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Question Number 178511 Answers: 1 Comments: 0

Simplify (p↓q)∧(∼q↓p)

$$\mathrm{Simplify}\: \\ $$$$\left(\mathrm{p}\downarrow\mathrm{q}\right)\wedge\left(\sim\mathrm{q}\downarrow\mathrm{p}\right) \\ $$

Question Number 178508 Answers: 3 Comments: 1

Question Number 178500 Answers: 1 Comments: 1

Question Number 178468 Answers: 0 Comments: 0

For the sequence {u_n } if u_1 =1, u_2 =2 and u_(n+2) ^2 =u_n ^2 +u_(n+1) ^2 −u_n u_(n+1) , for all natural number n. Find lim u_n ?

$${For}\:{the}\:{sequence}\:\left\{{u}_{{n}} \right\}\:{if}\:{u}_{\mathrm{1}} =\mathrm{1},\:{u}_{\mathrm{2}} =\mathrm{2}\:{and}\:{u}_{{n}+\mathrm{2}} ^{\mathrm{2}} ={u}_{{n}} ^{\mathrm{2}} +{u}_{{n}+\mathrm{1}} ^{\mathrm{2}} −{u}_{{n}} {u}_{{n}+\mathrm{1}} ,\:{for}\:{all}\:{natural}\:{number}\:{n}. \\ $$$${Find}\:{lim}\:{u}_{{n}} ? \\ $$

Question Number 178467 Answers: 1 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 178452 Answers: 1 Comments: 0

show that ((p∧q)⇒r)⇒((p∧∼r)⇒∼q) is tautology

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

Question Number 178450 Answers: 1 Comments: 3

Question Number 178448 Answers: 1 Comments: 0

Using the algebra propositions simplify (p↔q)→(p→q)

$$\mathrm{Using}\:\mathrm{the}\:\mathrm{algebra}\:\mathrm{propositions} \\ $$$$\mathrm{simplify} \\ $$$$\left(\mathrm{p}\leftrightarrow\mathrm{q}\right)\rightarrow\left(\mathrm{p}\rightarrow\mathrm{q}\right) \\ $$

Question Number 178454 Answers: 2 Comments: 0

In a chess board number of unit squares with 1)one vertex common? 2)2 vertices common?? 3)2 sides common??

$${In}\:{a}\:{chess}\:{board}\:{number}\:{of}\:{unit}\:{squares} \\ $$$$\left.{with}\:\mathrm{1}\right){one}\:{vertex}\:{common}? \\ $$$$\left.\mathrm{2}\right)\mathrm{2}\:{vertices}\:{common}?? \\ $$$$\left.\mathrm{3}\right)\mathrm{2}\:{sides}\:{common}?? \\ $$

Question Number 178434 Answers: 3 Comments: 0

Simplify by using law of algebra (a) [p∨(p∧q)]→∼p (b)(p∧q)→q

$$\mathrm{Simplify}\:\mathrm{by}\:\mathrm{using}\:\mathrm{law}\:\mathrm{of}\:\mathrm{algebra} \\ $$$$\left(\mathrm{a}\right)\:\left[\mathrm{p}\vee\left(\mathrm{p}\wedge\mathrm{q}\right)\right]\rightarrow\sim\mathrm{p} \\ $$$$\left(\mathrm{b}\right)\left(\mathrm{p}\wedge\mathrm{q}\right)\rightarrow\mathrm{q} \\ $$

Question Number 178433 Answers: 1 Comments: 0

Determine whether the following proposition is true or not [(p→∼q)∧(q∨r)∧p]→r

$$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{proposition}\:\mathrm{is}\:\mathrm{true}\:\mathrm{or}\:\mathrm{not} \\ $$$$\left[\left(\mathrm{p}\rightarrow\sim\mathrm{q}\right)\wedge\left(\mathrm{q}\vee\mathrm{r}\right)\wedge\mathrm{p}\right]\rightarrow\mathrm{r} \\ $$

Question Number 178423 Answers: 2 Comments: 0

(m/n) = (k/p) and (m/n) = (k/p) = 1,5 Find (m/n) + (k/p) = ?

$$\frac{\mathrm{m}}{\mathrm{n}}\:=\:\frac{\mathrm{k}}{\mathrm{p}}\:\:\:\mathrm{and}\:\:\:\frac{\mathrm{m}}{\mathrm{n}}\:=\:\frac{\mathrm{k}}{\mathrm{p}}\:=\:\mathrm{1},\mathrm{5} \\ $$$$\mathrm{Find}\:\:\:\frac{\mathrm{m}}{\mathrm{n}}\:+\:\frac{\mathrm{k}}{\mathrm{p}}\:=\:? \\ $$

Question Number 178415 Answers: 2 Comments: 0

If acosh x+bsinh x=c show that. x=ln [((c±(√(c^2 +b^2 −a^2 )))/(a+b))]

$$\mathrm{If}\:\mathrm{acosh}\:\mathrm{x}+\mathrm{bsinh}\:\mathrm{x}=\mathrm{c}\: \\ $$$$\mathrm{show}\:\mathrm{that}. \\ $$$$\mathrm{x}=\mathrm{ln}\:\left[\frac{\mathrm{c}\pm\sqrt{\mathrm{c}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }}{\mathrm{a}+\mathrm{b}}\right] \\ $$

Question Number 178413 Answers: 1 Comments: 2

(2x^3 y+3xy−5x^2 y^2 +12)÷(2x−4) Divide it using compound division

$$\left(\mathrm{2}{x}^{\mathrm{3}} {y}+\mathrm{3}{xy}−\mathrm{5}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{12}\right)\boldsymbol{\div}\left(\mathrm{2}{x}−\mathrm{4}\right) \\ $$$$ \\ $$Divide it using compound division

Question Number 178412 Answers: 1 Comments: 0

Express sinh^(−1) x−ln x in terms of natural logarithms.Hence find the limit as x→∞

$$\mathrm{Express}\:\mathrm{sinh}\:^{−\mathrm{1}} \mathrm{x}−\mathrm{ln}\:\mathrm{x}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of} \\ $$$$\mathrm{natural}\:\mathrm{logarithms}.\mathrm{Hence}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{limit}\:\mathrm{as}\:\mathrm{x}\rightarrow\infty \\ $$

Question Number 178400 Answers: 1 Comments: 0

evaluate Σ_(k=1) ^n k e^(kx)

$$\:\:\mathrm{evaluate}\:\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{k}\:\mathrm{e}^{\mathrm{kx}} \\ $$

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

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

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