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AllQuestion and Answers: Page 447

Question Number 172011 Answers: 1 Comments: 0

find integrate: ∫x^2 e^x dx

$${find}\:{integrate}: \\ $$$$\int{x}^{\mathrm{2}} {e}^{{x}} {dx} \\ $$

Question Number 172010 Answers: 1 Comments: 0

find integrate: ∫xe^x dx

$${find}\:{integrate}: \\ $$$$\int{xe}^{{x}} {dx} \\ $$

Question Number 172009 Answers: 1 Comments: 0

solve: if x=2017,y=2018 and z=2019, find x^2 +y^2 +z^2 −xy−yz−zx

$${solve}: \\ $$$${if}\:{x}=\mathrm{2017},{y}=\mathrm{2018}\:{and}\:{z}=\mathrm{2019},\: \\ $$$${find}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} −{xy}−{yz}−{zx} \\ $$

Question Number 172008 Answers: 0 Comments: 0

solve: 15(2n)_C_((n−1)) =28(2n−1)_C_n . find n

$${solve}: \\ $$$$\mathrm{15}\left(\mathrm{2}{n}\right)_{{C}_{\left({n}−\mathrm{1}\right)} } =\mathrm{28}\left(\mathrm{2}{n}−\mathrm{1}\right)_{{C}_{{n}} } .\:{find}\:{n} \\ $$

Question Number 172007 Answers: 1 Comments: 0

solve: x(√(x^2 +4)) −x^2 =−6

$${solve}: \\ $$$${x}\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:−{x}^{\mathrm{2}} =−\mathrm{6} \\ $$

Question Number 172006 Answers: 1 Comments: 0

solve: (√(x^2 +5x+2)) −(√(x^2 +5 )) =1

$${solve}: \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} +\mathrm{5}\:}\:=\mathrm{1} \\ $$

Question Number 172005 Answers: 2 Comments: 0

find x: (log_(10) x)^2 −log_(10) x=0

$${find}\:{x}:\:\left({log}_{\mathrm{10}} {x}\right)^{\mathrm{2}} −{log}_{\mathrm{10}} {x}=\mathrm{0} \\ $$

Question Number 172023 Answers: 0 Comments: 0

if: bx^3 −(3b+2)x^2 −2(5b−3)x+20=0 find b in term.

$${if}:\: \\ $$$${bx}^{\mathrm{3}} −\left(\mathrm{3}{b}+\mathrm{2}\right){x}^{\mathrm{2}} −\mathrm{2}\left(\mathrm{5}{b}−\mathrm{3}\right){x}+\mathrm{20}=\mathrm{0} \\ $$$${find}\:{b}\:{in}\:{term}. \\ $$

Question Number 172022 Answers: 1 Comments: 0

find the cubic of ((26+15(√3)))^(1/3) + ((26−15(√3)))^(1/3)

$${find}\:{the}\:{cubic}\:{of} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{26}+\mathrm{15}\sqrt{\mathrm{3}}}\:\:\:+\:\sqrt[{\mathrm{3}}]{\mathrm{26}−\mathrm{15}\sqrt{\mathrm{3}}} \\ $$

Question Number 172021 Answers: 1 Comments: 0

solve: 2^x^2 =x^(2x)

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

Question Number 172024 Answers: 1 Comments: 0

let α and β be the root of the equation ax^2 +bx+c=0. find the equation whose roots are ((1/α)+(1/β)) and ((1/α)−(1/β))

$${let}\:\alpha\:{and}\:\beta\:{be}\:{the}\:{root}\:{of}\:{the}\:{equation} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}.\:{find}\:{the}\:{equation}\:{whose}\:{roots} \\ $$$${are}\:\left(\frac{\mathrm{1}}{\alpha}+\frac{\mathrm{1}}{\beta}\right)\:{and}\:\left(\frac{\mathrm{1}}{\alpha}−\frac{\mathrm{1}}{\beta}\right) \\ $$

Question Number 172002 Answers: 0 Comments: 0

if y=bcoslog((x/n))^n , then (dy/dx)=?

$${if}\:{y}={bcoslog}\left(\frac{{x}}{{n}}\right)^{{n}} ,\:{then} \\ $$$$\frac{{dy}}{{dx}}=? \\ $$

Question Number 172001 Answers: 0 Comments: 0

solve: ∫(((√(x^2 +1)) −(√(x^2 −1)))/( (√(x^4 −1))))dx

$${solve}: \\ $$$$\int\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{\:\sqrt{{x}^{\mathrm{4}} −\mathrm{1}}}{dx} \\ $$

Question Number 172000 Answers: 0 Comments: 0

prove that: ((sinx)/(sin3x))+((tanx)/(tan3x))=1

$${prove}\:{that}: \\ $$$$\frac{{sinx}}{{sin}\mathrm{3}{x}}+\frac{{tanx}}{{tan}\mathrm{3}{x}}=\mathrm{1} \\ $$

Question Number 171999 Answers: 1 Comments: 0

resolve: ((4(x−4))/(x^2 −2x−3)) into partial fraction

$${resolve}: \\ $$$$\frac{\mathrm{4}\left({x}−\mathrm{4}\right)}{{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3}}\:{into}\:{partial}\:{fraction} \\ $$

Question Number 171998 Answers: 0 Comments: 0

if x^3 +(1/x^3 )=81, then find ((x^6 +1)/(x^5 +5x))

$${if} \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{81},\:{then}\:{find}\: \\ $$$$\frac{{x}^{\mathrm{6}} +\mathrm{1}}{{x}^{\mathrm{5}} +\mathrm{5}{x}} \\ $$

Question Number 172019 Answers: 0 Comments: 0

solve: x^3 +9x^2 y=10 y^3 +xy^2 =2

$${solve}: \\ $$$${x}^{\mathrm{3}} +\mathrm{9}{x}^{\mathrm{2}} {y}=\mathrm{10} \\ $$$${y}^{\mathrm{3}} +{xy}^{\mathrm{2}} =\mathrm{2} \\ $$

Question Number 172025 Answers: 1 Comments: 0

find the root of x^4 +4x^3 +11x^2 +14x−30=0.

$${find}\:{the}\:{root}\:{of}\: \\ $$$${x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} +\mathrm{11}{x}^{\mathrm{2}} +\mathrm{14}{x}−\mathrm{30}=\mathrm{0}. \\ $$

Question Number 171995 Answers: 0 Comments: 0

solve: ((x/(12)))^(log_(√3) x) =((x/(18)))^(log_(√2) x)

$${solve}: \\ $$$$\left(\frac{{x}}{\mathrm{12}}\right)^{{log}_{\sqrt{\mathrm{3}}} \:{x}} =\left(\frac{{x}}{\mathrm{18}}\right)^{{log}_{\sqrt{\mathrm{2}}} {x}} \\ $$$$ \\ $$

Question Number 171993 Answers: 0 Comments: 3

Question Number 172020 Answers: 1 Comments: 0

solve: 2^x =10x

$${solve}: \\ $$$$\mathrm{2}^{{x}} =\mathrm{10}{x} \\ $$

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

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