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Question Number 66274 Answers: 0 Comments: 1

Question Number 66275 Answers: 0 Comments: 2

Prove that for p,q,r∈N ((lcm(p,q,r))/(gcd(p,q,r)))=((p×q×r)/(gcd(p,q)×gcd(q,r)×gcd(r,p)))

$${Prove}\:{that}\:{for}\:{p},{q},{r}\in\mathbb{N} \\ $$$$\frac{\mathrm{lcm}\left({p},{q},{r}\right)}{\mathrm{gcd}\left({p},{q},{r}\right)}=\frac{{p}×{q}×{r}}{\mathrm{gcd}\left({p},{q}\right)×\mathrm{gcd}\left({q},{r}\right)×\mathrm{gcd}\left({r},{p}\right)} \\ $$

Question Number 66267 Answers: 0 Comments: 1

Question Number 66264 Answers: 0 Comments: 0

for x>0 what is the relation between Γ(x) and Γ((1/x))?

$${for}\:{x}>\mathrm{0}\:{what}\:{is}\:{the}\:{relation}\:{between}\:\Gamma\left({x}\right)\:{and}\:\Gamma\left(\frac{\mathrm{1}}{{x}}\right)? \\ $$

Question Number 66263 Answers: 0 Comments: 1

Question Number 66262 Answers: 0 Comments: 3

show that ^n c_(r+1) +^n c_(r ) =^(n+1) c_(r+1)

$$\boldsymbol{{show}}\:\boldsymbol{{that}}\: \\ $$$$\:^{\boldsymbol{{n}}} \boldsymbol{{c}}_{\boldsymbol{{r}}+\mathrm{1}} +^{\boldsymbol{{n}}} \boldsymbol{{c}}_{\boldsymbol{{r}}\:\:} =^{\boldsymbol{{n}}+\mathrm{1}} \boldsymbol{{c}}_{\boldsymbol{{r}}+\mathrm{1}} \\ $$

Question Number 66256 Answers: 0 Comments: 7

Find all points (a, b) of R^2 such that through (a, b) pass two tangent lines to the graph of f(x)=x^2 .

$${Find}\:{all}\:{points}\:\left({a},\:{b}\right)\:{of}\:\mathbb{R}^{\mathrm{2}} \:{such}\:{that}\: \\ $$$${through}\:\left({a},\:{b}\right)\:{pass}\:{two}\:{tangent}\:{lines} \\ $$$${to}\:{the}\:{graph}\:{of}\:{f}\left({x}\right)={x}^{\mathrm{2}} . \\ $$

Question Number 66253 Answers: 0 Comments: 1

prove by Rieman sum that ∫_0 ^1 xdx =(1/2)

$${prove}\:{by}\:{Rieman}\:{sum}\:{that}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{xdx}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 66249 Answers: 1 Comments: 0

The npn transistor in the voltage amplifier circuit operates satisfctorily on a quiescent collector current of 3mA. if the battery supply (V_(cc) ) is 6v, calculate the value of ; (a) the load resistor R_L (b) the base current for the quiescent collector−emitter voltage V_(ce) to be half the battery voltage. Th transistor dc current is 100. please help.

$$\mathrm{The}\:\mathrm{npn}\:\mathrm{transistor}\:\mathrm{in}\:\mathrm{the}\:\mathrm{voltage}\: \\ $$$$\mathrm{amplifier}\:\mathrm{circuit}\:\mathrm{operates}\:\mathrm{satisfctorily} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{quiescent}\:\mathrm{collector}\:\mathrm{current}\:\mathrm{of}\:\mathrm{3mA}. \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{battery}\:\mathrm{supply}\:\left(\mathrm{V}_{\mathrm{cc}} \right)\:\mathrm{is}\:\mathrm{6v},\:\mathrm{calculate} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:; \\ $$$$\left(\mathrm{a}\right)\:\mathrm{the}\:\mathrm{load}\:\mathrm{resistor}\:\mathrm{R}_{\mathrm{L}} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{base}\:\mathrm{current}\:\mathrm{for}\:\mathrm{the}\:\mathrm{quiescent} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{collector}−\mathrm{emitter}\:\mathrm{voltage}\:\mathrm{V}_{\mathrm{ce}} \:\mathrm{to} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{be}\:\mathrm{half}\:\mathrm{the}\:\mathrm{battery}\:\mathrm{voltage}. \\ $$$$\mathrm{Th}\:\mathrm{transistor}\:\mathrm{dc}\:\mathrm{current}\:\mathrm{is}\:\mathrm{100}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}. \\ $$

Question Number 66245 Answers: 1 Comments: 2

prove that ∫e^x dx = e^x + c

$${prove}\:{that} \\ $$$$ \\ $$$$\int{e}^{{x}} \:{dx}\:=\:{e}^{{x}} \:+\:{c} \\ $$

Question Number 66228 Answers: 0 Comments: 3

prove that ∫_2 ^4 ((6x +1)/((2x−3)(3x−2)))dx = ln 10

$${prove}\:{that}\: \\ $$$$\int_{\mathrm{2}} ^{\mathrm{4}} \frac{\mathrm{6}{x}\:+\mathrm{1}}{\left(\mathrm{2}{x}−\mathrm{3}\right)\left(\mathrm{3}{x}−\mathrm{2}\right)}{dx}\:=\:{ln}\:\mathrm{10} \\ $$

