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Question Number 178282 Answers: 2 Comments: 0

find unit digit of 1^1 +2^2 +3^3 +.......+63^(63) +64^(64)

$$ \\ $$$${find}\:{unit}\:{digit}\:{of}\: \\ $$$$\mathrm{1}^{\mathrm{1}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} +.......+\mathrm{63}^{\mathrm{63}} +\mathrm{64}^{\mathrm{64}} \\ $$

Question Number 178277 Answers: 0 Comments: 0

if 2^(pq) −2^(rs) =32; where p,q,r,s∈Z then possible values of p + q + r + s = ??

$$ \\ $$$${if}\:\mathrm{2}^{{pq}} −\mathrm{2}^{{rs}} =\mathrm{32};\:{where}\:{p},{q},{r},{s}\in\mathbb{Z}\: \\ $$$${then}\:{possible}\:{values}\:{of} \\ $$$${p}\:+\:{q}\:+\:{r}\:+\:{s}\:=\:?? \\ $$$$ \\ $$

Question Number 178254 Answers: 3 Comments: 0

Calcul 1−Σ_(n=1) ^(+∝) (2/(4n^2 −1)) 2−Σ_(n=1) ^(+∝) (n^2 /(n!)) 3− Σ_(n=1) ^(+∝) (n^3 /(n!)) 4− Σ_(n=1) ^(+∝) ln((n/(n−1)))

$${Calcul} \\ $$$$\mathrm{1}−\underset{{n}=\mathrm{1}} {\overset{+\propto} {\sum}}\frac{\mathrm{2}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\mathrm{2}−\underset{{n}=\mathrm{1}} {\overset{+\propto} {\sum}}\frac{{n}^{\mathrm{2}} }{{n}!} \\ $$$$\mathrm{3}−\:\underset{{n}=\mathrm{1}} {\overset{+\propto} {\sum}}\frac{{n}^{\mathrm{3}} }{{n}!} \\ $$$$\mathrm{4}−\:\underset{{n}=\mathrm{1}} {\overset{+\propto} {\sum}}{ln}\left(\frac{{n}}{{n}−\mathrm{1}}\right) \\ $$

Question Number 178251 Answers: 3 Comments: 0

solve (x^2 −5)^2 −x=5

$${solve} \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{5}\right)^{\mathrm{2}} −{x}=\mathrm{5} \\ $$

Question Number 178250 Answers: 2 Comments: 0

how is the solution of this qustion f(x)=x(x−1)(x−2)(x−3)(x−4)∙.......∙(x−100) f^′ (x)=? f′(1)=?

$${how}\:{is}\:{the}\:{solution}\:{of}\:{this}\:{qustion} \\ $$$${f}\left({x}\right)={x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)\left({x}−\mathrm{4}\right)\centerdot.......\centerdot\left({x}−\mathrm{100}\right) \\ $$$${f}^{'} \left({x}\right)=?\:\:\:\:\:\:\:\:\:\:{f}'\left(\mathrm{1}\right)=? \\ $$$$\:\: \\ $$

Question Number 178246 Answers: 1 Comments: 0

Question Number 178240 Answers: 1 Comments: 0

((a^(n+1) + b^(n+1) )/(a^n + b^n )) = (√(ab)) find n=?

$$\frac{\mathrm{a}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:+\:\mathrm{b}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} }{\mathrm{a}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{b}^{\boldsymbol{\mathrm{n}}} }\:=\:\sqrt{\mathrm{ab}}\:\:\:\mathrm{find}\:\:\:\mathrm{n}=? \\ $$

Question Number 178223 Answers: 2 Comments: 0

Question Number 178219 Answers: 2 Comments: 2

How many different words of 4 letters can be formed from the word Flat earth

$${How}\:{many}\:{different}\:{words}\:{of}\:\mathrm{4}\:{letters}\:{can} \\ $$$$\:{be}\:{formed}\:{from}\:{the}\:{word}\:\boldsymbol{{Flat}}\:\boldsymbol{{earth}} \\ $$$$ \\ $$

Question Number 178216 Answers: 0 Comments: 6

So why is it not possible to copy several lines at once?

$${So}\:{why}\:{is}\:{it}\:{not}\:{possible}\:{to}\:\boldsymbol{{copy}}\:\boldsymbol{{several}}\:\boldsymbol{{lines}} \\ $$$$\:{at}\:{once}?\: \\ $$

