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Question Number 80540    Answers: 0   Comments: 1

Question Number 80515    Answers: 0   Comments: 1

∫(dx/((1+x^φ )^φ ))

$$\int\frac{{dx}}{\left(\mathrm{1}+{x}^{\phi} \right)^{\phi} } \\ $$

Question Number 80505    Answers: 0   Comments: 8

Given that 7^k ≡1 (mod 15) a) Write down three values of k. b) Find the general solution of the equation 7^k ≡ 1 (mod 15)

$$\mathrm{Given}\:\mathrm{that}\:\:\mathrm{7}^{{k}} \:\equiv\mathrm{1}\:\left(\mathrm{mod}\:\mathrm{15}\right) \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Write}\:\mathrm{down}\:\mathrm{three}\:\mathrm{values}\:\mathrm{of}\:{k}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{equation}\:\:\mathrm{7}^{{k}} \:\equiv\:\mathrm{1}\:\left({mod}\:\mathrm{15}\right) \\ $$

Question Number 80504    Answers: 0   Comments: 2

Solve the system of congruences x ≡ 2 (mod 3) x ≡ 5( mod 7)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{congruences} \\ $$$${x}\:\equiv\:\mathrm{2}\:\left(\mathrm{mod}\:\mathrm{3}\right) \\ $$$${x}\:\equiv\:\mathrm{5}\left(\:\mathrm{mod}\:\mathrm{7}\right) \\ $$$$\: \\ $$

Question Number 80341    Answers: 1   Comments: 0

A particle moves round the polar curve r = a(1 + cos θ) with constant angular velocity ω . Find the transverse component of the velocity.

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{round}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{curve} \\ $$$${r}\:=\:{a}\left(\mathrm{1}\:+\:\mathrm{cos}\:\theta\right)\:\mathrm{with}\:\mathrm{constant}\:\mathrm{angular}\: \\ $$$$\mathrm{velocity}\:\omega\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{transverse}\:\mathrm{component} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{velocity}. \\ $$

Question Number 80340    Answers: 1   Comments: 0

If P = ((a,b,c,d),(c,d,a,b) ) , Q = ((a,b,c,d),(b,a,d,c) ) are permutations of the elements (a,b,c,d), then QP ≡

$$\mathrm{If}\:{P}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{c}}&{{d}}&{{a}}&{{b}}\end{pmatrix}\:\:,\:{Q}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{b}}&{{a}}&{{d}}&{{c}}\end{pmatrix}\:\mathrm{are} \\ $$$$\mathrm{permutations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{elements}\:\left({a},{b},{c},{d}\right),\:\mathrm{then}\: \\ $$$${QP}\:\equiv \\ $$$$\: \\ $$

Question Number 80293    Answers: 0   Comments: 12

Find all functions that satisfy to (E): ∀ x∈R xf(x)+∫_0 ^x f(x−t)cos(2t)dt=sin(2x)

$${Find}\:{all}\:{functions}\:{that}\:\:{satisfy}\:{to}\:\: \\ $$$$\left({E}\right):\:\forall\:{x}\in\mathbb{R}\:\:\:\:\:\:{xf}\left({x}\right)+\int_{\mathrm{0}} ^{{x}} {f}\left({x}−{t}\right){cos}\left(\mathrm{2}{t}\right){dt}={sin}\left(\mathrm{2}{x}\right) \\ $$$$\: \\ $$

Question Number 80175    Answers: 1   Comments: 1

∫_0 ^1 (dx/(√(x^2 +x+1))) = ?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}\:=\:? \\ $$

Question Number 80172    Answers: 0   Comments: 2

Given that lim_(x→0) ((√(f(x)+ x))/h) = L then lim_(x→0) ((√(f(x) + 2x))/h) = ?

$${Given}\:{that}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{f}\left({x}\right)+\:{x}}}{{h}}\:=\:{L}\:{then} \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{{f}\left({x}\right)\:+\:\mathrm{2}{x}}}{{h}}\:=\:? \\ $$

Question Number 80159    Answers: 1   Comments: 4

IF THE SUM OF p TERMS OF AN A.P. IS EQUAL TO SUM OF ITS q TERMS. PROVE THAT THE SUM OF (p+q) TERMS OF IT IS EQUAL TO 0(ZERO).

