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Question Number 74742 Answers: 2 Comments: 1

If α and β are the roots of x^2 − x + 1 = 0, Find α^(23) + β^(23) without demoivre′s theorem.

$$\mathrm{If}\:\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{1}\:\:\:=\:\:\mathrm{0},\:\: \\ $$$$\mathrm{Find}\:\:\:\:\:\:\:\:\:\alpha^{\mathrm{23}} \:+\:\beta^{\mathrm{23}} \:\:\:\:\:\mathrm{without}\:\mathrm{demoivre}'\mathrm{s}\:\mathrm{theorem}. \\ $$

Question Number 74723 Answers: 1 Comments: 1

3xy+x^2 +y^2 =5 find the second derivative

$$\mathrm{3}{xy}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{5} \\ $$$${find}\:{the}\:{second}\:{derivative} \\ $$

Question Number 74720 Answers: 2 Comments: 5

Question Number 74716 Answers: 1 Comments: 0

Question Number 74713 Answers: 1 Comments: 1

Question Number 74712 Answers: 0 Comments: 2

Question Number 74711 Answers: 0 Comments: 0

Question Number 74944 Answers: 0 Comments: 0

∫(e^(−cos(2x)) /(sin^2 (x))) dx

$$\int\frac{{e}^{−{cos}\left(\mathrm{2}{x}\right)} }{{sin}^{\mathrm{2}} \left({x}\right)}\:{dx} \\ $$

Question Number 74726 Answers: 1 Comments: 3

Question Number 74703 Answers: 1 Comments: 0

let b and r be two positive prime numbers such that b≠r and b×r is a divisor of 138. Consider an arithmetic progression in which the first term is b, the ratio is r and the fourth term is 71. What is the value of b+r?

$${let}\:\boldsymbol{{b}}\:{and}\:\boldsymbol{{r}}\:{be}\:{two}\:{positive}\:{prime}\: \\ $$$${numbers}\:{such}\:{that}\:{b}\neq{r}\:{and}\:{b}×{r}\:{is} \\ $$$${a}\:{divisor}\:{of}\:\mathrm{138}.\:{Consider}\:{an}\: \\ $$$${arithmetic}\:{progression}\:{in}\:{which} \\ $$$${the}\:{first}\:{term}\:{is}\:\boldsymbol{{b}},\:{the}\:{ratio}\:{is}\:\boldsymbol{{r}} \\ $$$${and}\:{the}\:{fourth}\:{term}\:{is}\:\mathrm{71}.\:{What}\:{is}\:{the} \\ $$$${value}\:{of}\:\boldsymbol{{b}}+\boldsymbol{{r}}? \\ $$

Question Number 74698 Answers: 2 Comments: 1

Question Number 74778 Answers: 0 Comments: 0

Question Number 74688 Answers: 0 Comments: 0

y = f(x) Can we tranform this into a real life problem and solve with several condition.

$$\mathrm{y}\:\:=\:\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\mathrm{Can}\:\mathrm{we}\:\mathrm{tranform}\:\mathrm{this}\:\mathrm{into}\:\mathrm{a}\:\mathrm{real}\:\mathrm{life}\:\mathrm{problem}\:\mathrm{and}\:\mathrm{solve}\:\mathrm{with} \\ $$$$\mathrm{several}\:\mathrm{condition}. \\ $$

Question Number 74675 Answers: 0 Comments: 0

Question Number 74697 Answers: 1 Comments: 0

Question Number 74655 Answers: 1 Comments: 1

$$. \\ $$

Question Number 74663 Answers: 1 Comments: 0

If x^x y^y z^z = c show that at x = y = z (∂^2 z/(∂x∂y)) = − (x log ex)^(−1)

$$\mathrm{If}\:\:\:\:\mathrm{x}^{\mathrm{x}} \:\mathrm{y}^{\mathrm{y}} \:\mathrm{z}^{\mathrm{z}} \:\:\:=\:\:\:\mathrm{c}\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{at}\:\:\:\:\:\mathrm{x}\:\:=\:\:\mathrm{y}\:\:=\:\:\mathrm{z} \\ $$$$\:\:\:\:\:\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}\partial\mathrm{y}}\:\:\:=\:\:\:−\:\left(\mathrm{x}\:\mathrm{log}\:\mathrm{ex}\right)^{−\mathrm{1}} \\ $$

Question Number 74649 Answers: 2 Comments: 1

Question Number 74647 Answers: 0 Comments: 2

Question Number 74639 Answers: 0 Comments: 4

$${If} \\ $$

Question Number 74634 Answers: 0 Comments: 6

Question Number 74632 Answers: 0 Comments: 1

$$. \\ $$

Question Number 74623 Answers: 1 Comments: 1

Question Number 74622 Answers: 0 Comments: 4

Expand 1+(2/3)∙(Σ_(k=1) ^(n−1) [cos(((2π)/3)x)]+2n−2)

$$\mathrm{Expand} \\ $$$$\mathrm{1}+\frac{\mathrm{2}}{\mathrm{3}}\centerdot\left(\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}\left[{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}{x}\right)\right]+\mathrm{2}{n}−\mathrm{2}\right) \\ $$

Question Number 74621 Answers: 1 Comments: 1

Question Number 74620 Answers: 1 Comments: 0

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