e) ^( e) (dx/((1 + x^2 )(1 + x log^7 x)))

$$\mathrm{Find}\:\mathrm{without}\:\mathrm{softs}: \\ $$$$\int_{\frac{\mathrm{1}}{\boldsymbol{\mathrm{e}}}} ^{\:\boldsymbol{\mathrm{e}}} \:\frac{\mathrm{dx}}{\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}\:+\:\mathrm{x}\:\mathrm{log}^{\mathrm{7}} \:\mathrm{x}\right)} \\ $$

Question Number 171985 Answers: 0 Comments: 0

In △ABC , O-circumcentr , G-centroid. Prove that: OG∥BC⇔(b^2 −c^2 )^2 =4a^2 (9R^2 −a^2 −b^2 −c^2 )

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:,\:\mathrm{O}-\mathrm{circumcentr}\:,\:\mathrm{G}-\mathrm{centroid}. \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{OG}\parallel\mathrm{BC}\Leftrightarrow\left(\mathrm{b}^{\mathrm{2}} −\mathrm{c}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{4a}^{\mathrm{2}} \left(\mathrm{9R}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} −\mathrm{c}^{\mathrm{2}} \right) \\ $$

Question Number 171944 Answers: 0 Comments: 5

if a+b+c=2196 (a)^(1/3) +b+c=2076 a+(b)^(1/3) +c=1860 a+b+(c)^(1/3) =480, determine the value of a^(2/3) +b^(2/3) +c^(2/3) , if a,b,c are all integer.

$${if} \\ $$$${a}+{b}+{c}=\mathrm{2196} \\ $$$$\sqrt[{\mathrm{3}}]{{a}}\:+{b}+{c}=\mathrm{2076} \\ $$$${a}+\sqrt[{\mathrm{3}}]{{b}}\:+{c}=\mathrm{1860} \\ $$$${a}+{b}+\sqrt[{\mathrm{3}}]{{c}}\:=\mathrm{480},\:{determine}\:{the}\:{value}\:{of} \\ $$$${a}^{\frac{\mathrm{2}}{\mathrm{3}}} +{b}^{\frac{\mathrm{2}}{\mathrm{3}}} +{c}^{\frac{\mathrm{2}}{\mathrm{3}}} ,\:{if}\:{a},{b},{c}\:{are}\:{all}\:{integer}. \\ $$

Question Number 171941 Answers: 0 Comments: 3

(√a)+(√b)=(√(2009)). find a and b.

$$\sqrt{{a}}+\sqrt{{b}}=\sqrt{\mathrm{2009}}.\:{find}\:{a}\:{and}\:{b}. \\ $$

Question Number 171930 Answers: 0 Comments: 0

Question Number 171986 Answers: 0 Comments: 0

Question Number 171927 Answers: 1 Comments: 0

solve: x^(√x) =((x)^(1/4) )^(1+(√x))

$${solve}: \\ $$$${x}^{\sqrt{{x}}} =\left(\sqrt[{\mathrm{4}}]{{x}}\right)^{\mathrm{1}+\sqrt{{x}}} \\ $$

Question Number 171926 Answers: 0 Comments: 3

∫ (((x^(−6) −64)/(4+2x^(−1) +x^(−2) )).(x^2 /(4−4x^(−1) +x^(−2) )) − ((4x^2 (2x+1))/(1−2x)))dx

$$\int\:\left(\frac{{x}^{−\mathrm{6}} −\mathrm{64}}{\mathrm{4}+\mathrm{2}{x}^{−\mathrm{1}} +{x}^{−\mathrm{2}} }.\frac{{x}^{\mathrm{2}} }{\mathrm{4}−\mathrm{4}{x}^{−\mathrm{1}} +{x}^{−\mathrm{2}} }\:−\:\frac{\mathrm{4}{x}^{\mathrm{2}} \left(\mathrm{2}{x}+\mathrm{1}\right)}{\mathrm{1}−\mathrm{2}{x}}\right){dx} \\ $$

Question Number 171922 Answers: 0 Comments: 2

if α and β are the positive roots of the eqn x^2 +px+q=0, find the sum M=(α)^(1/4) +(β)^(1/4)

$${if}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{positive}\:{roots}\:{of}\:{the}\:{eqn} \\ $$$${x}^{\mathrm{2}} +{px}+{q}=\mathrm{0},\:{find}\:{the}\:{sum}\:{M}=\sqrt[{\mathrm{4}}]{\alpha}\:+\sqrt[{\mathrm{4}}]{\beta} \\ $$

Question Number 171921 Answers: 1 Comments: 0

(((x^2 −9))^(1/3) /( ((x+3))^(1/3) ))=3, find x

$$\frac{\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} −\mathrm{9}}}{\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{3}}}=\mathrm{3},\:{find}\:{x} \\ $$

Question Number 171919 Answers: 0 Comments: 0

if a+b+c=2196 (a)^(1/3) +b+c=2076 a+(b)^(1/3) +c=1860 a+b+(c)^(1/3) =480, determine the value of a^(2/3) +b^(2/3) +c^(2/3) , if a,b,c are all integer.

Question Number 171910 Answers: 3 Comments: 0

∫ (dx/(9 − 4x^2 )) using the trigonometric substitution.

$$\int\:\frac{\mathrm{dx}}{\mathrm{9}\:\:\:−\:\:\:\mathrm{4x}^{\mathrm{2}} } \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{trigonometric}\:\mathrm{substitution}. \\ $$

Question Number 171908 Answers: 0 Comments: 4

Question Number 171906 Answers: 0 Comments: 0

a fource f facts on a body of mass (t+2)kg and it′s momentum was (t^2 +6t+8) kg . m/ sec what is the average power in the first 3 seconds

$${a}\:{fource}\:{f}\:{facts}\:{on}\:{a}\:{body}\:{of}\:{mass} \\ $$$$\left({t}+\mathrm{2}\right){kg}\:{and}\:{it}'{s}\:{momentum}\:{was} \\ $$$$\left({t}^{\mathrm{2}} +\mathrm{6}{t}+\mathrm{8}\right)\:{kg}\:.\:{m}/\:{sec} \\ $$$$\:{what}\:{is}\:{the}\:{average}\:{power}\:{in}\:{the} \\ $$$${first}\:\mathrm{3}\:{seconds} \\ $$

Question Number 171883 Answers: 0 Comments: 0

The function f(x)=ax^2 +bx+c has gradient function 4x+2 and stationary value 1. Find the values of a,b and c.

$$\mathrm{The}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}\:\mathrm{has}\:\mathrm{gradient} \\ $$$$\mathrm{function}\:\mathrm{4x}+\mathrm{2}\:\mathrm{and}\:\mathrm{stationary}\:\mathrm{value}\:\mathrm{1}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{a},{b}\:\mathrm{and}\:{c}. \\ $$

Question Number 171873 Answers: 1 Comments: 2

solve: ((x+(√(x^2 −1)))/(x−(√(x^2 −1)))) −((x−(√(x^2 −1)))/(x+(√(x^2 −1)))) =8x(√(x^2 −3x+2))

$${solve}: \\ $$$$\frac{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:−\frac{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:\:=\mathrm{8}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$

Question Number 171872 Answers: 1 Comments: 0

Solve for real numbers: (1/(1 + tan^4 x)) + (1/(10)) = (2/(1 + 3 tan^2 x))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{tan}^{\mathrm{4}} \:\mathrm{x}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{10}}\:\:=\:\:\frac{\mathrm{2}}{\mathrm{1}\:+\:\mathrm{3}\:\mathrm{tan}^{\mathrm{2}} \:\mathrm{x}} \\ $$

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