$$\boldsymbol{{IF}}\:\:\boldsymbol{{THE}}\:\:\:\boldsymbol{{SUM}}\:\:\:\boldsymbol{{OF}}\:\:\:\boldsymbol{{p}}\:\:\boldsymbol{{TERMS}} \\ $$$$\boldsymbol{{OF}}\:\:\boldsymbol{{AN}}\:\:\:\:\boldsymbol{{A}}.\boldsymbol{{P}}.\:\:\:\boldsymbol{{IS}}\:\:\:\boldsymbol{{EQUAL}}\:\:\boldsymbol{{TO}} \\ $$$$\boldsymbol{{SUM}}\:\:\boldsymbol{{OF}}\:\:\:\boldsymbol{{ITS}}\:\:\:\boldsymbol{{q}}\:\:\:\boldsymbol{{TERMS}}.\:\: \\ $$$$\boldsymbol{{PROVE}}\:\:\boldsymbol{{THAT}}\:\:\boldsymbol{{THE}}\:\:\boldsymbol{{SUM}}\:\:\boldsymbol{{OF}} \\ $$$$\left(\boldsymbol{{p}}+\boldsymbol{{q}}\right)\:\:\boldsymbol{{TERMS}}\:\:\boldsymbol{{OF}}\:\:\:\boldsymbol{{IT}}\:\:\:\boldsymbol{{IS}}\:\:\: \\ $$$$\boldsymbol{{EQUAL}}\:\:\boldsymbol{{TO}}\:\:\mathrm{0}\left(\boldsymbol{{ZERO}}\right). \\ $$

Question Number 80102    Answers: 0   Comments: 0

Question Number 80088    Answers: 0   Comments: 0

When the father was son′s age, the son was ten years old; when the son will be father′s age, the father will be seventy. What are their ages ?

$$\:{When}\:\:{the}\:\:{father}\:\:{was}\:{son}'{s}\:\:{age},\:\:{the}\:\:{son} \\ $$$$\:\:{was}\:\:{ten}\:\:{years}\:\:{old};\:\:{when}\:\:{the}\:\:{son}\:\:{will}\:\:{be}\:\:{father}'{s}\:\:{age}, \\ $$$$\:\:{the}\:\:{father}\:\:{will}\:\:{be}\:\:{seventy}. \\ $$$$\:\:{What}\:\:{are}\:\:{their}\:\:{ages}\:\:? \\ $$

Question Number 79969    Answers: 1   Comments: 0

find the general solution for 2sin 3x = sin 2x

$${find}\:{the}\:{general}\:{solution}\:{for}\: \\ $$$$\:\:\mathrm{2sin}\:\mathrm{3}{x}\:=\:\mathrm{sin}\:\mathrm{2}{x} \\ $$

Question Number 79968    Answers: 0   Comments: 3

Find the 50^(th) entry of 3.127356432...

$${Find}\:{the}\:\mathrm{50}^{{th}} \:{entry}\:{of}\:\:\mathrm{3}.\mathrm{127356432}... \\ $$

Question Number 79943    Answers: 1   Comments: 5

Question Number 79751    Answers: 2   Comments: 0

prove that cos^6 θ + sin^6 θ = 1 − (3/4) sin^2 2θ

$${prove}\:{that}\:\mathrm{cos}\:^{\mathrm{6}} \theta\:+\:\mathrm{sin}\:^{\mathrm{6}} \theta\:=\:\mathrm{1}\:−\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}\theta \\ $$

Question Number 79738    Answers: 0   Comments: 0

The forces F_1 = (2i + bj) N, F_2 = (−i + 2j) N and F_3 = (ai −4j)N act through the points with position vectors r_1 = (i + 3j)m ,r_2 =(xi + 5j) m and r_3 =(−i + j)m respectively . Given that this system of forces is equivalent to a couple of magnitude 12 N m, find a) the valueof the scalars a and b b) the possible values of the scalar x.

