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Question Number 178395 Answers: 2 Comments: 0

How many 5 digit numbers with different digits are multiple of 9?

$${How}\:{many}\:\mathrm{5}\:{digit}\:{numbers}\:{with} \\ $$$${different}\:{digits}\:{are}\:{multiple}\:{of}\:\mathrm{9}? \\ $$

Question Number 178476 Answers: 1 Comments: 0

Find a∈R Such that x_1 ^(16) + x_2 ^(16) + x_3 ^(16) = 30 Where x_1 ,x_2 ,x_3 − are the roots of the equation: x^3 + ax + 1 = 0

$$\mathrm{Find}\:\:\mathrm{a}\in\mathbb{R} \\ $$$$\mathrm{Such}\:\mathrm{that}\:\:\mathrm{x}_{\mathrm{1}} ^{\mathrm{16}} \:+\:\mathrm{x}_{\mathrm{2}} ^{\mathrm{16}} \:+\:\mathrm{x}_{\mathrm{3}} ^{\mathrm{16}} \:=\:\mathrm{30} \\ $$$$\mathrm{Where}\:\:\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} ,\mathrm{x}_{\mathrm{3}} −\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{ax}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 178389 Answers: 1 Comments: 0

show that p⇒((p⇒q)⇒q) is tautology

$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{p}\Rightarrow\left(\left(\mathrm{p}\Rightarrow\mathrm{q}\right)\Rightarrow\mathrm{q}\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{is}\:\mathrm{tautology}\: \\ $$

Question Number 178388 Answers: 2 Comments: 0

p(sin^(77) ((50)/(19)),cos((27)/(13))) 1) VI 2)III 3)II 4)I In which region of the fixed coordinate system is this point located?

$$\:{p}\left({sin}^{\mathrm{77}} \frac{\mathrm{50}}{\mathrm{19}},{cos}\frac{\mathrm{27}}{\mathrm{13}}\right) \\ $$$$\left.\mathrm{1}\left.\right)\left.\:\left.{VI}\:\:\:\:\mathrm{2}\right){III}\:\:\:\:\:\mathrm{3}\right){II}\:\:\:\:\:\:\:\mathrm{4}\right){I} \\ $$In which region of the fixed coordinate system is this point located?

Question Number 178375 Answers: 1 Comments: 1

calculer une primitive de −3x/(√(x^2 +3))

$${calculer}\:{une}\:{primitive}\:{de}\:−\mathrm{3}{x}/\sqrt{{x}^{\mathrm{2}} +\mathrm{3}} \\ $$

Question Number 178374 Answers: 1 Comments: 0

Let the points ABC form a triangle on the cartesian plane, whose area is 20. Let the coordinates of said points be A(8, 6) B(2, 4) and C(x, y) If ∣AC∣=∣BC∣, find the coordinates of point C.

$${Let}\:{the}\:{points}\:{ABC}\:{form}\:{a}\:{triangle}\:{on}\:{the} \\ $$$${cartesian}\:{plane},\:{whose}\:{area}\:{is}\:\mathrm{20}.\:{Let}\:{the}\:{coordinates} \\ $$$${of}\:{said}\:{points}\:{be}\:{A}\left(\mathrm{8},\:\mathrm{6}\right)\:{B}\left(\mathrm{2},\:\mathrm{4}\right)\:{and}\:{C}\left({x},\:{y}\right) \\ $$$${If}\:\mid{AC}\mid=\mid{BC}\mid,\:{find}\:{the}\:{coordinates}\:{of}\:{point}\:{C}. \\ $$

Question Number 180641 Answers: 4 Comments: 0

if a+b+c+d+e=8 and a^2 +b^2 +c^2 +d^2 +e^2 =16, what is the maximal value of a ?

$${if}\:{a}+{b}+{c}+{d}+{e}=\mathrm{8}\:{and} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} +{e}^{\mathrm{2}} =\mathrm{16},\:{what}\:{is}\:{the} \\ $$$${maximal}\:{value}\:{of}\:{a}\:? \\ $$

Question Number 178358 Answers: 0 Comments: 0

Show that when x is small ln (cosh x)≈(x^2 /2)−(x^4 /(12))+... and that when x is large ln (cosh x)≈x−ln 2

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{when}\:\mathrm{x}\:\mathrm{is}\:\mathrm{small}\: \\ $$$$\mathrm{ln}\:\left(\mathrm{cosh}\:\mathrm{x}\right)\approx\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{12}}+...\:\mathrm{and} \\ $$$$\mathrm{that}\:\mathrm{when}\:\mathrm{x}\:\mathrm{is}\:\mathrm{large}\:\mathrm{ln}\:\left(\mathrm{cosh}\:\mathrm{x}\right)\approx\mathrm{x}−\mathrm{ln}\:\mathrm{2} \\ $$

Question Number 178357 Answers: 1 Comments: 0

Given that sinh^(−1) x=sech^(−1) x show x=(√((((√5)−1)/2) ))

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{sinh}\:^{−\mathrm{1}} \mathrm{x}=\mathrm{sech}\:^{−\mathrm{1}} \mathrm{x}\:\:\: \\ $$$$\mathrm{show} \\ $$$$\mathrm{x}=\sqrt{\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\:} \\ $$

