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Question Number 168247 Answers: 2 Comments: 0

Solve for x ((8^x +27^x )/(12^x +18^x ))=(7/6) Mastermind

$${Solve}\:{for}\:{x} \\ $$$$\frac{\mathrm{8}^{{x}} +\mathrm{27}^{{x}} }{\mathrm{12}^{{x}} +\mathrm{18}^{{x}} }=\frac{\mathrm{7}}{\mathrm{6}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168187 Answers: 2 Comments: 0

Prove that : sinh^(−1) tanθ = log tan((θ/2)+(π/4)) Mastermind

$${Prove}\:{that}\::\: \\ $$$${sinh}^{−\mathrm{1}} {tan}\theta\:=\:{log}\:{tan}\left(\frac{\theta}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168185 Answers: 0 Comments: 0

Separate cos^(−1) e^(iθ) into real and imaginary parts. Mastermind

$${Separate}\:{cos}^{−\mathrm{1}} {e}^{{i}\theta} \:{into}\: \\ $$$${real}\:{and}\:{imaginary}\:{parts}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168118 Answers: 1 Comments: 0

If tan(θ+iφ)=cosα+isinα, prove that : θ=((nΠ)/2)+(Π/4) and φ=(1/2)log tan((Π/4)+(α/2))

$${If}\:{tan}\left(\theta+{i}\phi\right)={cos}\alpha+{isin}\alpha,\: \\ $$$${prove}\:{that}\::\:\theta=\frac{{n}\Pi}{\mathrm{2}}+\frac{\Pi}{\mathrm{4}}\:{and}\:\phi=\frac{\mathrm{1}}{\mathrm{2}}{log}\:{tan}\left(\frac{\Pi}{\mathrm{4}}+\frac{\alpha}{\mathrm{2}}\right) \\ $$

Question Number 167978 Answers: 0 Comments: 0

(((3 2 )),((4 5)) ) [A] = determinant (((3 2)),((4 5)))

$$\begin{pmatrix}{\mathrm{3}\:\:\:\:\:\mathrm{2}\:}\\{\mathrm{4}\:\:\:\:\:\:\mathrm{5}}\end{pmatrix}\:\:\left[{A}\right]\:=\begin{vmatrix}{\mathrm{3}\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{4}\:\:\:\:\:\:\mathrm{5}}\end{vmatrix} \\ $$

Question Number 167977 Answers: 1 Comments: 0

Prove that I_n =(1/2^(n+1) )∫_π ^(4nπ) xcos (x/2)dx=((2−π)/2^(np) )

$${Prove}\:{that} \\ $$$${I}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}^{{n}+\mathrm{1}} }\int_{\pi} ^{\mathrm{4}{n}\pi} {x}\mathrm{cos}\:\frac{{x}}{\mathrm{2}}{dx}=\frac{\mathrm{2}−\pi}{\mathrm{2}^{{np}} } \\ $$

Question Number 167963 Answers: 0 Comments: 0

show that_β_(1 =( nΣxy−ΣxΣy)/(nΣx^2 −(Σx)^2 )=Σxy/Σ(xy)^(2 ) where x=(x−x^− ) and y=(y−y^− ) )

$$\:{show}\:{that}_{\beta_{\mathrm{1}\:=\left(\:{n}\Sigma{xy}−\Sigma{x}\Sigma{y}\right)/\left({n}\Sigma{x}^{\mathrm{2}} −\left(\Sigma{x}\right)^{\mathrm{2}} \right)=\Sigma{xy}/\Sigma\left({xy}\right)^{\mathrm{2}\:} \:\:\:\:\:\:\:{where}\:{x}=\left({x}−\overset{−} {{x}}\right)\:{and}\:{y}=\left({y}−\overset{−} {{y}}\right)\:\:} } \: \\ $$$$ \\ $$