$${The}\:{forces}\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} =\:\left(\mathrm{2}\boldsymbol{{i}}\:+\:{b}\boldsymbol{{j}}\right)\:{N},\:\boldsymbol{{F}}_{\mathrm{2}} =\:\left(−\boldsymbol{{i}}\:+\:\mathrm{2}\boldsymbol{{j}}\right)\:{N} \\ $$$${and}\:\boldsymbol{{F}}_{\mathrm{3}} =\:\left({a}\boldsymbol{{i}}\:−\mathrm{4}\boldsymbol{{j}}\right){N}\:{act}\:{through}\:{the}\:{points}\:{with} \\ $$$${position}\:{vectors}\:\boldsymbol{{r}}_{\mathrm{1}} =\:\left(\boldsymbol{{i}}\:+\:\mathrm{3}\boldsymbol{{j}}\right){m}\:,\boldsymbol{{r}}_{\mathrm{2}} =\left({x}\boldsymbol{{i}}\:+\:\mathrm{5}\boldsymbol{{j}}\right)\:{m} \\ $$$${and}\:\boldsymbol{{r}}_{\mathrm{3}} =\left(−\boldsymbol{{i}}\:+\:\boldsymbol{{j}}\right){m}\:{respectively}\:. \\ $$$${Given}\:{that}\:{this}\:{system}\:{of}\:{forces}\:{is}\:{equivalent}\:{to}\:{a}\:{couple} \\ $$$${of}\:{magnitude}\:\mathrm{12}\:{N}\:{m},\:{find}\: \\ $$$$\left.{a}\right)\:{the}\:{valueof}\:{the}\:{scalars}\:{a}\:{and}\:{b} \\ $$$$\left.{b}\right)\:{the}\:{possible}\:{values}\:{of}\:{the}\:{scalar}\:{x}. \\ $$

Question Number 79735    Answers: 1   Comments: 0

write tanhx in terms of e, hence prove that tanh2x = ((2tanhx)/(1+tanh^2 x))

$${write}\:{tanhx}\:{in}\:{terms}\:{of}\:{e},\:{hence}\:{prove}\:{that}\: \\ $$$${tanh}\mathrm{2}{x}\:=\:\frac{\mathrm{2}{tanhx}}{\mathrm{1}+{tanh}^{\mathrm{2}} {x}} \\ $$

Question Number 79718    Answers: 0   Comments: 0

$$ \\ $$

Question Number 79705    Answers: 0   Comments: 3

if L{f(t)}=L{g(t)} then why f(t)=g(t)? is there any proof

$$\mathrm{if}\:\mathscr{L}\left\{\mathrm{f}\left(\mathrm{t}\right)\right\}=\mathscr{L}\left\{\mathrm{g}\left(\mathrm{t}\right)\right\} \\ $$$$\mathrm{then}\:\mathrm{why}\:\mathrm{f}\left(\mathrm{t}\right)=\mathrm{g}\left(\mathrm{t}\right)? \\ $$$$\mathrm{is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{proof} \\ $$

Question Number 79491    Answers: 0   Comments: 4

Find the number of used place

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{used}\:\mathrm{place} \\ $$

Question Number 79423    Answers: 1   Comments: 0

solve for x and y sinh x − 2cosh y = 0 3cosh x + 6 sihn y = 5

$${solve}\:{for}\:{x}\:{and}\:{y}\: \\ $$$$\:\:\:{sinh}\:{x}\:−\:\mathrm{2}{cosh}\:{y}\:=\:\mathrm{0} \\ $$$$\:\:\:\mathrm{3}{cosh}\:{x}\:+\:\mathrm{6}\:{sihn}\:{y}\:=\:\mathrm{5} \\ $$

Question Number 79394    Answers: 1   Comments: 0

Question Number 79311    Answers: 0   Comments: 2

Question Number 79177    Answers: 1   Comments: 0

Question Number 79111    Answers: 0   Comments: 3

Show that E={(x,y,z) ∈ R^3 / x−2y+z=0} is a subspace vector of which we will determine one base. please help sirs...

$$\mathrm{Show}\:\mathrm{that} \\ $$$$\mathrm{E}=\left\{\left({x},\mathrm{y},{z}\right)\:\in\:\mathbb{R}^{\mathrm{3}} \:\:/\:\:{x}−\mathrm{2}{y}+{z}=\mathrm{0}\right\} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{subspace}\:\mathrm{vector}\:\mathrm{of}\:\mathrm{which}\:\mathrm{we} \\ $$$$\mathrm{will}\:\mathrm{determine}\:\mathrm{one}\:\mathrm{base}. \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{sirs}... \\ $$

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