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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)=?

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

Question Number 59685 Answers: 0 Comments: 0

Question Number 59683 Answers: 3 Comments: 0

prove (1+tanx)(1+tany)=2 if x+y=45°

$${prove}\:\left(\mathrm{1}+{tanx}\right)\left(\mathrm{1}+\mathrm{tany}\right)=\mathrm{2}\:\:{if}\:\:{x}+{y}=\mathrm{45}° \\ $$$$ \\ $$

Question Number 59682 Answers: 2 Comments: 2

if H=X^2 +Y^2 +Z^2 prove (∂^2 H/∂X^2 )+(∂^2 H/∂Y^2 )+(∂^2 H/∂Z^2 )=(2/H)

$${if} \\ $$$$ \\ $$$${H}={X}^{\mathrm{2}} +{Y}^{\mathrm{2}} +{Z}^{\mathrm{2}} \\ $$$$ \\ $$$${prove} \\ $$$$ \\ $$$$\frac{\partial^{\mathrm{2}} {H}}{\partial{X}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {H}}{\partial{Y}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {H}}{\partial{Z}^{\mathrm{2}} }=\frac{\mathrm{2}}{{H}} \\ $$

Question Number 59679 Answers: 3 Comments: 0

Evaluate ∫_0 ^3 (((x^2 +3x)/x^3 ))

$${Evaluate} \\ $$$$\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\left(\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}}{{x}^{\mathrm{3}} }\right) \\ $$$$ \\ $$

Question Number 59678 Answers: 0 Comments: 0

Determine a,b,c in terms of α,β,γ. (a/b)−c=γ (b/c)−a=α (c/a)−b=β

$$\mathcal{D}{etermine}\:{a},{b},{c}\:{in}\:{terms}\:{of}\:\alpha,\beta,\gamma. \\ $$$$\:\:\:\:\frac{{a}}{{b}}−{c}=\gamma \\ $$$$\:\:\:\:\frac{{b}}{{c}}−{a}=\alpha \\ $$$$\:\:\:\:\frac{{c}}{{a}}−{b}=\beta \\ $$

Question Number 59675 Answers: 0 Comments: 0

you are welcome sir ali.

$${you}\:{are}\:{welcome}\:{sir}\:{ali}. \\ $$

Question Number 59667 Answers: 1 Comments: 0

Question Number 59659 Answers: 1 Comments: 5

Question Number 59655 Answers: 1 Comments: 3

Question Number 59647 Answers: 1 Comments: 1

Question Number 59639 Answers: 0 Comments: 3

Question Number 59637 Answers: 1 Comments: 1

lim_(x→∞) (1/x)∫_0 ^x ∣sin x∣

$$\underset{{x}\rightarrow\infty} {{lim}}\frac{\mathrm{1}}{{x}}\int_{\mathrm{0}} ^{{x}} \mid\mathrm{sin}\:{x}\mid \\ $$

Question Number 59631 Answers: 2 Comments: 3

1) calculate ∫_0 ^(2π) (dx/(acosx +bsinx)) with a , b reals 2)find also ∫_0 ^(2π) ((cosx dx)/((acosx +bsinx)^2 )) and ∫_0 ^(2π) ((sinx dx)/((acosx +bsinx)^2 )) 3) find the value of ∫_0 ^(2π) (dx/(2cosx +(√3)sinx))

$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{{acosx}\:+{bsinx}} \\ $$$${with}\:{a}\:,\:{b}\:{reals} \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cosx}\:{dx}}{\left({acosx}\:+{bsinx}\right)^{\mathrm{2}} }\:\:{and} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sinx}\:{dx}}{\left({acosx}\:+{bsinx}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{\mathrm{2}{cosx}\:+\sqrt{\mathrm{3}}{sinx}} \\ $$

Question Number 59627 Answers: 1 Comments: 0

Question Number 59626 Answers: 1 Comments: 0

Rationalize the denominator of (2/(1 − (√(2 + (4)^(1/3) ))))

$${Rationalize}\:\:{the}\:\:{denominator}\:\:{of} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{2}}{\mathrm{1}\:−\:\sqrt{\mathrm{2}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{4}}}} \\ $$

Question Number 59625 Answers: 0 Comments: 0

Sum the series: ((( ^n C_1 )/( ^n C_0 )))^2 + (2 × (( ^n C_2 )/( ^n C_1 ))) + (3 × (( ^n C_3 )/( ^n C_2 )))^2 + .... n terms

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\:\:\:\:\:\left(\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{1}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{0}} }\right)^{\mathrm{2}} \:+\:\left(\mathrm{2}\:×\:\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{2}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{1}} }\right)\:+\:\left(\mathrm{3}\:×\:\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{3}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{2}} }\right)^{\mathrm{2}} \:+\:....\:\:\boldsymbol{\mathrm{n}}\:\mathrm{terms} \\ $$

Question Number 59624 Answers: 1 Comments: 0

Rationalize the denominator of (2/((√(x+2)) + (√(x+1)) + (√x)))

$${Rationalize}\:\:\:{the}\:\:{denominator}\:\:{of} \\ $$$$\:\:\:\:\:\:\frac{\mathrm{2}}{\sqrt{{x}+\mathrm{2}}\:\:+\:\:\sqrt{{x}+\mathrm{1}}\:\:+\:\:\sqrt{{x}}} \\ $$

Question Number 59620 Answers: 1 Comments: 2

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