Question Number 66227 Answers: 0 Comments: 0

Using a good counter procedure, prove that (∂y/∂x) = lim_(∂x→0) ((f(∂ + x) −f(x))/∂x) for a given function f(x) in x.

$${Using}\:{a}\:{good}\:{counter}\:{procedure},\:{prove}\:{that}\: \\ $$$$\:\:\:\frac{\partial{y}}{\partial{x}}\:=\:\underset{\partial{x}\rightarrow\mathrm{0}} {{lim}}\frac{{f}\left(\partial\:+\:{x}\right)\:−{f}\left({x}\right)}{\partial{x}} \\ $$$${for}\:{a}\:{given}\:{function}\:\:{f}\left({x}\right)\:{in}\:{x}. \\ $$

Question Number 66226 Answers: 0 Comments: 1

the equation f(x)=0 has real roots in the interval (a, b) if A −f(a)>0 and f(b) >0 B f(a) <0 and f(b) <0 C −f(a) >0 and f(b) =0 D f(a) >0 and f(b) < 0

$${the}\:{equation}\:\:{f}\left({x}\right)=\mathrm{0}\:{has}\:{real}\:{roots}\:{in}\: \\ $$$${the}\:{interval}\:\left({a},\:{b}\right)\:{if} \\ $$$${A}\:\:\:\:−{f}\left({a}\right)>\mathrm{0}\:\:{and}\:{f}\left({b}\right)\:>\mathrm{0} \\ $$$${B}\:\:\:{f}\left({a}\right)\:<\mathrm{0}\:{and}\:{f}\left({b}\right)\:<\mathrm{0} \\ $$$${C}\:\:−{f}\left({a}\right)\:>\mathrm{0}\:\:{and}\:{f}\left({b}\right)\:=\mathrm{0} \\ $$$${D}\:\:{f}\left({a}\right)\:>\mathrm{0}\:\:{and}\:{f}\left({b}\right)\:<\:\mathrm{0} \\ $$

Question Number 66225 Answers: 1 Comments: 2

Given that f(x)= { ((−x + 1, x≤ 3_ )),((kx −8, x >3)) :} is continuous then f(5) = A 2 B 0 C −2 D −1

$${Given}\:{that}\:\:\:\:\:{f}\left({x}\right)=\begin{cases}{−{x}\:+\:\mathrm{1},\:\:{x}\leqslant\:\mathrm{3}_{} }\\{{kx}\:−\mathrm{8},\:\:\:\:{x}\:>\mathrm{3}}\end{cases} \\ $$$${is}\:{continuous}\:{then}\:\:{f}\left(\mathrm{5}\right)\:=\: \\ $$$${A}\:\:\:\mathrm{2} \\ $$$${B}\:\:\:\mathrm{0} \\ $$$${C}\:\:−\mathrm{2} \\ $$$${D}\:\:−\mathrm{1} \\ $$$$ \\ $$

Question Number 66216 Answers: 1 Comments: 2

∣a ∣ = 3 ,∣b∣= 5 , a.b =−14 ∣a − b∣ = ?

$$\mid{a}\:\mid\:=\:\mathrm{3}\:,\mid{b}\mid=\:\mathrm{5}\:,\:{a}.{b}\:=−\mathrm{14} \\ $$$$\:\:\mid{a}\:−\:{b}\mid\:=\:? \\ $$

Question Number 66816 Answers: 0 Comments: 3

let x>0 and f(x)=∫_1 ^2 (t+1)(√(t^2 −2xt−1))dt 1) find a explicit form of f(x) 2) determine also g(x)=∫_1 ^2 ((t^2 +t)/(√(t^2 −2xt−1)))dt 3)find the value of integrals ∫_1 ^2 (t+1)(√(t^2 −t−1))dt and ∫_1 ^2 ((t^(2 ) +t)/(√(t^2 −t−1)))dt .

$${let}\:{x}>\mathrm{0}\:{and}\:{f}\left({x}\right)=\int_{\mathrm{1}} ^{\mathrm{2}} \left({t}+\mathrm{1}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{2}{xt}−\mathrm{1}}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{t}^{\mathrm{2}} \:+{t}}{\sqrt{{t}^{\mathrm{2}} −\mathrm{2}{xt}−\mathrm{1}}}{dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:{integrals}\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \left({t}+\mathrm{1}\right)\sqrt{{t}^{\mathrm{2}} −{t}−\mathrm{1}}{dt} \\ $$$${and}\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\frac{{t}^{\mathrm{2}\:} +{t}}{\sqrt{{t}^{\mathrm{2}} −{t}−\mathrm{1}}}{dt}\:. \\ $$$$ \\ $$

Question Number 66815 Answers: 2 Comments: 1

solve the congruence equation 6x ≡ 4 (mod 5) i need help please with some explanations

$${solve}\:{the}\:{congruence}\:{equation}\: \\ $$$$\:\:\mathrm{6}{x}\:\equiv\:\mathrm{4}\:\left({mod}\:\mathrm{5}\right)\:\:{i}\:{need}\:{help}\:{please}\:{with}\:{some}\:{explanations} \\ $$

Question Number 66213 Answers: 0 Comments: 3

calculate A_n =∫_0 ^∞ cos(x^n )dx and B_n =∫_0 ^∞ sin(x^n )dx with n integr and n≥2

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{{n}} \right){dx}\:{and}\:{B}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{{n}} \right){dx} \\ $$$${with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$

Question Number 66211 Answers: 1 Comments: 4