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AllQuestion and Answers: Page 1506

Question Number 59814 Answers: 1 Comments: 1

Question Number 59812 Answers: 1 Comments: 1

(6/(3+(3)^(1/3) +(9)^(1/3) )) simplify.

$$\frac{\mathrm{6}}{\mathrm{3}+\sqrt[{\mathrm{3}}]{\mathrm{3}}+\sqrt[{\mathrm{3}}]{\mathrm{9}}}\:\:\:\boldsymbol{\mathrm{simplify}}. \\ $$

Question Number 59811 Answers: 1 Comments: 2

(((tg^2 (590°))/(cos^2 (320°)))+((sin(111°))/(cos(159°))))(((cos(279°))/(sin(549°)))+((ctg(950°))/(sin^2 (400°)))) simplify.

Question Number 59803 Answers: 0 Comments: 3

Question Number 59802 Answers: 0 Comments: 1

Question Number 59800 Answers: 2 Comments: 0

find the general solution y(t) of the ordinary differential equation y′′ + ω^2 y=cos ωt ,where w>0

$${find}\:{the}\:{general}\:{solution}\:{y}\left({t}\right)\:{of}\:{the} \\ $$$${ordinary}\:{differential}\:{equation} \\ $$$${y}''\:+\:\omega^{\mathrm{2}} {y}=\mathrm{cos}\:\omega{t}\:,{where}\:{w}>\mathrm{0} \\ $$

Question Number 59788 Answers: 2 Comments: 4

find the local minimum and maximum value a^2 y=x^2 (a−x) f(x)=(4/(2−x))+(9/(x−3))

$${find}\:{the}\:{local}\:{minimum}\:{and}\:{maximum}\:{value} \\ $$$$ \\ $$$${a}^{\mathrm{2}} {y}={x}^{\mathrm{2}} \left({a}−{x}\right) \\ $$$${f}\left({x}\right)=\frac{\mathrm{4}}{\mathrm{2}−{x}}+\frac{\mathrm{9}}{{x}−\mathrm{3}} \\ $$

Question Number 59787 Answers: 2 Comments: 0

Question Number 59781 Answers: 0 Comments: 0

Question Number 59780 Answers: 1 Comments: 0

An earth-based observer sees rocket A moving at 0.70c directly towards rocket B,which is moving towards A at 0.80c. How fast does rocket A sees rocket B approaching?

$${An}\:{earth}-{based}\:{observer}\:{sees}\:{rocket}\:{A} \\ $$$${moving}\:{at}\:\mathrm{0}.\mathrm{70}{c}\:{directly}\:{towards}\:{rocket} \\ $$$${B},{which}\:{is}\:{moving}\:{towards}\:{A}\:{at}\:\mathrm{0}.\mathrm{80}{c}. \\ $$$${How}\:{fast}\:{does}\:{rocket}\:{A}\:{sees}\:{rocket}\:{B} \\ $$$${approaching}? \\ $$$$ \\ $$

Question Number 59777 Answers: 0 Comments: 4

Question Number 59764 Answers: 1 Comments: 0

((2+(√3))/((√2)+(√(2+(√3)))))+((2−(√3))/((√2)−(√(2−(√3))))). simplify.

$$\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\sqrt{\mathrm{2}}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}+\frac{\mathrm{2}−\sqrt{\mathrm{3}}}{\sqrt{\mathrm{2}}−\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}}. \\ $$$$\boldsymbol{\mathrm{simplify}}. \\ $$

Question Number 59763 Answers: 1 Comments: 0

((2+(√3))/((√2)+(√(2+(√3)))))+((2+(√3))/((√2)−(√(2−(√3))))) simplify.

$$\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\sqrt{\mathrm{2}}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}+\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\sqrt{\mathrm{2}}−\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}} \\ $$$$\boldsymbol{\mathrm{simplify}}. \\ $$