Question Number 178213 Answers: 1 Comments: 1

Let S= {1, 2, 3, 4, ..., 28, 29, 30} How many subgroups of 3 elements are in the S so that their sum is a multiple of 3 The answer is 1 360 subgroups

$${Let}\:{S}=\:\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:...,\:\mathrm{28},\:\mathrm{29},\:\mathrm{30}\right\} \\ $$$$\:{How}\:{many}\:{subgroups}\:{of}\:\mathrm{3}\:{elements}\:{are}\:{in}\:{the}\:{S} \\ $$$$\:\:{so}\:{that}\:{their}\:{sum}\:{is}\:{a}\:{multiple}\:{of}\:\mathrm{3} \\ $$$$ \\ $$$$\:{The}\:{answer}\:{is}\:\mathrm{1}\:\mathrm{360}\:{subgroup}\mathrm{s} \\ $$$$ \\ $$

Question Number 178204 Answers: 0 Comments: 8

Following up on comments is hard! isn′t it supposed to receive notifications to make it easy to follow up on friends′comments?

$$\:{Following}\:{up}\:{on}\:{comments}\:{is}\:{hard}! \\ $$$$\:{isn}'{t}\:{it}\:{supposed}\:{to}\:{receive}\:\boldsymbol{{notifications}}\:{to}\:{make} \\ $$$$\:{it}\:{easy}\:{to}\:{follow}\:{up}\:{on}\:{friends}'{comments}? \\ $$$$ \\ $$

Question Number 178200 Answers: 1 Comments: 0

Question Number 178182 Answers: 0 Comments: 2

(1/(cos80))−((√3)/(sin80))=?

$$\frac{\mathrm{1}}{{cos}\mathrm{80}}−\frac{\sqrt{\mathrm{3}}}{{sin}\mathrm{80}}=? \\ $$

Question Number 178181 Answers: 2 Comments: 1

((cosα cotα−sinα tanα)/(cscα secα))=?

$$\frac{{cos}\alpha\:{cot}\alpha−{sin}\alpha\:{tan}\alpha}{{csc}\alpha\:{sec}\alpha}=? \\ $$

Question Number 178180 Answers: 2 Comments: 1

x+(1/x)=−1 x^(1377) =?

$${x}+\frac{\mathrm{1}}{{x}}=−\mathrm{1}\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{1377}} =? \\ $$

Question Number 178178 Answers: 1 Comments: 0

Question Number 178173 Answers: 2 Comments: 0

Question Number 178166 Answers: 1 Comments: 0

8.5g of hydrated copper (ii) sulphate CuSO_4 .xH_2 O was heated to dryness.if 4.0g of anhydrous copper (ii) sulphate[CuSO_4 ] obtain Find number of molecule of water of crystallization

$$\mathrm{8}.\mathrm{5g}\:\mathrm{of}\:\mathrm{hydrated}\:\mathrm{copper}\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{sulphate}\:\mathrm{CuSO}_{\mathrm{4}} .\mathrm{xH}_{\mathrm{2}} \mathrm{O}\:\mathrm{was}\:\mathrm{heated} \\ $$$$\mathrm{to}\:\mathrm{dryness}.\mathrm{if}\:\:\mathrm{4}.\mathrm{0g}\:\mathrm{of}\:\mathrm{anhydrous} \\ $$$$\mathrm{copper}\:\left(\mathrm{ii}\right)\:\mathrm{sulphate}\left[\mathrm{CuSO}_{\mathrm{4}} \right]\:\mathrm{obtain} \\ $$$$\mathrm{Find}\:\mathrm{number}\:\mathrm{of}\:\mathrm{molecule}\:\mathrm{of}\:\mathrm{water}\:\mathrm{of} \\ $$$$\mathrm{crystallization} \\ $$

Question Number 178165 Answers: 2 Comments: 0

2.86g of hydrated Sodium carbonate Na_2 CO_3 .nH_2 O was dissolved into water to make 250cm^3 solution of 0.04M Find the value of n

$$\mathrm{2}.\mathrm{86g}\:\mathrm{of}\:\mathrm{hydrated}\:\mathrm{Sodium}\:\mathrm{carbonate} \\ $$$$\boldsymbol{\mathrm{Na}}_{\mathrm{2}} \boldsymbol{\mathrm{CO}}_{\mathrm{3}} .\boldsymbol{\mathrm{nH}}_{\mathrm{2}} \boldsymbol{\mathrm{O}}\:\mathrm{was}\:\mathrm{dissolved} \\ $$$$\mathrm{into}\:\mathrm{water}\:\mathrm{to}\:\mathrm{make}\:\mathrm{250cm}^{\mathrm{3}} \:\mathrm{solution} \\ $$$$\mathrm{of}\:\:\mathrm{0}.\mathrm{04M}\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n} \\ $$