Question Number 167928 Answers: 1 Comments: 0

Show that ∣1−i∣^x =2^x has no nonzero integral solution

$${Show}\:{that}\:\mid\mathrm{1}−{i}\mid^{{x}} =\mathrm{2}^{{x}} \:{has}\:{no}\:{nonzero}\:{integral}\:{solution}\: \\ $$

Question Number 167882 Answers: 2 Comments: 0

Calculate I=∫(1/x)((√((1−x)/(1+x))))dx Indication poser t=(√((1−x)/(1+x)))

$${Calculate} \\ $$$${I}=\int\frac{\mathrm{1}}{{x}}\left(\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\right){dx} \\ $$$${Indication}\:{poser}\:{t}=\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}} \\ $$

Question Number 167773 Answers: 2 Comments: 0

Calculate ∫((xtan x)/(cos^4 x))dx

$${Calculate} \\ $$$$\int\frac{{x}\mathrm{tan}\:{x}}{\mathrm{cos}\:^{\mathrm{4}} {x}}{dx} \\ $$

Question Number 167757 Answers: 1 Comments: 1

Calculate ∫sec^2 xsec xdx

$${Calculate} \\ $$$$\int\mathrm{sec}\:^{\mathrm{2}} {x}\mathrm{sec}\:{xdx} \\ $$

Question Number 167740 Answers: 0 Comments: 0

I_n =∫_0 ^(π/4) (1/(cos^(2n+1) x))dx Prove by parts that: 2nI_n =(2n−1)I_(n−1) +(2^n /( (√2)))

$${I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{2}{n}+\mathrm{1}} {x}}{dx} \\ $$$${Prove}\:{by}\:{parts}\:{that}: \\ $$$$\mathrm{2}{nI}_{{n}} =\left(\mathrm{2}{n}−\mathrm{1}\right){I}_{{n}−\mathrm{1}} +\frac{\mathrm{2}^{{n}} }{\:\sqrt{\mathrm{2}}} \\ $$

Question Number 167730 Answers: 1 Comments: 2

Question Number 167496 Answers: 0 Comments: 0

Question Number 167468 Answers: 1 Comments: 0

Question Number 168097 Answers: 0 Comments: 0

Question Number 167372 Answers: 1 Comments: 0

Calculate ∫_(−2) ^2 (∣x∣+x)e^(−∣x∣) dx

$${Calculate}\: \\ $$$$\int_{−\mathrm{2}} ^{\mathrm{2}} \left(\mid{x}\mid+{x}\right){e}^{−\mid{x}\mid} {dx} \\ $$

Question Number 167330 Answers: 2 Comments: 0

Calculate ∫(1/(x+(√(x^2 +x+1))))dx

$${Calculate} \\ $$$$\int\frac{\mathrm{1}}{{x}+\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$

Question Number 167275 Answers: 0 Comments: 0

Question Number 167200 Answers: 1 Comments: 0

Question Number 167122 Answers: 0 Comments: 0

Question Number 166573 Answers: 1 Comments: 1

Question Number 166346 Answers: 1 Comments: 1

∫(dx/(1+(√x)+(√(1+x))))

$$\int\frac{{dx}}{\mathrm{1}+\sqrt{{x}}+\sqrt{\mathrm{1}+{x}}} \\ $$

Question Number 166301 Answers: 2 Comments: 0

∫(x/( (√(1+x^2 +(√((1+x^2 )^3 ))))))dx

$$\int\frac{{x}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +\sqrt{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }}}{dx} \\ $$

Question Number 165816 Answers: 1 Comments: 0

The GCF of two numbers is 8 and theirLCM is 360.if one of the number is72 find the other number.

$$\mathrm{The}\:\mathrm{GCF}\:\mathrm{of}\:\mathrm{two}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{8}\:\mathrm{and}\: \\ $$$$\mathrm{theirLCM}\:\mathrm{is}\:\mathrm{360}.\mathrm{if}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}\: \\ $$$$\mathrm{is72}\:\mathrm{find}\:\mathrm{the}\:\mathrm{other}\:\mathrm{number}. \\ $$

Question Number 165893 Answers: 1 Comments: 1

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