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Question Number 184706 Answers: 1 Comments: 0

deg[3p(x)+Q(x)]=6 deg[p(x)+x^4 ]=5 deg[(((x^4 +1)p(x^2 ))/(x^3 ∙Q(x)))]=? deg=degree

$$\mathrm{deg}\left[\mathrm{3p}\left(\mathrm{x}\right)+\mathrm{Q}\left(\mathrm{x}\right)\right]=\mathrm{6} \\ $$$$\mathrm{deg}\left[\mathrm{p}\left(\mathrm{x}\right)+\mathrm{x}^{\mathrm{4}} \right]=\mathrm{5} \\ $$$$\mathrm{deg}\left[\frac{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)\mathrm{p}\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} \centerdot\mathrm{Q}\left(\mathrm{x}\right)}\right]=? \\ $$$$\mathrm{deg}=\mathrm{degree}\: \\ $$

Question Number 184705 Answers: 0 Comments: 0

Question Number 184683 Answers: 1 Comments: 0

x′′ − (5/t) x′ + (8/t^2 ) x = ((2 ln t)/t^2 ) solve the differential eqn

$${x}''\:−\:\frac{\mathrm{5}}{{t}}\:{x}'\:+\:\frac{\mathrm{8}}{{t}^{\mathrm{2}} }\:{x}\:=\:\frac{\mathrm{2}\:{ln}\:{t}}{{t}^{\mathrm{2}} } \\ $$$${solve}\:{the}\:{differential}\:{eqn} \\ $$

Question Number 184669 Answers: 0 Comments: 3

Question Number 184668 Answers: 0 Comments: 0

Question Number 184656 Answers: 1 Comments: 0

prove that the area of a triangle whose two sides are A^− and B^− is given by (1/2)∣A×B∣. Also find the direction−cosine of normal to this area. Help!

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{whose}\:\mathrm{two}\:\mathrm{sides}\:\mathrm{are}\:\overset{−} {\mathrm{A}}\:\mathrm{and}\:\overset{−} {\mathrm{B}}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by}\:\frac{\mathrm{1}}{\mathrm{2}}\mid\mathrm{A}×\mathrm{B}\mid. \\ $$$$\mathrm{Also}\:\mathrm{find}\:\mathrm{the}\:\mathrm{direction}−\mathrm{cosine} \\ $$$$\mathrm{of}\:\mathrm{normal}\:\mathrm{to}\:\mathrm{this}\:\mathrm{area}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184655 Answers: 1 Comments: 0

prove that an angle inscribe in a semi−circle is a right angle. Help!

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{inscribe}\:\mathrm{in}\:\mathrm{a}\: \\ $$$$\mathrm{semi}−\mathrm{circle}\:\mathrm{is}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angle}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184645 Answers: 1 Comments: 0

Question Number 184633 Answers: 1 Comments: 0

Question Number 184638 Answers: 0 Comments: 6

Question Number 184618 Answers: 1 Comments: 0

If xy≤ax^2 +2y^2 is always true for any 1≤x≤2, 2≤y≤3 Then find the range of a.

$$\mathrm{If}\:{xy}\leqslant{ax}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{always}\:\mathrm{true}\:\mathrm{for}\:\mathrm{any}\:\mathrm{1}\leqslant{x}\leqslant\mathrm{2},\:\mathrm{2}\leqslant{y}\leqslant\mathrm{3} \\ $$$$\mathrm{Then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{a}. \\ $$

Question Number 184622 Answers: 1 Comments: 0

Solve for real numbers: sinx (√(1 − sin^2 x)) = 1 + cosy (√(1 − cos^2 y))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{sinx}\:\sqrt{\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\:=\:\mathrm{1}\:+\:\mathrm{cosy}\:\sqrt{\mathrm{1}\:−\:\mathrm{cos}^{\mathrm{2}} \mathrm{y}}\: \\ $$

Question Number 184620 Answers: 3 Comments: 1

Question Number 184609 Answers: 2 Comments: 0

Question Number 184607 Answers: 0 Comments: 3

solve { ((x^2 −xy+y^2 =16)),((y^2 −yz+z^2 =25)),((z^2 −zx+x^2 =49)) :}

$${solve} \\ $$$$\begin{cases}{{x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} =\mathrm{16}}\\{{y}^{\mathrm{2}} −{yz}+{z}^{\mathrm{2}} =\mathrm{25}}\\{{z}^{\mathrm{2}} −{zx}+{x}^{\mathrm{2}} =\mathrm{49}}\end{cases} \\ $$

