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Question Number 188881 Answers: 1 Comments: 0

Q : the non−zero vector a^→ = (a_1 , a_( 2) , a_( 3) ) with the coordinate axes makes the angles , α , β and γ . prove that the following equality. cos^( 2) (α ) +cos^( 2) (β )+ cos^( 2) ( γ )= 1

$$ \\ $$$$\:\:\:\:\mathrm{Q}\::\:\:\mathrm{the}\:\mathrm{non}−\mathrm{zero}\:\mathrm{vector}\:\overset{\rightarrow} {{a}}\:=\:\left({a}_{\mathrm{1}} \:,\:{a}_{\:\mathrm{2}} \:,\:{a}_{\:\mathrm{3}} \:\right)\:\mathrm{with} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{the}\:\:\mathrm{coordinate}\:\mathrm{axes}\:\mathrm{makes}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{angles}\:\:,\:\:\alpha\:\:\:,\:\:\beta\:\:\mathrm{and}\:\:\:\gamma\:.\:\:\mathrm{prove} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{that}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{equality}. \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{cos}^{\:\mathrm{2}} \:\left(\alpha\:\right)\:+\mathrm{cos}^{\:\mathrm{2}} \:\left(\beta\:\:\right)+\:\mathrm{cos}^{\:\mathrm{2}} \:\left(\:\gamma\:\right)=\:\mathrm{1} \\ $$$$ \\ $$$$ \\ $$

Question Number 188879 Answers: 2 Comments: 3

Find the sum of all three digit numbers started with odd number when each digit are different. Please help...

$${Find}\:{the}\:{sum}\:{of}\:{all}\:{three}\:{digit}\:{numbers} \\ $$$${started}\:{with}\:{odd}\:{number}\:{when}\:{each}\:{digit} \\ $$$${are}\:{different}. \\ $$$$ \\ $$$${Please}\:{help}... \\ $$

Question Number 188861 Answers: 2 Comments: 0

Question Number 188860 Answers: 0 Comments: 0

Question Number 188864 Answers: 0 Comments: 0

Question Number 188845 Answers: 3 Comments: 0

Question Number 188834 Answers: 0 Comments: 8

does the multinomial name a polynomial?

$${does}\:{the}\:{multinomial}\:{name}\:{a}\:{polynomial}? \\ $$

Question Number 188826 Answers: 0 Comments: 1

prove that lim_(n→∞) (((1! 2! 3!∙∙∙∙∙n!))^(1/(n(n+1))) /( (√n)))=e^((−3)/4)

$${prove}\:{that} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt[{{n}\left({n}+\mathrm{1}\right)}]{\mathrm{1}!\:\mathrm{2}!\:\mathrm{3}!\centerdot\centerdot\centerdot\centerdot\centerdot{n}!}}{\:\sqrt{{n}}}={e}^{\frac{−\mathrm{3}}{\mathrm{4}}} \\ $$

Question Number 188821 Answers: 0 Comments: 0

Question Number 188819 Answers: 2 Comments: 1

calculate lim_( x→ 0^( +) ) ( (√( cos ( (√x) ))) )^( cot( x )) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{calculate}\: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{lim}_{\:{x}\rightarrow\:\mathrm{0}^{\:+} } \left(\:\sqrt{\:\mathrm{cos}\:\left(\:\sqrt{{x}}\:\right)}\:\right)^{\:\mathrm{cot}\left(\:{x}\:\right)} \:=\:?\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$

Question Number 188806 Answers: 2 Comments: 0

Find minimum value of 2x^2 +2xy+4y+5y^2 −x for x and y real numbers

$${Find}\:{minimum}\:{value}\:{of}\: \\ $$$$\:\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{xy}+\mathrm{4}{y}+\mathrm{5}{y}^{\mathrm{2}} −{x}\: \\ $$$$\:{for}\:{x}\:{and}\:{y}\:{real}\:{numbers} \\ $$

Question Number 188798 Answers: 1 Comments: 0

Question Number 188796 Answers: 1 Comments: 1

Question Number 188808 Answers: 0 Comments: 2

how is solution 72.5gr of the [C_3 H_6 O] how many Molecule of [H] exist?

