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Question Number 57074 Answers: 1 Comments: 0

Solve the system. ^x C_(y + 1) = 20, ^(x − 1) C_y = 10

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}. \\ $$$$\:\:\:\:\:\:\overset{\mathrm{x}} {\:}\mathrm{C}_{\mathrm{y}\:+\:\mathrm{1}} \:\:=\:\:\mathrm{20},\:\:\:\:\:\:\:\:\:\:\:\overset{\mathrm{x}\:−\:\mathrm{1}} {\:}\mathrm{C}_{\mathrm{y}} \:\:=\:\:\mathrm{10} \\ $$

Question Number 57073 Answers: 0 Comments: 2

f(x)=A f : [0, ∞) g : [1, 0] g(x)=B lim_(n→∞) (1/n)∫_0 ^n f(x)g((x/n))dx=...

$${f}\left({x}\right)={A} \\ $$$${f}\::\:\left[\mathrm{0},\:\infty\right)\: \\ $$$${g}\::\:\left[\mathrm{1},\:\mathrm{0}\right] \\ $$$${g}\left({x}\right)={B} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{{n}}\int_{\mathrm{0}} ^{{n}} {f}\left({x}\right){g}\left(\frac{{x}}{{n}}\right){dx}=... \\ $$

Question Number 57071 Answers: 1 Comments: 1

Question Number 57062 Answers: 2 Comments: 2

find the sum of all three digital natural numbers that are divisible by 7

$${find}\:{the}\:{sum}\:{of}\:{all} \\ $$$${three}\:{digital}\:{natural} \\ $$$${numbers}\:{that}\:{are}\: \\ $$$${divisible}\:{by}\:\mathrm{7} \\ $$

Question Number 57060 Answers: 0 Comments: 0

Question Number 57051 Answers: 0 Comments: 5

F_n = ((ϕ^n − (1 − ϕ)^n )/(√5)) , with { ((ϕ = ((1 + (√5))/2))) :} (G_n ) : { ((G_1 = 1)),((G_2 = 1)),((G_m = G_(m−1) + G_(m−2) )) :} Give a proof for F_n = G_n , ∀n∈N^∗ . Thank you

$$ \\ $$$$\:\:\boldsymbol{{F}}_{\boldsymbol{{n}}} \:=\:\frac{\varphi^{{n}} \:−\:\left(\mathrm{1}\:−\:\varphi\right)^{{n}} }{\sqrt{\mathrm{5}}}\:,\:\:\mathrm{with}\:\begin{cases}{\varphi\:=\:\frac{\mathrm{1}\:+\:\sqrt{\mathrm{5}}}{\mathrm{2}}}\end{cases} \\ $$$$ \\ $$$$\:\:\left(\boldsymbol{{G}}_{\boldsymbol{{n}}} \right)\::\:\begin{cases}{\boldsymbol{{G}}_{\mathrm{1}} \:=\:\mathrm{1}}\\{\boldsymbol{{G}}_{\mathrm{2}} \:=\:\mathrm{1}}\\{\boldsymbol{{G}}_{{m}} \:=\:\boldsymbol{{G}}_{\mathrm{m}−\mathrm{1}} \:+\:\boldsymbol{{G}}_{{m}−\mathrm{2}} }\end{cases} \\ $$$$ \\ $$$$\:\:\mathrm{Give}\:\mathrm{a}\:\mathrm{proof}\:\mathrm{for}\:\boldsymbol{{F}}_{\boldsymbol{{n}}} \:=\:\boldsymbol{{G}}_{\boldsymbol{{n}}} \:,\:\forall{n}\in\mathbb{N}^{\ast} .\: \\ $$$$\:\:\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 57048 Answers: 2 Comments: 1

Question Number 57046 Answers: 0 Comments: 1

Question Number 57044 Answers: 1 Comments: 1

Question Number 57042 Answers: 1 Comments: 1

Question Number 57024 Answers: 0 Comments: 1

If f(x−1)=2x^3 −3x^2 +7x+10. Find f(3).

$$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{2x}^{\mathrm{3}} −\mathrm{3x}^{\mathrm{2}} +\mathrm{7x}+\mathrm{10}.\:\mathrm{Find}\:\mathrm{f}\left(\mathrm{3}\right). \\ $$

Question Number 57023 Answers: 1 Comments: 0

There are 28 players in a national football team. 14 play midfield and defence, 15 play defence and attack and 3 play midfield only. the number of players who play attack only is twice those who play defence only, and the number who play defence is equal to those who play attack. If 18 play midfield represent the information on a venn diagram. Find i. how many play at most two games ii. how many play neither attack nor defence iii. how many play either midfield or attack.

