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Question Number 176841    Answers: 0   Comments: 0

If 3 of 10 elective courses are been delivered at the same time. How many possibilities are there to take 5 courses ?

$$\mathrm{If}\:\mathrm{3}\:\mathrm{of}\:\mathrm{10}\:\mathrm{elective}\:\mathrm{courses}\:\mathrm{are}\:\mathrm{been}\:\mathrm{delivered}\: \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{time}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{possibilities}\: \\ $$$$\mathrm{are}\:\mathrm{there}\:\mathrm{to}\:\mathrm{take}\:\mathrm{5}\:\mathrm{courses}\:? \\ $$

Question Number 171627    Answers: 0   Comments: 5

A mass 10kg is placed at the foot of an inclined plane 13m long, whose upper end is 5m higher than the foot. The mass is connected by a light inextensible string, passing over a smooth pulley at the top of the plane, to another mass 10kg which hangs level with the top of the plane, 5m above the floor. If the coefficient of friction between the first mass and then plane is ½ and the system is released from rest, find the acceleration and tension In the string. [Take g = 9.8m/s²]

A mass 10kg is placed at the foot of an inclined plane 13m long, whose upper end is 5m higher than the foot. The mass is connected by a light inextensible string, passing over a smooth pulley at the top of the plane, to another mass 10kg which hangs level with the top of the plane, 5m above the floor. If the coefficient of friction between the first mass and then plane is ½ and the system is released from rest, find the acceleration and tension In the string. [Take g = 9.8m/s²]

Question Number 171626    Answers: 0   Comments: 0

x=(√(19)) +((91)/( (√(19))+((91)/( (√(19))+((91)/( (√(19))+((91)/( (√(19))+…))))))))

$$\:\:\:{x}=\sqrt{\mathrm{19}}\:+\frac{\mathrm{91}}{\:\sqrt{\mathrm{19}}+\frac{\mathrm{91}}{\:\sqrt{\mathrm{19}}+\frac{\mathrm{91}}{\:\sqrt{\mathrm{19}}+\frac{\mathrm{91}}{\:\sqrt{\mathrm{19}}+\ldots}}}} \\ $$

Question Number 171622    Answers: 0   Comments: 0

Question Number 171620    Answers: 0   Comments: 4

Question Number 171614    Answers: 0   Comments: 11

A particle is moving along a straight line such that it's position from a fixed point is S = ( 12 - 15t² + 5t³ )m where t is in seconds. Determine: A. Total distance travelled by the particle from t = 1sec to t = 3sec B. The average speed of the particle during this time.

A particle is moving along a straight line such that it's position from a fixed point is S = ( 12 - 15t² + 5t³ )m where t is in seconds. Determine: A. Total distance travelled by the particle from t = 1sec to t = 3sec B. The average speed of the particle during this time.

Question Number 171613    Answers: 0   Comments: 0

Question Number 171612    Answers: 0   Comments: 4

f(f(x))=(1/(1+x^2 )) f(x)=?

$${f}\left({f}\left({x}\right)\right)=\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:{f}\left({x}\right)=? \\ $$

Question Number 171611    Answers: 1   Comments: 0

∫_0 ^∞ xe^(−x) cos(x)log^n (x)dx how can we do these

$$\int_{\mathrm{0}} ^{\infty} \boldsymbol{\mathrm{xe}}^{−\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{log}}^{\boldsymbol{\mathrm{n}}} \left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}} \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{we}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{these}} \\ $$

Question Number 171608    Answers: 1   Comments: 0

montrer que ∫_o ^(+oo) ((sin^2 t)/t^2 )e^(−xt) dt est continu sur R^+

$${montrer}\:{que} \\ $$$$\int_{{o}} ^{+{oo}} \frac{{sin}^{\mathrm{2}} {t}}{{t}^{\mathrm{2}} }{e}^{−{xt}} {dt} \\ $$$${est}\:{continu}\:{sur}\:{R}^{+} \\ $$

Question Number 171601    Answers: 0   Comments: 0

Question Number 171599    Answers: 0   Comments: 0

Ω=∫_0 ^1 Log(((Log^2 (x))/x^(x^5 −x^4 +x^3 −x^2 +x−1) ))dx Mastermind

$$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} {Log}\left(\frac{{Log}^{\mathrm{2}} \left({x}\right)}{{x}^{{x}^{\mathrm{5}} −{x}^{\mathrm{4}} +{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +{x}−\mathrm{1}} }\right){dx} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171596    Answers: 1   Comments: 3

Show that ((cos 70°−cos 20°)/(sin 70°−sin 20°)) = −1

$${Show}\:{that}\:\frac{\mathrm{cos}\:\mathrm{70}°−\mathrm{cos}\:\mathrm{20}°}{\mathrm{sin}\:\mathrm{70}°−\mathrm{sin}\:\mathrm{20}°}\:=\:−\mathrm{1} \\ $$

Question Number 171594    Answers: 1   Comments: 0

charis wants to resize a 4 inch by 6 inch photo by a factor of 4/3. what are the dimensions of the new photo?

$$ \\ $$charis wants to resize a 4 inch by 6 inch photo by a factor of 4/3. what are the dimensions of the new photo?