$${how}\:{is}\:{solution} \\ $$$$\mathrm{72}.\mathrm{5}{gr}\:\:\:{of}\:{the}\:\left[{C}_{\mathrm{3}} {H}_{\mathrm{6}} {O}\right]\:{how}\:{many}\:\mathrm{Molecule}\:{of}\:\left[{H}\right]\:{exist}? \\ $$

Question Number 188786 Answers: 1 Comments: 1

Question Number 188776 Answers: 3 Comments: 1

Prove that n^2 +3n+2 is divisible by 2 for any n∈Z

$$\mathrm{Prove}\:\mathrm{that}\:{n}^{\mathrm{2}} +\mathrm{3}{n}+\mathrm{2}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{2} \\ $$$$\mathrm{for}\:\mathrm{any}\:{n}\in\mathbb{Z} \\ $$

Question Number 188774 Answers: 1 Comments: 0

Question Number 188775 Answers: 1 Comments: 0

how is solution 72.5gr of the [C_3 H_6 O] how many Molecule of [H] exist?

Question Number 188771 Answers: 0 Comments: 1

Question Number 188761 Answers: 0 Comments: 1

How we can use the polynomial in daily life? please tell me an example!

$${How}\:{we}\:{can}\:{use}\:{the}\:{polynomial}\:{in}\: \\ $$$${daily}\:{life}?\:{please}\:{tell}\:{me}\:{an}\:{example}! \\ $$

Question Number 188759 Answers: 3 Comments: 0

Question Number 188758 Answers: 3 Comments: 0

the sum of the first three terms of an AP is 21 and the sum of the first five terms is 55. find. (1) the first term (2) common difference (3) the sum of the first ten term of the sequence

$${the}\:{sum}\:{of}\:{the}\:\:{first}\:{three}\:{terms} \\ $$$${of}\:{an}\:{AP}\:{is}\:\mathrm{21}\:{and}\:\:{the}\:{sum}\:{of}\:{the} \\ $$$${first}\:\:{five}\:{terms}\:{is}\:\mathrm{55}.\:{find}. \\ $$$$\left(\mathrm{1}\right)\:{the}\:{first}\:{term} \\ $$$$\left(\mathrm{2}\right)\:{common}\:{difference} \\ $$$$\left(\mathrm{3}\right)\:{the}\:{sum}\:{of}\:{the}\:{first}\:{ten}\:{term} \\ $$$${of}\:{the}\:\:{sequence} \\ $$$$ \\ $$

Question Number 188755 Answers: 0 Comments: 2

Question Number 188753 Answers: 1 Comments: 0

x^2 − y^2 = 2023 x, y ∈ N How many pair of (x, y)

$$\:{x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:=\:\mathrm{2023}\:\:\:\:\:\:\:\:\:{x},\:{y}\:\in\:\mathrm{N} \\ $$$$\:\mathrm{H}{ow}\:{many}\:{pair}\:{of}\:\left({x},\:{y}\right) \\ $$

Question Number 188752 Answers: 1 Comments: 1

Question Number 188730 Answers: 2 Comments: 2

let p(x) = (5/3)−6x−9x^2 and Q(y) = −4y^2 −4y+((13)/2) if there exist unique pair of real number (x,y) such that p(x)×Q(y) = 20 then find the value 6x+10y = ?

$$\:\:\mathrm{let}\:{p}\left({x}\right)\:=\:\frac{\mathrm{5}}{\mathrm{3}}−\mathrm{6}{x}−\mathrm{9}{x}^{\mathrm{2}} \:\mathrm{and}\:{Q}\left({y}\right)\:=\:−\mathrm{4}{y}^{\mathrm{2}} −\mathrm{4}{y}+\frac{\mathrm{13}}{\mathrm{2}} \\ $$$$\mathrm{if}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{unique}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{real}\:\mathrm{number} \\ $$$$\:\left({x},{y}\right)\:\mathrm{such}\:\mathrm{that}\:{p}\left({x}\right)×{Q}\left({y}\right)\:=\:\mathrm{20}\:\mathrm{then} \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{6}{x}+\mathrm{10}{y}\:=\:? \\ $$

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