Question Number 57020 Answers: 0 Comments: 3

[f(x+1)−f(x)]^2 =4[f(x)−1] f(x)=? −−−−−−−−−−−−− f(0)=0

$$\left[{f}\left({x}+\mathrm{1}\right)−{f}\left({x}\right)\right]^{\mathrm{2}} =\mathrm{4}\left[{f}\left({x}\right)−\mathrm{1}\right] \\ $$$${f}\left({x}\right)=? \\ $$$$−−−−−−−−−−−−− \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$

Question Number 57012 Answers: 2 Comments: 0

Find the local minimum value of f(x) where f(x)= (x−(1/x))+((2/(x−(1/x)))) ?

$${Find}\:{the}\:{local}\:{minimum}\:{value}\:{of}\:{f}\left({x}\right) \\ $$$${where}\:{f}\left({x}\right)=\:\left({x}−\frac{\mathrm{1}}{{x}}\right)+\left(\frac{\mathrm{2}}{{x}−\frac{\mathrm{1}}{{x}}}\right)\:? \\ $$

Question Number 57011 Answers: 1 Comments: 0

f(((x+y)/2))f(((x−y)/2))=g(x) g(x+y)g(x−y)=[f(x)]^2 −[f(y)]^2 f(x),g(x)=?

$${f}\left(\frac{{x}+{y}}{\mathrm{2}}\right){f}\left(\frac{{x}−{y}}{\mathrm{2}}\right)={g}\left({x}\right) \\ $$$${g}\left({x}+{y}\right){g}\left({x}−{y}\right)=\left[{f}\left({x}\right)\right]^{\mathrm{2}} −\left[{f}\left({y}\right)\right]^{\mathrm{2}} \\ $$$${f}\left({x}\right),{g}\left({x}\right)=? \\ $$

Question Number 57010 Answers: 1 Comments: 1

f(((x+y)/2))=((f(x)f(y))/(f(2))) f(x)=?

$${f}\left(\frac{{x}+{y}}{\mathrm{2}}\right)=\frac{{f}\left({x}\right){f}\left({y}\right)}{{f}\left(\mathrm{2}\right)} \\ $$$${f}\left({x}\right)=? \\ $$

Question Number 57007 Answers: 1 Comments: 3

cosec ((π/(14))) − 4 cos (((2π)/7)) = ?

$$\mathrm{cosec}\:\left(\frac{\pi}{\mathrm{14}}\right)\:−\:\mathrm{4}\:\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)\:\:=\:\:? \\ $$

Question Number 57001 Answers: 0 Comments: 1

construct an analytic function f(z) whose real part is e^x cos y

$${construct}\:{an}\:{analytic}\:{function}\:{f}\left({z}\right)\:{whose}\:{real}\:{part}\:{is}\:{e}^{{x}} \mathrm{cos}\:{y} \\ $$

Question Number 57000 Answers: 3 Comments: 1

If (x+2)^2 is a factor of the polynomial f(x)=mx^3 +x^2 +x+n, find; the values of m and n.

$$\mathrm{If}\:\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polynomial} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{mx}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{n},\:\mathrm{find}; \\ $$$$\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{m}\:\mathrm{and}\:\mathrm{n}. \\ $$

Question Number 56991 Answers: 0 Comments: 4

x! − x^2 = 8 , Find x

$$\:\:\mathrm{x}!\:−\:\mathrm{x}^{\mathrm{2}} \:\:=\:\:\mathrm{8}\:,\:\:\:\:\mathrm{Find}\:\:\mathrm{x} \\ $$$$ \\ $$

Question Number 56986 Answers: 2 Comments: 1

Question Number 56971 Answers: 1 Comments: 1

Question Number 56962 Answers: 1 Comments: 1

find S_n =Σ_(k=0) ^n k^2 C_n ^k cos(2kx) interms of n.

$${find}\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \:{cos}\left(\mathrm{2}{kx}\right) \\ $$$${interms}\:{of}\:{n}. \\ $$

Question Number 56961 Answers: 1 Comments: 0

Out of 6 mathematicians and 7 physicists a committee consisting of 3 mathematicians and 3 physicists is to be formed. In how many ways can this be done if two particular mathematicians cannot be on the commitee?

$$\mathrm{Out}\:\mathrm{of}\:\mathrm{6}\:\mathrm{mathematicians}\:\mathrm{and}\:\mathrm{7}\:\mathrm{physicists} \\ $$$$\mathrm{a}\:\mathrm{committee}\:\mathrm{consisting}\:\mathrm{of}\:\mathrm{3}\:\mathrm{mathematicians} \\ $$$$\mathrm{and}\:\mathrm{3}\:\mathrm{physicists}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{formed}.\:\mathrm{In}\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{done}\:\mathrm{if}\:\mathrm{two}\: \\ $$$$\mathrm{particular}\:\mathrm{mathematicians}\:\mathrm{cannot}\:\mathrm{be} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{commitee}? \\ $$

Question Number 56954 Answers: 2 Comments: 1

Find minimum value of : cos(ω−φ)+cos(φ−ϕ)+cos (ϕ−ω).

$${Find}\:{minimum}\:{value}\:{of}\:: \\ $$$${cos}\left(\omega−\phi\right)+\mathrm{cos}\left(\phi−\varphi\right)+\mathrm{cos}\:\left(\varphi−\omega\right). \\ $$

Question Number 56951 Answers: 0 Comments: 2

The deviations from the mean of a set of numbers are (x+2), (2x−11), −9, (x+1)^2 , (x−4)^2 , (1−3x). find the value of x where x>0.

$$\mathrm{The}\:\mathrm{deviations}\:\mathrm{from}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{set}\:\mathrm{of}\:\mathrm{numbers}\:\mathrm{are}\:\left(\mathrm{x}+\mathrm{2}\right),\:\left(\mathrm{2x}−\mathrm{11}\right), \\ $$$$−\mathrm{9},\:\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} ,\:\left(\mathrm{x}−\mathrm{4}\right)^{\mathrm{2}} ,\:\left(\mathrm{1}−\mathrm{3x}\right).\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{where}\:\mathrm{x}>\mathrm{0}. \\ $$

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