Question Number 184602 Answers: 1 Comments: 1

Question Number 184600 Answers: 0 Comments: 3

Question Number 184594 Answers: 1 Comments: 0

If f(x)=ln∣a+(1/(1−x))∣+b is an odd function, then find the value of a, b.

$$\mathrm{If}\:{f}\left({x}\right)=\mathrm{ln}\mid{a}+\frac{\mathrm{1}}{\mathrm{1}−{x}}\mid+{b}\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a},\:{b}. \\ $$

Question Number 184590 Answers: 0 Comments: 0

Question Number 184574 Answers: 0 Comments: 5

Test whether this is Convergent or Divergent Σ_(n=0) ^∞ (−1)^n ((n!x^n )/(5n)) Help!

$$\mathrm{Test}\:\mathrm{whether}\:\mathrm{this}\:\mathrm{is}\:\mathrm{Convergent}\:\mathrm{or} \\ $$$$\mathrm{Divergent} \\ $$$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \frac{\mathrm{n}!\mathrm{x}^{\mathrm{n}} }{\mathrm{5n}} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184573 Answers: 4 Comments: 2

Question Number 184567 Answers: 1 Comments: 0

Resoudre dans Z^+ (√a) +(√b) =z (a,b,z)∈N^3 a,b ?

$${Resoudre}\:{dans}\:\mathbb{Z}^{+} \\ $$$$\sqrt{{a}}\:\:+\sqrt{{b}}\:={z}\:\:\:\:\left({a},{b},{z}\right)\in\mathbb{N}^{\mathrm{3}} \\ $$$${a},{b}\:? \\ $$

Question Number 184557 Answers: 1 Comments: 1

Determiner 1•AB, BC AC en fonction de r 2• ∡CBA ; ∡BAC ;et ∡BCA

$${Determiner} \\ $$$$\mathrm{1}\bullet\mathrm{AB},\:\:\mathrm{BC}\:\:\mathrm{AC}\:\mathrm{en}\:\mathrm{fonction}\:\mathrm{de}\:\boldsymbol{\mathrm{r}} \\ $$$$\mathrm{2}\bullet\:\:\measuredangle\mathrm{CBA}\:;\:\:\measuredangle\mathrm{BAC}\:;{et}\:\measuredangle\mathrm{BCA} \\ $$

Question Number 184555 Answers: 3 Comments: 6

Suppose that the sum of the square of complex numbers x or y is 7 , and the sum of their cubes is 10. Find the largest true value of the sum x+y that satisfies these conditions. A)4 B)5 C)6 D)7 E)8

$$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of} \\ $$$$\mathrm{complex}\:\mathrm{numbers}\:\:\boldsymbol{\mathrm{x}}\:\mathrm{or}\:\boldsymbol{\mathrm{y}}\:\mathrm{is}\:\mathrm{7}\:,\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{cubes}\:\mathrm{is}\:\mathrm{10}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{largest} \\ $$$$\mathrm{true}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sum}\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\:\:\mathrm{that}\:\mathrm{satisfies} \\ $$$$\mathrm{these}\:\mathrm{conditions}. \\ $$$$\left.\mathrm{A}\left.\right)\left.\mathrm{4}\left.\:\left.\:\:\mathrm{B}\right)\mathrm{5}\:\:\:\mathrm{C}\right)\mathrm{6}\:\:\:\mathrm{D}\right)\mathrm{7}\:\:\:\mathrm{E}\right)\mathrm{8} \\ $$

Question Number 184552 Answers: 2 Comments: 0

I_1 =∫_0 ^∞ (((√(x+(√(x^2 +1))))/( (√(x^2 +1))))−((√2)/( (√x))))dx=? I_2 =∫_0 ^∞ (((√(x^2 +1))/( (√(x+(√(x^2 +1))))))−((√x)/( (√2))))dx=?

$${I}_{\mathrm{1}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}−\frac{\sqrt{\mathrm{2}}}{\:\sqrt{{x}}}\right){dx}=? \\ $$$${I}_{\mathrm{2}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{\:\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}}−\frac{\sqrt{{x}}}{\:\sqrt{\mathrm{2}}}\right){dx}=? \\ $$

Question Number 184551 Answers: 1 Comments: 0

Resoudre dans Z^+ x+y+(√(xy)) =39

$${Resoudre}\:{dans}\:\mathbb{Z}^{+} \\ $$$${x}+{y}+\sqrt{{xy}}\:\:\:\:=\mathrm{39} \\ $$

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