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Question Number 107196 Answers: 2 Comments: 8

How many different words can be formed with the same letters as in TINKUTARA if no two same letters are next to each other.

$${How}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$$${formed}\:{with}\:{the}\:{same}\:{letters}\:{as}\:{in} \\ $$$${TINKUTARA}\:{if}\:{no}\:{two}\:{same}\:{letters} \\ $$$${are}\:{next}\:{to}\:{each}\:{other}. \\ $$

Question Number 107193 Answers: 1 Comments: 0

∫_0 ^4 ((ln x)/(√(4x−x^2 ))) dx ?

$$\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\frac{\mathrm{ln}\:\mathrm{x}}{\sqrt{\mathrm{4x}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:? \\ $$

Question Number 107187 Answers: 1 Comments: 3

Prove that (√8)=1+(3/4)+((3.5)/(4.8))+((3.5.7)/(4.8.12))+......

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\sqrt{\mathrm{8}}=\mathrm{1}+\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{3}.\mathrm{5}}{\mathrm{4}.\mathrm{8}}+\frac{\mathrm{3}.\mathrm{5}.\mathrm{7}}{\mathrm{4}.\mathrm{8}.\mathrm{12}}+...... \\ $$

Question Number 107184 Answers: 2 Comments: 0

@bemath@ ∫_0 ^2 x ((8−x^3 ))^(1/3) dx =?

$$\:\:\:\:\:\:\:@{bemath}@ \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\:{x}\:\sqrt[{\mathrm{3}}]{\mathrm{8}−{x}^{\mathrm{3}} }\:{dx}\:=?\: \\ $$

Question Number 107178 Answers: 1 Comments: 1

Question Number 107171 Answers: 0 Comments: 0

Question Number 107170 Answers: 0 Comments: 0

Question Number 107169 Answers: 2 Comments: 1

If a,b,c,d∈R a+b=8 ab+c+d=23 ad+bc=28 cd=12 Find a^2 +b^2 +c^2 +d^2 .

$$\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\in\mathbb{R} \\ $$$$\mathrm{a}+\mathrm{b}=\mathrm{8} \\ $$$$\mathrm{ab}+\mathrm{c}+\mathrm{d}=\mathrm{23} \\ $$$$\mathrm{ad}+\mathrm{bc}=\mathrm{28} \\ $$$$\mathrm{cd}=\mathrm{12} \\ $$$$\mathrm{Find}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} . \\ $$$$ \\ $$

Question Number 107163 Answers: 2 Comments: 0

Question Number 107162 Answers: 1 Comments: 1

Question Number 107157 Answers: 0 Comments: 0

Question Number 107155 Answers: 2 Comments: 0

Question Number 107153 Answers: 1 Comments: 0

@bemath@ (((14)/5))^(((28)/(√x))−5) = ((5/(14)))^((5/(√x))−160)

$$\:\:\:\:\:\:@{bemath}@ \\ $$$$\left(\frac{\mathrm{14}}{\mathrm{5}}\right)^{\frac{\mathrm{28}}{\sqrt{{x}}}−\mathrm{5}} =\:\left(\frac{\mathrm{5}}{\mathrm{14}}\right)^{\frac{\mathrm{5}}{\sqrt{{x}}}−\mathrm{160}} \\ $$

Question Number 107151 Answers: 0 Comments: 0

@JS@ (D^2 +7D+12)y = e^x cos 2x

$$\:\:\:\:\:\:\:\:\:@\mathrm{JS}@ \\ $$$$\left(\mathrm{D}^{\mathrm{2}} +\mathrm{7D}+\mathrm{12}\right)\mathrm{y}\:=\:\mathrm{e}^{\mathrm{x}} \:\mathrm{cos}\:\mathrm{2x}\: \\ $$

Question Number 107147 Answers: 0 Comments: 0

find lim_(x→0^+ ) ((∫_0 ^x e^t ln(t)dt)/(e^x lnx))

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}^{+} } \:\:\:\:\frac{\int_{\mathrm{0}} ^{\mathrm{x}} \:\mathrm{e}^{\mathrm{t}} \mathrm{ln}\left(\mathrm{t}\right)\mathrm{dt}}{\mathrm{e}^{\mathrm{x}} \mathrm{lnx}} \\ $$

Question Number 107144 Answers: 1 Comments: 0

solve x^2 y^(′′) −xy^′ +2y =xe^(−x) sin(2x)

$$\mathrm{solve}\:\mathrm{x}^{\mathrm{2}} \mathrm{y}^{''} −\mathrm{xy}^{'} \:+\mathrm{2y}\:=\mathrm{xe}^{−\mathrm{x}} \mathrm{sin}\left(\mathrm{2x}\right) \\ $$

Question Number 107141 Answers: 0 Comments: 0

∫(x^3 +x^6 )(((x^3 +2))^(1/3) )dx

$$\int\left({x}^{\mathrm{3}} +{x}^{\mathrm{6}} \right)\left(\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{2}}\right){dx} \\ $$

Question Number 107133 Answers: 0 Comments: 0

Question Number 107124 Answers: 2 Comments: 0

Question Number 107123 Answers: 0 Comments: 0

Question Number 107122 Answers: 1 Comments: 0

Question Number 107121 Answers: 0 Comments: 0

Question Number 107117 Answers: 2 Comments: 0

Question Number 107113 Answers: 0 Comments: 0

Question Number 107108 Answers: 1 Comments: 3

y′′+y=(1/(cosx))

$$\mathrm{y}''+\mathrm{y}=\frac{\mathrm{1}}{\mathrm{cosx}} \\ $$

Question Number 107107 Answers: 1 Comments: 2

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