Question Number 178356 Answers: 1 Comments: 0

Solve simultaneous sinh x+cosh y=5 sinh^2 x+cosh^2 y=13

$$\mathrm{Solve}\:\mathrm{simultaneous} \\ $$$$\mathrm{sinh}\:\mathrm{x}+\mathrm{cosh}\:\mathrm{y}=\mathrm{5} \\ $$$$\mathrm{sinh}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cosh}\:^{\mathrm{2}} \mathrm{y}=\mathrm{13} \\ $$

Question Number 178355 Answers: 1 Comments: 0

Show that cosh x>sinh x

$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{cosh}\:\mathrm{x}>\mathrm{sinh}\:\mathrm{x} \\ $$

Question Number 178354 Answers: 1 Comments: 0

Show that the minimum value of sinh x+ncosh x is (√(n^2 −1)) and this occurs x=0.5ln (((n−1)/(n+1)))

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{sinh}\:\mathrm{x}+\mathrm{ncosh}\:\mathrm{x}\:\mathrm{is}\:\sqrt{\mathrm{n}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\mathrm{and}\:\mathrm{this}\:\mathrm{occurs}\:\mathrm{x}=\mathrm{0}.\mathrm{5ln}\:\left(\frac{\mathrm{n}−\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right) \\ $$

Question Number 179992 Answers: 0 Comments: 0

What is the absolute error for the measurements: (a) 250m to the nearest 10m. (b) 143m to three sig. figures. (c) 41500cm to the nearest 100.

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{absolute}\:\mathrm{error}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{measurements}: \\ $$$$\:\:\:\:\left({a}\right)\:\mathrm{250}{m}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{10}{m}. \\ $$$$\:\:\:\:\left({b}\right)\:\mathrm{143}{m}\:\mathrm{to}\:\mathrm{three}\:\mathrm{sig}.\:\mathrm{figures}. \\ $$$$\:\:\:\:\left({c}\right)\:\:\mathrm{41500}{cm}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{100}. \\ $$

Question Number 179991 Answers: 1 Comments: 0

Question Number 178349 Answers: 1 Comments: 0

etudier la fonction suivante 4x^3 −9x^2 +6x+1 calculer les limites puis dresser son tableau de variation

$${etudier}\:{la}\:{fonction}\:{suivante}\:\mathrm{4}{x}^{\mathrm{3}} −\mathrm{9}{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{1} \\ $$$${calculer}\:{les}\:{limites}\:{puis}\:{dresser}\:{son}\:{tableau}\:{de}\:{variation} \\ $$

Question Number 178347 Answers: 2 Comments: 0

Let f(x)= (ax+1)^5 .(1+bx)^4 ; a,b ∈ N if times of x equal 62 so what are possible values of the sum a, b?

$${Let}\:{f}\left({x}\right)=\:\left({ax}+\mathrm{1}\right)^{\mathrm{5}} .\left(\mathrm{1}+{bx}\right)^{\mathrm{4}} \:;\:{a},{b}\:\in\:\mathbb{N} \\ $$$$\:{if}\:{times}\:{of}\:{x}\:{equal}\:\mathrm{62}\:{so}\:{what}\:{are}\:{possible}\:{values} \\ $$$$\:{of}\:{the}\:{sum}\:{a},\:{b}? \\ $$$$ \\ $$

Question Number 178346 Answers: 0 Comments: 0

find n^(th) terms of 2,3,5,7,11,13,15,17

$${find}\:{n}^{{th}} \:{terms}\:{of}\:\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{11},\mathrm{13},\mathrm{15},\mathrm{17} \\ $$

Question Number 178341 Answers: 1 Comments: 0

Question Number 178339 Answers: 1 Comments: 4

Determiner le temps necessaire pour remplir le verre a la hauteur h.

$${Determiner}\:{le}\:{temps}\:{necessaire}\:{pour} \\ $$$${remplir}\:{le}\:{verre}\:{a}\:{la}\:{hauteur}\:{h}. \\ $$

Question Number 178338 Answers: 3 Comments: 1

Let S= {1, 2, ..., 9, 0} A: How many multiples of eight of four digits can be formed from S B: The same question for different digits

$${Let}\:{S}=\:\left\{\mathrm{1},\:\mathrm{2},\:...,\:\mathrm{9},\:\mathrm{0}\right\}\:\boldsymbol{{A}}:\:{How}\:{many}\:{multiples} \\ $$$$\:{of}\:{eight}\:{of}\:{four}\:{digits}\:{can}\:{be}\:{formed}\:{from}\:{S} \\ $$$$\:\boldsymbol{{B}}:\:{The}\:{same}\:{question}\:{for}\:{different}\:{digits} \\ $$

Question Number 178323 Answers: 1 Comments: 3

Question Number 178320 Answers: 1 Comments: 2

Question Number 178305 Answers: 0 Comments: 0

Question Number 178299 Answers: 1 Comments: 0

Question Number 181568 Answers: 0 Comments: 0

Question Number 178751 Answers: 3 Comments: 0

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