Question Number 178161 Answers: 3 Comments: 1

Question Number 178153 Answers: 1 Comments: 0

Question Number 178152 Answers: 0 Comments: 0

Question Number 178137 Answers: 1 Comments: 2

Let f(x)= (ax+1)^5 .(1+bx)^4 ; a,b ∈ N if times of x equal 62 so what are possible values of the sum a, b?

$${Let}\:{f}\left({x}\right)=\:\left({ax}+\mathrm{1}\right)^{\mathrm{5}} .\left(\mathrm{1}+{bx}\right)^{\mathrm{4}} \:;\:{a},{b}\:\in\:\mathbb{N} \\ $$$$\:{if}\:{times}\:{of}\:{x}\:{equal}\:\mathrm{62}\:{so}\:{what}\:{are}\:{possible}\:{values} \\ $$$$\:{of}\:{the}\:{sum}\:{a},\:{b}? \\ $$$$ \\ $$

Question Number 178136 Answers: 0 Comments: 0

Journey inside a regular hexagon The operation is to connect three dots of a regular hexagon′s heads. 1• How many types of geometric shapes will we get? 2• How many each type?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{Journey}}\:\boldsymbol{{inside}}\:\boldsymbol{{a}}\:\boldsymbol{{regular}}\:\boldsymbol{{hexagon}} \\ $$$$\:{The}\:{operation}\:{is}\:{to}\:{connect}\:{three}\:{dots}\:{of} \\ $$$$\:{a}\:{regular}\:{hexagon}'{s}\:{heads}. \\ $$$$\mathrm{1}\bullet\:{How}\:{many}\:{types}\:{of}\:{geometric}\:{shapes}\:{will}\:{we}\:{get}? \\ $$$$\mathrm{2}\bullet\:{How}\:{many}\:{each}\:{type}? \\ $$$$ \\ $$

Question Number 178134 Answers: 0 Comments: 8

Am not a friend with this isssue: 6 red, 1 black and 3 white balls We draw 3 balls in a raw, returning the drawn ball each time. How many different results which include at least one black ball. Way_1 : 1000−9^3 = 271 results That′s very ok Way_2 : 1×9×9_(very ok) ×3_(Omg, Why?) + 1×1×9×3_(the same confused above) + 1×1×1_(very ok and i like it.... but why not ×3) = 271 result Explanation_(about the story of ×3) ?

$${Am}\:{not}\:{a}\:{friend}\:{with}\:{this}\:{isssue}: \\ $$$$\mathrm{6}\:{red},\:\mathrm{1}\:{black}\:{and}\:\mathrm{3}\:{white}\:{balls} \\ $$$${We}\:{draw}\:\mathrm{3}\:{balls}\:{in}\:{a}\:{raw},\:{returning}\:{the} \\ $$$$\:{drawn}\:{ball}\:{each}\:{time}. \\ $$$${How}\:{many}\:{different}\:{results}\:{which}\:{include} \\ $$$$\:\boldsymbol{{at}}\:\boldsymbol{{least}}\:{one}\:{black}\:{ball}. \\ $$$$ \\ $$$$\:{Way}_{\mathrm{1}} :\:\mathrm{1000}−\mathrm{9}^{\mathrm{3}} =\:\mathrm{271}\:{results}\:{That}'{s}\:{very}\:{ok} \\ $$$$ \\ $$$$\:{Way}_{\mathrm{2}} :\:\mathrm{1}×\mathrm{9}×\mathrm{9}_{{very}\:{ok}} ×\mathrm{3}_{\boldsymbol{{Omg}},\:\boldsymbol{{Why}}?} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\:\mathrm{1}×\mathrm{1}×\mathrm{9}×\mathrm{3}_{{the}\:{same}\:{confused}\:{above}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\:\mathrm{1}×\mathrm{1}×\mathrm{1}_{{very}\:{ok}\:{and}\:{i}\:{like}\:{it}....\:{but}\:{why}\:{not}\:×\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{271}\:{result} \\ $$$$ \\ $$$$\:{Explanation}_{{about}\:{the}\:{story}\:{of}\:×\mathrm{3}} ? \\ $$$$ \\ $$

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