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Question Number 171314    Answers: 1   Comments: 0

If C_r , C_s are cyclic groups such that g.c.d(r,s)=1, then show that C_r ×C_s is a cyclic group. Mastermind

$${If}\:{C}_{{r}} ,\:{C}_{{s}} \:{are}\:{cyclic}\:{groups}\:{such}\:{that} \\ $$$${g}.{c}.{d}\left({r},{s}\right)=\mathrm{1},\:{then}\:{show}\:{that}\:{C}_{{r}} ×{C}_{{s}} \:{is} \\ $$$${a}\:{cyclic}\:{group}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171312    Answers: 0   Comments: 4

Question Number 171311    Answers: 0   Comments: 0

2^x^(−i^2 ) +2^x^2 =2^(x^3 −i^2 ) x=?

$$\mathrm{2}^{{x}^{−{i}^{\mathrm{2}} } } +\mathrm{2}^{{x}^{\mathrm{2}} } =\mathrm{2}^{{x}^{\mathrm{3}} −{i}^{\mathrm{2}} } \\ $$$${x}=? \\ $$

Question Number 171318    Answers: 1   Comments: 1

if f(x)=x^((13)/5) and g(x)=(x^(13) )^(1/5) Which one is correct? 1) f(x)=g(x) 2)f(x)≠g(x)

$${if}\:{f}\left({x}\right)={x}^{\frac{\mathrm{13}}{\mathrm{5}}} \:{and}\:{g}\left({x}\right)=\sqrt[{\mathrm{5}}]{{x}^{\mathrm{13}} }\: \\ $$$${Which}\:{one}\:{is}\:{correct}? \\ $$$$\left.\mathrm{1}\left.\right)\:{f}\left({x}\right)={g}\left({x}\right)\:\:\:\:\mathrm{2}\right){f}\left({x}\right)\neq{g}\left({x}\right) \\ $$

Question Number 171307    Answers: 1   Comments: 1

Simplify Σ_(k=0) ^(n−1) 3^k 2^(n−k)

$$\mathrm{Simplify} \\ $$$$\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\mathrm{3}^{{k}} \mathrm{2}^{{n}−{k}} \\ $$

Question Number 171301    Answers: 0   Comments: 1

∫_1 ^2 6x^2 −2x+3

$$\int_{\mathrm{1}} ^{\mathrm{2}} \mathrm{6}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3} \\ $$

Question Number 171296    Answers: 0   Comments: 1

Question Number 176853    Answers: 2   Comments: 0

Question Number 171289    Answers: 1   Comments: 0

(x,y)∈R x^2 −xy−12y^2 =0 ((2x^2 +4y^2 )/(xy))=?

$$\left({x},{y}\right)\in{R}\:\:\:{x}^{\mathrm{2}} −{xy}−\mathrm{12}{y}^{\mathrm{2}} =\mathrm{0} \\ $$$$\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} }{{xy}}=? \\ $$

Question Number 171284    Answers: 2   Comments: 0

g(x)=−x^2 +1−ln∣x∣ Study the variations of the function g and draw up its table of variations

$${g}\left({x}\right)=−{x}^{\mathrm{2}} +\mathrm{1}−{ln}\mid{x}\mid \\ $$Study the variations of the function g and draw up its table of variations

Question Number 171281    Answers: 0   Comments: 0

Question Number 171283    Answers: 0   Comments: 2

Question Number 171267    Answers: 0   Comments: 2

Find the coordinates of the point on the curve y=(x/(1+x)) at which the tangents to the curve are parallel to the line x−y+8=0. Find the equations of the tangents at these points.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{coordinates}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\mathrm{y}=\frac{{x}}{\mathrm{1}+{x}}\:\mathrm{at}\:\mathrm{which}\:\mathrm{the}\:\mathrm{tangents}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\mathrm{are}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{line}\:{x}−{y}+\mathrm{8}=\mathrm{0}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangents}\:\mathrm{at} \\ $$$$\mathrm{these}\:\mathrm{points}. \\ $$

Question Number 171265    Answers: 0   Comments: 0

find the drivative of f(x,y,z)=cos(xy)+e^(zy) +ln(zy) at point (1,0,(1/2)) in the direction v=i+2j+2k

$${find}\:{the}\:{drivative}\:{of}\: \\ $$$${f}\left({x},{y},{z}\right)={cos}\left({xy}\right)+{e}^{{zy}} +{ln}\left({zy}\right) \\ $$$${at}\:{point}\:\left(\mathrm{1},\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right)\:{in}\:{the}\:{direction} \\ $$$${v}={i}+\mathrm{2}{j}+\mathrm{2}{k} \\ $$

Question Number 171260    Answers: 1   Comments: 0

Change to polar coordinates: ∫^( 4a) _0 ∫_(y^2 /4a) ^a (((x^2 −y^2 )/(x^2 +y^2 ))) dx dy

$$\underline{{Change}\:{to}\:{polar}\:{coordinates}:} \\ $$$$\underset{\mathrm{0}} {\int}^{\:\:\mathrm{4}{a}} \underset{{y}^{\mathrm{2}} /\mathrm{4}{a}} {\int}\overset{{a}} {\:}\:\:\left(\frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right)\:{dx}\:{dy} \\ $$

Question Number 171255    Answers: 1   Comments: 2

Question Number 171253    Answers: 2   Comments: 0

Question Number 171247    Answers: 2   Comments: 0

lim_(x→2) ((x^2 −4)/(x−2))=...

$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} −\mathrm{4}}{{x}−\mathrm{2}}=... \\ $$

Question Number 171244    Answers: 2   Comments: 3

(x/y)+(y/x)=((26)/5) ((x+y)/(x−y))=? (/)

$$\frac{{x}}{{y}}+\frac{{y}}{{x}}=\frac{\mathrm{26}}{\mathrm{5}} \\ $$$$\frac{{x}+{y}}{{x}−{y}}=? \\ $$$$\frac{}{} \\ $$

Question Number 171243    Answers: 1   Comments: 3

Question Number 171237    Answers: 0   Comments: 2

Question Number 171235    Answers: 1   Comments: 2

Question Number 171229    Answers: 0   Comments: 1

Question Number 171226    Answers: 0   Comments: 4

Possible number of order pairs satisfy 16^(x^2 +y) +16^(y^2 +x) =1 is

$${Possible}\:{number}\:{of}\:{order}\:{pairs} \\ $$$${satisfy}\:\mathrm{16}^{{x}^{\mathrm{2}} +{y}} +\mathrm{16}^{{y}^{\mathrm{2}} +{x}} =\mathrm{1}\:{is} \\ $$

Question Number 171223    Answers: 0   Comments: 0

In how many ways can you select 4 from 40 persons if every two persons may be selected together at most one time?

$${In}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{select}\:\mathrm{4} \\ $$$${from}\:\mathrm{40}\:{persons}\:{if}\:{every}\:{two}\:{persons} \\ $$$${may}\:{be}\:{selected}\:{together}\:{at}\:{most}\:{one}\: \\ $$$${time}? \\ $$

Question Number 171221    Answers: 0   Comments: 0

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