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Question Number 198443 Answers: 1 Comments: 0

Proove Σ_(i=1) ^n Σ_(j=1) ^m (xi+yj)=mΣ_(i=1) ^n xi+nΣ_(j=1) ^m yj

$${Proove}\: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\underset{{j}=\mathrm{1}} {\overset{{m}} {\sum}}\left({xi}+{yj}\right)={m}\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{xi}+{n}\underset{{j}=\mathrm{1}} {\overset{{m}} {\sum}}{yj} \\ $$

Question Number 198439 Answers: 0 Comments: 4

Question Number 198435 Answers: 1 Comments: 0

Question Number 198434 Answers: 1 Comments: 1

Question Number 198431 Answers: 2 Comments: 0

f : R → R f (3x − 1) = x + 5 Find: f(x) = ?

$$\mathrm{f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R} \\ $$$$\mathrm{f}\:\left(\mathrm{3x}\:−\:\mathrm{1}\right)\:=\:\mathrm{x}\:+\:\mathrm{5} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$

Question Number 198428 Answers: 0 Comments: 0

Question Number 198427 Answers: 0 Comments: 0

Question Number 198423 Answers: 2 Comments: 0

show that ((1+sin∅)/(cos∅)) =((cos∅)/(1−sin∅)) Pls help

$$\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}+\mathrm{sin}\varnothing}{\mathrm{cos}\varnothing}\:=\frac{\mathrm{cos}\varnothing}{\mathrm{1}−\mathrm{sin}\varnothing} \\ $$$$\mathrm{Pls}\:\mathrm{help} \\ $$$$ \\ $$

Question Number 198421 Answers: 1 Comments: 3

Question Number 198420 Answers: 1 Comments: 0

Question Number 198419 Answers: 0 Comments: 0

Please Help... ∫∫_S x^2 dydz+y^2 dzdx+2z(xy−x−y)dxdy where S is the surface of the cube. 0≤x≤1, 0≤y≤1, 0≤z≤1

$$\:\:{Please}\:{Help}... \\ $$$$\:\:\int\underset{{S}} {\int}{x}^{\mathrm{2}} {dydz}+{y}^{\mathrm{2}} {dzdx}+\mathrm{2}{z}\left({xy}−{x}−{y}\right){dxdy}\:{where} \\ $$$$\:\:\:{S}\:{is}\:{the}\:{surface}\:{of}\:{the}\:{cube}.\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1},\:\mathrm{0}\leqslant{y}\leqslant\mathrm{1}, \\ $$$$\:\:\:\:\mathrm{0}\leqslant{z}\leqslant\mathrm{1} \\ $$$$ \\ $$

Question Number 198418 Answers: 1 Comments: 0

20^(22) −1 = ... (mod 1000)

$$\:\mathrm{20}^{\mathrm{22}} −\mathrm{1}\:=\:...\:\left(\mathrm{mod}\:\mathrm{1000}\right) \\ $$$$ \\ $$

Question Number 198414 Answers: 0 Comments: 0

(3/8)(3h−p)^2 +3ph=(3h^2 −1) and (((3h−p)^3 )/(16))+p(3h^2 −1)=h^3 −h−c Find p and h in terms of 0<c<(2/(3(√3)))∙

$$\frac{\mathrm{3}}{\mathrm{8}}\left(\mathrm{3}{h}−{p}\right)^{\mathrm{2}} +\mathrm{3}{ph}=\left(\mathrm{3}{h}^{\mathrm{2}} −\mathrm{1}\right) \\ $$$${and} \\ $$$$\frac{\left(\mathrm{3}{h}−{p}\right)^{\mathrm{3}} }{\mathrm{16}}+{p}\left(\mathrm{3}{h}^{\mathrm{2}} −\mathrm{1}\right)={h}^{\mathrm{3}} −{h}−{c} \\ $$$${Find}\:\:{p}\:{and}\:{h}\:\:{in}\:{terms}\:{of}\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\centerdot \\ $$

Question Number 198413 Answers: 1 Comments: 1

Question Number 198403 Answers: 1 Comments: 0

Question Number 198400 Answers: 3 Comments: 0

20^(11) −1 = ...(mod 1000)

$$\:\:\mathrm{20}^{\mathrm{11}} −\mathrm{1}\:=\:...\left(\mathrm{mod}\:\mathrm{1000}\right) \\ $$

Question Number 198395 Answers: 0 Comments: 4

Question Number 198391 Answers: 2 Comments: 1

Question Number 198426 Answers: 0 Comments: 0

Question Number 198380 Answers: 0 Comments: 2

Question Number 198377 Answers: 1 Comments: 0

Question Number 198373 Answers: 0 Comments: 0

Question Number 198372 Answers: 1 Comments: 1

(1/(1×5)) + (1/(4×8)) + (1/(7×11)) +(1/(10×14)) + …=?

$$\:\:\:\frac{\mathrm{1}}{\mathrm{1}×\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{4}×\mathrm{8}}\:+\:\frac{\mathrm{1}}{\mathrm{7}×\mathrm{11}}\:+\frac{\mathrm{1}}{\mathrm{10}×\mathrm{14}}\:+\:\ldots=? \\ $$

Question Number 198367 Answers: 0 Comments: 7

if f(x) = ((x^2 −(b+1)x+b)/(x^2 −(a+1)x+a)) (a≠b & a,b ∈ R ∼ {1}) can take all values except two values α & β such that α+β = 0 then ∣((a^3 +b^3 −8)/(ab))∣ = ??

$$\:\:\mathrm{if}\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{{x}^{\mathrm{2}} −\left({b}+\mathrm{1}\right){x}+{b}}{{x}^{\mathrm{2}} −\left({a}+\mathrm{1}\right){x}+{a}}\:\:\left({a}\neq{b}\:\&\:{a},{b}\:\in\:\mathbb{R}\:\sim\:\left\{\mathrm{1}\right\}\right) \\ $$$$\:\:\mathrm{can}\:\mathrm{take}\:\mathrm{all}\:\mathrm{values}\:\mathrm{except}\:\mathrm{two}\:\mathrm{values}\:\alpha\:\&\:\beta \\ $$$$\:\:\mathrm{such}\:\mathrm{that}\:\alpha+\beta\:=\:\mathrm{0}\:\:\mathrm{then}\:\mid\frac{\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} −\mathrm{8}}{\mathrm{ab}}\mid\:\:=\:\:?? \\ $$

Question Number 198363 Answers: 2 Comments: 0

Question Number 198357 Answers: 0 Comments: 0

let a∈R, z∈C resolve (z+1)^n =e^(iπna) deduce that P_n =Π_(k=0) ^(n−1) sin(a+((kπ)/n))

$$\boldsymbol{{let}}\:\:\boldsymbol{{a}}\in\mathbb{R},\:\boldsymbol{{z}}\in\mathbb{C} \\ $$$$\boldsymbol{{resolve}}\: \\ $$$$\left(\boldsymbol{{z}}+\mathrm{1}\right)^{\boldsymbol{{n}}} =\boldsymbol{{e}}^{\boldsymbol{{i}}\pi\boldsymbol{{na}}} \\ $$$$\boldsymbol{{deduce}}\:\boldsymbol{{that}}\:\boldsymbol{{P}}_{\boldsymbol{{n}}} =\underset{{k}=\mathrm{0}} {\overset{\boldsymbol{{n}}−\mathrm{1}} {\prod}}\boldsymbol{{sin}}\left(\boldsymbol{{a}}+\frac{\boldsymbol{{k}}\pi}{\boldsymbol{{n}}}\right) \\ $$

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