Question Number 59753 Answers: 2 Comments: 0

x=(a+b)cosx−bcos(((a+b)/b))x y=(a+b)sinx−bsin(((a+b)/b))x find (dy/dx)=tan((a/(2b))+1)x

$$\mathrm{x}=\left(\mathrm{a}+\mathrm{b}\right)\mathrm{cosx}−\mathrm{bcos}\left(\frac{\mathrm{a}+\mathrm{b}}{\mathrm{b}}\right)\mathrm{x} \\ $$$$\mathrm{y}=\left(\mathrm{a}+\mathrm{b}\right)\mathrm{sinx}−\mathrm{bsin}\left(\frac{\mathrm{a}+\mathrm{b}}{\mathrm{b}}\right)\mathrm{x} \\ $$$$\mathrm{find}\:\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{tan}\left(\frac{\mathrm{a}}{\mathrm{2b}}+\mathrm{1}\right)\mathrm{x} \\ $$

Question Number 59752 Answers: 1 Comments: 2

Question Number 59807 Answers: 1 Comments: 0

∫((x−1)/(√(2x−x^2 ))) dx

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

Question Number 59733 Answers: 2 Comments: 2

If y=(√x) ,find approximate value of (√(101))

$$\mathrm{If}\:\mathrm{y}=\sqrt{\mathrm{x}}\:\:,\mathrm{find}\:\mathrm{approximate}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\sqrt{\mathrm{101}} \\ $$

Question Number 59732 Answers: 2 Comments: 0

find I_n =∫ (dx/(sin^n x)) with n integr natural.

$${find}\:{I}_{{n}} =\int\:\:\frac{{dx}}{{sin}^{{n}} {x}}\:\:{with}\:\:{n}\:{integr}\:{natural}. \\ $$

Question Number 59730 Answers: 1 Comments: 0

5^(2x−1 ) =25^(x−1) +100 find value of 3^(3−x)

$$\mathrm{5}^{\mathrm{2}{x}−\mathrm{1}\:} =\mathrm{25}^{{x}−\mathrm{1}} +\mathrm{100}\:{find}\:{value}\:{of}\:\mathrm{3}^{\mathrm{3}−{x}} \\ $$

Question Number 59727 Answers: 3 Comments: 0

a=b^(2p ) b=c^(2q ) c=a^(2r) prove that pqr=(1/8)

$${a}={b}^{\mathrm{2}{p}\:\:} {b}={c}^{\mathrm{2}{q}\:} \:{c}={a}^{\mathrm{2}{r}} \:{prove}\:{that}\:{pqr}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$

Question Number 59720 Answers: 2 Comments: 1

Find (dy/dx) from first principle, if y = sin^2 (x)

$$\mathrm{Find}\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\mathrm{from}\:\mathrm{first}\:\mathrm{principle},\:\:\mathrm{if}\:\:\:\:\mathrm{y}\:=\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right) \\ $$

Question Number 59714 Answers: 2 Comments: 0

Find the greatest four digit number which when divided by 18 and 12 leaves a remainder of 4 in each case

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{four}\:\mathrm{digit}\:\mathrm{number} \\ $$$$\mathrm{which}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{18}\:\mathrm{and}\:\mathrm{12} \\ $$$$\mathrm{leaves}\:\mathrm{a}\:\mathrm{remainder}\:\mathrm{of}\:\mathrm{4}\:\mathrm{in}\:\mathrm{each}\:\mathrm{case} \\ $$

Question Number 59704 Answers: 1 Comments: 0

A space ship moving towards you at 0.5c shine a light at you.At what speed do you see the light approaching?

$${A}\:{space}\:{ship}\:{moving}\:{towards}\:{you}\:{at} \\ $$$$\mathrm{0}.\mathrm{5}{c}\:{shine}\:{a}\:{light}\:{at}\:{you}.{At}\:{what}\:{speed} \\ $$$${do}\:{you}\:{see}\:{the}\:{light}\:{approaching}? \\ $$

Question Number 59703 Answers: 1 Comments: 0

Question Number 59700 Answers: 0 Comments: 5

Question Number 59694 Answers: 0 Comments: 1

lim_(x→0) ((cos((√(∣x∣)−1)))/x)=?

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{cos}\left(\sqrt{\left.\mid{x}\mid\right)−\mathrm{1}}\right.}{{x}}=? \\ $$

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