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AlgebraQuestion and Answers: Page 233

Question Number 125670 Answers: 1 Comments: 0

N<10200 , N has five digits. N≡22[23] and N≡5[17]. Determinate the integer N.

$${N}<\mathrm{10200}\:,\:{N}\:{has}\:{five}\:{digits}. \\ $$$${N}\equiv\mathrm{22}\left[\mathrm{23}\right]\:{and}\:{N}\equiv\mathrm{5}\left[\mathrm{17}\right]. \\ $$$${Determinate}\:{the}\:{integer}\:{N}. \\ $$

Question Number 125669 Answers: 1 Comments: 0

we are in C. solve z^5 =1. show that the sum of its solutions is null the deduct that cos(((2π)/5))+cos(((4π)/5))=−(1/2)

$${we}\:{are}\:{in}\:\mathbb{C}. \\ $$$${solve}\:{z}^{\mathrm{5}} =\mathrm{1}. \\ $$$${show}\:{that}\:{the}\:{sum}\:{of}\:{its}\:{solutions}\:{is} \\ $$$${null}\:{the}\:{deduct}\:{that}\:{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right)+{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 125654 Answers: 1 Comments: 1

Question Number 125632 Answers: 1 Comments: 0

Question Number 125577 Answers: 1 Comments: 1

Question Number 125539 Answers: 2 Comments: 1

Question Number 125504 Answers: 1 Comments: 0

n!=2^(10) ∙10!(1∙3∙5∙7∙∙∙19) n=??? help me

$${n}!=\mathrm{2}^{\mathrm{10}} \centerdot\mathrm{10}!\left(\mathrm{1}\centerdot\mathrm{3}\centerdot\mathrm{5}\centerdot\mathrm{7}\centerdot\centerdot\centerdot\mathrm{19}\right)\:\:\:\:\:\:\:\:{n}=??? \\ $$$${help}\:{me} \\ $$

Question Number 125465 Answers: 1 Comments: 0

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Question Number 125442 Answers: 1 Comments: 0

find 2^2^2^2

$${find}\:\mathrm{2}^{\mathrm{2}^{\mathrm{2}^{\mathrm{2}} } } \\ $$

Question Number 125428 Answers: 0 Comments: 1

Question Number 125288 Answers: 1 Comments: 2

Question Number 125262 Answers: 0 Comments: 1

Find GP the matrix permutation where P = ((a,b,c,d),(b,c,a,d) ) and G = ((a,b,c,d),(a,c,d,b) ) explain

$$\mathrm{Find}\:{GP}\:\mathrm{the}\:\mathrm{matrix}\:\mathrm{permutation}\:\mathrm{where} \\ $$$$\:{P}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{b}}&{{c}}&{{a}}&{{d}}\end{pmatrix}\:\mathrm{and}\:{G}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{a}}&{{c}}&{{d}}&{{b}}\end{pmatrix} \\ $$$$\mathrm{explain} \\ $$

Question Number 125258 Answers: 0 Comments: 1

a,b,c => ▲ tomonlari (p−a)(p−b)+(p−c)(p−a)+(p−b)(p−c)≥(√3) S

$${a},{b},{c}\:\:=>\:\:\blacktriangle\:\boldsymbol{{tomonlari}} \\ $$$$\left(\boldsymbol{{p}}−\boldsymbol{{a}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{b}}\right)+\left(\boldsymbol{{p}}−\boldsymbol{{c}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{a}}\right)+\left(\boldsymbol{{p}}−\boldsymbol{{b}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{c}}\right)\geqslant\sqrt{\mathrm{3}}\:\boldsymbol{{S}} \\ $$

Question Number 125226 Answers: 0 Comments: 5

Question Number 125202 Answers: 2 Comments: 0

Solve the reccurence relation a_n = 2(a_(n−1) −a_(n−2) ) ; given a_0 =1 and a_1 = 0.

$$\:{Solve}\:{the}\:{reccurence}\:{relation} \\ $$$${a}_{{n}} \:=\:\mathrm{2}\left({a}_{{n}−\mathrm{1}} −{a}_{{n}−\mathrm{2}} \right)\:;\:{given}\:{a}_{\mathrm{0}} =\mathrm{1}\: \\ $$$${and}\:{a}_{\mathrm{1}} =\:\mathrm{0}. \\ $$

Question Number 125186 Answers: 1 Comments: 0

Question Number 125169 Answers: 0 Comments: 3

algebra

$${algebra} \\ $$

Question Number 125136 Answers: 1 Comments: 3

Suppose a,b,c are nonzero real numbers satisfying (ab+bc+ca)^3 =abc(a+b+c)^3 . Provd that a,b,c must be terms of a Geometric Progession

$${Suppose}\:{a},{b},{c}\:{are}\:{nonzero}\:{real}\:{numbers} \\ $$$${satisfying}\:\left({ab}+{bc}+{ca}\right)^{\mathrm{3}} ={abc}\left({a}+{b}+{c}\right)^{\mathrm{3}} . \\ $$$${Provd}\:{that}\:{a},{b},{c}\:{must}\:{be}\:{terms}\:{of}\:{a}\:{Geometric} \\ $$$${Progession} \\ $$$$ \\ $$

Question Number 125132 Answers: 0 Comments: 0

Find the number of real roots of ax^7 −4x^4 +x^2 +1=0 where a>2

$${Find}\:{the}\:{number}\:{of}\:{real}\:{roots}\:{of}\:{ax}^{\mathrm{7}} −\mathrm{4}{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}=\mathrm{0} \\ $$$${where}\:{a}>\mathrm{2} \\ $$

Question Number 125131 Answers: 0 Comments: 0

Let a,b,c∈ complex numbers such that the roots of the equation ax^2 +bx+c=0 have same modulus Prove that a=0 iff b=0

$${Let}\:{a},{b},{c}\in\:{complex}\:{numbers}\:{such}\:{that}\:{the}\:{roots} \\ $$$${of}\:{the}\:{equation}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}\:{have}\:{same}\:{modulus} \\ $$$${Prove}\:{that}\:{a}=\mathrm{0}\:{iff}\:{b}=\mathrm{0} \\ $$

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Question Number 124963 Answers: 2 Comments: 1

∫_0 ^( (π/4)) ((sin(ς)dς)/(cos(ς)+sin(ς)))dς where ς : zeta

$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin}\left(\varsigma\right)\mathrm{d}\varsigma}{\mathrm{cos}\left(\varsigma\right)+\mathrm{sin}\left(\varsigma\right)}\mathrm{d}\varsigma \\ $$$$\mathrm{where}\:\varsigma\::\:\mathrm{zeta}\: \\ $$

Question Number 124907 Answers: 0 Comments: 0

Question Number 125185 Answers: 1 Comments: 0

{ (((√x) + y = 11)),((x + (√y) = 7 )) :}

$$\:\begin{cases}{\sqrt{{x}}\:+\:{y}\:=\:\mathrm{11}}\\{{x}\:+\:\sqrt{{y}}\:=\:\mathrm{7}\:}\end{cases} \\ $$

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