Question Number 171583    Answers: 2   Comments: 3

if f(f(x))=x^2 −x+1, find f(0)=?

$${if}\:{f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −{x}+\mathrm{1},\:{find}\:{f}\left(\mathrm{0}\right)=? \\ $$

Question Number 171575    Answers: 0   Comments: 3

Question Number 171574    Answers: 1   Comments: 0

Question Number 171572    Answers: 1   Comments: 1

Show that 4^(3n−2) +5 is divisible by 9 then simplify ((4^(3n−2) +5)/9)

$$\mathrm{Show}\:\mathrm{that} \\ $$$$\mathrm{4}^{\mathrm{3}{n}−\mathrm{2}} +\mathrm{5}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{9} \\ $$$$\mathrm{then}\:\mathrm{simplify}\:\frac{\mathrm{4}^{\mathrm{3}{n}−\mathrm{2}} +\mathrm{5}}{\mathrm{9}} \\ $$

Question Number 171566    Answers: 0   Comments: 0

prove that ∫_o ^(+oo) ((sin^2 t)/t^2 )e^(−xt) dt is continious R^+

$${prove}\:{that}\:\int_{{o}} ^{+{oo}} \frac{{sin}^{\mathrm{2}} {t}}{{t}^{\mathrm{2}} }{e}^{−{xt}} {dt}\: \\ $$$${is}\:{continious}\:{R}^{+} \\ $$

Question Number 171565    Answers: 0   Comments: 4

Question Number 171563    Answers: 1   Comments: 0

evaluate ((√(((a−b)^7 + (b−c)^7 + (c−a)^7 )/((a−b)^3 + (b−c)^3 + (c−a)^3 )))/(a^2 +b^2 +c^2 −ab−bc−ca)) = ??

$$\:\:\:\:\:\:\:\:{evaluate}\:\:\: \\ $$$$\:\:\:\:\:\frac{\sqrt{\frac{\left({a}−{b}\right)^{\mathrm{7}} \:+\:\left({b}−{c}\right)^{\mathrm{7}} \:+\:\left({c}−{a}\right)^{\mathrm{7}} }{\left({a}−{b}\right)^{\mathrm{3}} \:+\:\left({b}−{c}\right)^{\mathrm{3}} \:+\:\left({c}−{a}\right)^{\mathrm{3}} }}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{ab}−{bc}−{ca}}\:=\:\:?? \\ $$

Question Number 171558    Answers: 0   Comments: 0

In △ABC , I-incenter ID⊥BC , IE⊥CA , IF⊥AB D∈(BC) , E∈(CA) , F∈(AB) I_a , I_b , I_c -excenters. Prove that: Σ_(cyc) ((EF)/(sin (A/2))) + Π_(cyc) ((EF)/(sin (A/2))) = ((1 + 4r^2 )/R) ∙ [I_a I_b I_c ]

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:,\:\mathrm{I}-\mathrm{incenter} \\ $$$$\mathrm{ID}\bot\mathrm{BC}\:,\:\mathrm{IE}\bot\mathrm{CA}\:,\:\mathrm{IF}\bot\mathrm{AB} \\ $$$$\mathrm{D}\in\left(\mathrm{BC}\right)\:,\:\mathrm{E}\in\left(\mathrm{CA}\right)\:,\:\mathrm{F}\in\left(\mathrm{AB}\right) \\ $$$$\mathrm{I}_{\boldsymbol{\mathrm{a}}} \:,\:\mathrm{I}_{\boldsymbol{\mathrm{b}}} \:,\:\mathrm{I}_{\boldsymbol{\mathrm{c}}} -\mathrm{excenters}.\:\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{EF}}{\mathrm{sin}\:\frac{\mathrm{A}}{\mathrm{2}}}\:\:+\:\:\underset{\boldsymbol{\mathrm{cyc}}} {\prod}\:\frac{\mathrm{EF}}{\mathrm{sin}\:\frac{\mathrm{A}}{\mathrm{2}}}\:\:=\:\:\frac{\mathrm{1}\:+\:\mathrm{4}\boldsymbol{\mathrm{r}}^{\mathrm{2}} }{\mathrm{R}}\:\centerdot\:\left[\mathrm{I}_{\boldsymbol{\mathrm{a}}} \mathrm{I}_{\boldsymbol{\mathrm{b}}} \mathrm{I}_{\boldsymbol{\mathrm{c}}} \right] \\ $$

Question Number 171552    Answers: 2   Comments: 0

Question Number 171593    Answers: 0   Comments: 2

The maximum value of the expression ∣(√(sin^2 x+2a^2 )) −(√(2a^2 −1−cos^2 x)) ∣ where a and x real numbers is−−−

$$\:{The}\:{maximum}\:{value}\:{of}\:{the} \\ $$$${expression}\:\mid\sqrt{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{2}{a}^{\mathrm{2}} }\:−\sqrt{\mathrm{2}{a}^{\mathrm{2}} −\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}}\:\mid\: \\ $$$${where}\:{a}\:{and}\:{x}\:{real}\:{numbers}\:{is}−−− \\ $$

Question Number 171549    Answers: 1   Comments: 0

Solve for real numbers: { ((2x^2 + 3y^2 + z^2 = 7)),((x^2 + y^2 + z^2 = (√2) z (x + y))) :}

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{3y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{7}}\\{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\sqrt{\mathrm{2}}\:\mathrm{z}\:\left(\mathrm{x}\:+\:\mathrm{y}\right)}\end{cases} \\ $$

Question Number 171546    Answers: 0   Comments: 1

f(x)=((−ln∣x∣)/x)+x−2 , g(x)=−x^2 +1−ln∣x∣ Calculate the derivative of f(x) as a function of g(x)

$${f}\left({x}\right)=\frac{−{ln}\mid{x}\mid}{{x}}+{x}−\mathrm{2}\:\:,\:\:\:{g}\left({x}\right)=−{x}^{\mathrm{2}} +\mathrm{1}−{ln}\mid{x}\mid \\ $$$$ \\ $$Calculate the derivative of f(x) as a function of g(x)

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