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AllQuestion and Answers: Page 1378

Question Number 74112 Answers: 1 Comments: 0

Question Number 74111 Answers: 1 Comments: 1

Question Number 74109 Answers: 1 Comments: 3

Question Number 74087 Answers: 0 Comments: 15

(Q73828) prove that no cube exists whose corners are located on all faces of an other cube.

$$\left({Q}\mathrm{73828}\right) \\ $$$${prove}\:{that}\:{no}\:{cube}\:{exists}\:{whose}\:{corners} \\ $$$${are}\:{located}\:{on}\:{all}\:{faces}\:{of}\:{an}\:{other}\:{cube}. \\ $$

Question Number 74075 Answers: 0 Comments: 1

Question Number 74068 Answers: 1 Comments: 4

Question Number 74063 Answers: 0 Comments: 0

Question Number 74041 Answers: 0 Comments: 3

Question Number 74040 Answers: 1 Comments: 1

Find orthogonal trajectories of the curves: (x−c)^2 +y^2 =c^2 .

$${Find}\:{orthogonal}\:{trajectories}\:{of}\:{the} \\ $$$${curves}:\:\left({x}−{c}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} ={c}^{\mathrm{2}} . \\ $$

Question Number 74037 Answers: 1 Comments: 0

∫_0^ ^(Π/2) xcos^n xdx by reduction formula

$$\int_{\mathrm{0}^{} } ^{\Pi/\mathrm{2}} {x}\mathrm{cos}^{{n}} {xdx}\:\:\:{by}\:{reduction}\:{formula} \\ $$

Question Number 74026 Answers: 1 Comments: 5

U_n is a sequence wich verfy ∀n ∈N 2^n ( U_n +U_(n+1) )=1 1) calculate U_n interms of n 2) is (U_n ) cojverhent ?

$${U}_{{n}} {is}\:{a}\:{sequence}\:{wich}\:{verfy}\: \\ $$$$\forall{n}\:\in{N}\:\:\:\:\:\:\:\:\mathrm{2}^{{n}} \left(\:{U}_{{n}} +{U}_{{n}+\mathrm{1}} \right)=\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{is}\:\left({U}_{{n}} \right)\:{cojverhent}\:? \\ $$

Question Number 74024 Answers: 1 Comments: 1

{ ((h^2 +y^2 +(k−z)^2 =s^2 )),((a^2 +(b−y)^2 +z^2 =s^2 )),((ah+y(y−b)+z(z−k)=0)),((((h+a)/2)+yz−(b−y)(k−z)=1)),((b+a(k−z)+hz=1)),((k+h(b−y)+ay=1)) :} Find s_(min) or at least express s=f(y) or g(z).

$$\begin{cases}{{h}^{\mathrm{2}} +{y}^{\mathrm{2}} +\left({k}−{z}\right)^{\mathrm{2}} ={s}^{\mathrm{2}} }\\{{a}^{\mathrm{2}} +\left({b}−{y}\right)^{\mathrm{2}} +{z}^{\mathrm{2}} ={s}^{\mathrm{2}} }\\{{ah}+{y}\left({y}−{b}\right)+{z}\left({z}−{k}\right)=\mathrm{0}}\\{\frac{{h}+{a}}{\mathrm{2}}+{yz}−\left({b}−{y}\right)\left({k}−{z}\right)=\mathrm{1}}\\{{b}+{a}\left({k}−{z}\right)+{hz}=\mathrm{1}}\\{{k}+{h}\left({b}−{y}\right)+{ay}=\mathrm{1}}\end{cases} \\ $$$${Find}\:\:{s}_{{min}} \:{or}\:{at}\:{least}\:{express} \\ $$$$\:{s}={f}\left({y}\right)\:{or}\:{g}\left({z}\right). \\ $$

Question Number 74042 Answers: 0 Comments: 3

Question Number 74019 Answers: 1 Comments: 3

let the matrix A = (((1 2)),((0 −3)) ) 1) calculate A^n for n integr 2) find e^A and e^(−A) .

$${let}\:{the}\:{matrix}\:\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:−\mathrm{3}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \:\:{for}\:{n}\:{integr} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{e}^{{A}} \:\:{and}\:{e}^{−{A}} . \\ $$

Question Number 74017 Answers: 0 Comments: 3

let f(x)=∫_x ^(x^2 +3) e^(−xt) ln(1+e^(−xt) )dt with x>0 1) calculate f(x) 2)find lim_(x→+∞) f(x).

$${let}\:{f}\left({x}\right)=\int_{{x}} ^{{x}^{\mathrm{2}} +\mathrm{3}} \:{e}^{−{xt}} \:{ln}\left(\mathrm{1}+{e}^{−{xt}} \right){dt}\:\:\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right). \\ $$

Question Number 74016 Answers: 1 Comments: 5

let g(x) =(1/x)∫_x ^(2x+1) arctan(xt)dt find lim_(x→0) g(x) and lim_(x→+∞) g(x).

$${let}\:{g}\left({x}\right)\:=\frac{\mathrm{1}}{{x}}\int_{{x}} ^{\mathrm{2}{x}+\mathrm{1}} \:\:{arctan}\left({xt}\right){dt} \\ $$$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{g}\left({x}\right)\:\:{and}\:{lim}_{{x}\rightarrow+\infty} {g}\left({x}\right). \\ $$

Question Number 74015 Answers: 0 Comments: 1

let f(x) =∫_x ^x^2 ((sh(xt))/(sin(xt)))dt calculate lim_(x→0) f(x)

$${let}\:{f}\left({x}\right)\:=\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{sh}\left({xt}\right)}{{sin}\left({xt}\right)}{dt} \\ $$$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} {f}\left({x}\right) \\ $$

Question Number 74014 Answers: 0 Comments: 1

let W(x)=Σ_(1≤i<j≤n) (x^(i+j) /(ij)) calculate W^′ (x).

$$\:\: \\ $$$$\:\:{let}\:{W}\left({x}\right)=\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\frac{{x}^{{i}+{j}} }{{ij}} \\ $$$${calculate}\:{W}\:^{'} \left({x}\right). \\ $$

Question Number 74013 Answers: 1 Comments: 3

let P(x)= Σ_(0≤i<j≤n) x^(i+j) 1) calculate P^′ (x) 2) find ∫_0 ^1 P(x)dx

$${let}\:\:\:{P}\left({x}\right)=\:\sum_{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} \:{x}^{{i}+{j}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{P}\:^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{P}\left({x}\right){dx} \\ $$

Question Number 74000 Answers: 1 Comments: 0

if p_r ^n =840 , c_r ^n =35 find value of r? pleas sir help me?

$${if}\:{p}_{{r}} ^{{n}} =\mathrm{840}\:,\:{c}_{{r}} ^{{n}} =\mathrm{35}\:{find}\:{value}\:{of}\:{r}? \\ $$$${pleas}\:{sir}\:{help}\:{me}? \\ $$

Question Number 74006 Answers: 1 Comments: 1

If 3x^2 e^(log _x 27) =27000 then find x

$${If}\:\mathrm{3}{x}^{\mathrm{2}} {e}^{\mathrm{log}\:_{{x}} \mathrm{27}} =\mathrm{27000}\:{then}\:{find}\:{x} \\ $$

Question Number 74005 Answers: 0 Comments: 0

find C_8 ^(15) +C_9 ^(15) −C_7 ^(15) −C_6 ^(15) ? pleas help me sir ?

$${find}\:{C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{7}} ^{\mathrm{15}} −{C}_{\mathrm{6}} ^{\mathrm{15}} \:? \\ $$$${pleas}\:{help}\:{me}\:{sir}\:? \\ $$

Question Number 74003 Answers: 0 Comments: 1

find C_8 ^(15) +C_9 ^(15) −C_7 ^(15) −C_6 ^(15) ? pleas help me sir ?

$${find}\:{C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{7}} ^{\mathrm{15}} −{C}_{\mathrm{6}} ^{\mathrm{15}} \:? \\ $$$${pleas}\:{help}\:{me}\:{sir}\:? \\ $$

Question Number 73983 Answers: 2 Comments: 0

if p_r ^n =49 , c_r ^n =196 find the valve of r and n? pleas sir help me

$${if}\:{p}_{{r}} ^{{n}} =\mathrm{49}\:,\:{c}_{{r}} ^{{n}} =\mathrm{196}\:{find}\:{the}\:{valve}\:{of}\:{r}\:{and}\:{n}? \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 73982 Answers: 0 Comments: 2

if p_r ^n =49 , c_r ^n =196 find the valve of r and n? pleas sir help me

$${if}\:{p}_{{r}} ^{{n}} =\mathrm{49}\:,\:{c}_{{r}} ^{{n}} =\mathrm{196}\:{find}\:{the}\:{valve}\:{of}\:{r}\:{and}\:{n}? \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 73974 Answers: 1 Comments: 0

Prove this equation ((2^(x−1) (x−(1/2))!)/((1/2)!))=(((2x−1)!)/(2^(x−1) (x−1)!))

$$\mathrm{Prove}\:\mathrm{this}\:\mathrm{equation} \\ $$$$\frac{\mathrm{2}^{{x}−\mathrm{1}} \left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)!}{\frac{\mathrm{1}}{\mathrm{2}}!}=\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)!}{\mathrm{2}^{{x}−\mathrm{1}} \left({x}−\mathrm{1}\right)!} \\ $$

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