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Question Number 190665 Answers: 0 Comments: 0

Question Number 190660 Answers: 2 Comments: 0

if y = sin^(−1) (2x(√(1−x^2 ))) where x∈[−(1/( (√2))), (1/( (√2)))], then find (dy/dx).

$${if}\:{y}\:=\:{sin}^{−\mathrm{1}} \left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:{where}\:{x}\in\left[−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}},\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right],\:{then}\:{find}\:\frac{{dy}}{{dx}}. \\ $$

Question Number 190659 Answers: 0 Comments: 0

Prove that: ((cos (π/9)))^(1/3) − ((cos ((2π)/9)))^(1/3) − ((cos ((4π)/9)))^(1/3) = ((3 − (3/2) (9)^(1/3) ))^(1/3)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\pi}{\mathrm{9}}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{9}}} \\ $$$$=\:\sqrt[{\mathrm{3}}]{\mathrm{3}\:−\:\frac{\mathrm{3}}{\mathrm{2}}\:\sqrt[{\mathrm{3}}]{\mathrm{9}}}\: \\ $$

Question Number 190652 Answers: 0 Comments: 0

Question Number 190636 Answers: 0 Comments: 0

Question Number 190634 Answers: 2 Comments: 6

The volume of a right circular cone is 5litres. Calculate the volume of the part into which the cone is divided by a plane parallel to the base one−third of the way down from the vertex to the base giving your answer to the nearest millimetres. Help!

$$\mathrm{The}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}\:\mathrm{circular}\:\mathrm{cone} \\ $$$$\mathrm{is}\:\mathrm{5litres}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{part}\:\mathrm{into}\:\mathrm{which}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{is} \\ $$$$\mathrm{divided}\:\mathrm{by}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{base}\:\mathrm{one}−\mathrm{third}\:\mathrm{of}\:\mathrm{the}\:\mathrm{way}\:\mathrm{down} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{vertex}\:\mathrm{to}\:\mathrm{the}\:\mathrm{base}\:\mathrm{giving} \\ $$$$\mathrm{your}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\: \\ $$$$\mathrm{millimetres}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 190629 Answers: 0 Comments: 1

Question Number 190625 Answers: 1 Comments: 0

solve in R : ⌊ (1/x) ⌋ + ⌊ x ⌋ = 2

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{solve}\:\mathrm{in}\:\:\:\mathbb{R}\:\:\:: \\ $$$$\:\:\:\:\:\:\:\:\lfloor\:\frac{\mathrm{1}}{{x}}\:\rfloor\:\:+\:\lfloor\:{x}\:\rfloor\:=\:\mathrm{2}\:\:\:\:\: \\ $$$$ \\ $$

Question Number 190624 Answers: 2 Comments: 0

Question Number 190623 Answers: 2 Comments: 0

calculate : Σ_(n=1) ^∞ (( (−1)^( n−1) )/n) cos ((( nπ)/3) ) =?

$$ \\ $$$$\:\:\:\:\:\:\mathrm{calculate}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} }{{n}}\:\mathrm{cos}\:\left(\frac{\:{n}\pi}{\mathrm{3}}\:\right)\:=? \\ $$$$ \\ $$

Question Number 190639 Answers: 1 Comments: 0

The points A, B and C have position vectors i−j , 5i−3j and 11i−6j respectively . Show that A, B and C are collinear.

$$\:{The}\:{points}\:{A},\:{B}\:{and}\:{C}\:{have}\:{position} \\ $$$$\:{vectors}\:{i}−{j}\:,\:\mathrm{5}{i}−\mathrm{3}{j}\:{and}\:\mathrm{11}{i}−\mathrm{6}{j}\: \\ $$$${respectively}\:.\:{Show}\:{that}\:{A},\:{B}\:{and}\:{C} \\ $$$${are}\:{collinear}. \\ $$

Question Number 190622 Answers: 1 Comments: 0

prove : ∫_(−∞) ^( ∞) ((( x)/( ⋮ )^2 dx= Σ_(k=1) ^∞ (1/( k^2 )) ⋖))

$$ \\ $$$$\:\:\:{prove}\:: \\ $$$$\:\:\int_{−\infty} ^{\:\infty} \:\:\:\left(\frac{\:{x}}{\left.\:\underline{\vdots} \right)^{\mathrm{2}} \mathrm{d}{x}=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\:{k}\:^{\mathrm{2}} }\:\:\:\lessdot}\right. \\ $$

Question Number 190618 Answers: 1 Comments: 0

f(x−f(x))=x ,f(5)=−1 f(−1)=?

$$\mathrm{f}\left(\mathrm{x}−\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}\:\:,\mathrm{f}\left(\mathrm{5}\right)=−\mathrm{1} \\ $$$$\mathrm{f}\left(−\mathrm{1}\right)=? \\ $$

Question Number 190615 Answers: 1 Comments: 1

Question Number 190611 Answers: 0 Comments: 2

Montrer que: 1•c^2 =a^2 +b^2 2• rayon r=(c/(1+(√2)))−((a+b)/(2+(√2)))

$$\mathrm{Montrer}\:\mathrm{que}: \\ $$$$\mathrm{1}\bullet\boldsymbol{\mathrm{c}}^{\mathrm{2}} =\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} \\ $$$$\mathrm{2}\bullet\:\mathrm{rayon}\:\:\:\:\:\boldsymbol{\mathrm{r}}=\frac{\boldsymbol{\mathrm{c}}}{\mathrm{1}+\sqrt{\mathrm{2}}}−\frac{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}}{\mathrm{2}+\sqrt{\mathrm{2}}} \\ $$$$ \\ $$

Question Number 190607 Answers: 0 Comments: 0

Question Number 190602 Answers: 1 Comments: 0

let S={a,b,c,d,e,f} if we take any subset S (same subset is allowed), it also can be S, which will form S if we join them, order of operation does not matter ({a,b,c,d},{d,e,f}) is the same as ({d,e,f},{a,b,c,d}) how many ways can we choose?

$$ \\ $$$$\: \\ $$$$\:{let}\:{S}=\left\{{a},{b},{c},{d},{e},{f}\right\} \\ $$$$\:{if}\:{we}\:{take}\:{any}\:{subset}\:{S}\:\left({same}\:{subset}\:{is}\:{allowed}\right), \\ $$$$\:{it}\:{also}\:{can}\:{be}\:{S},\:{which}\:{will}\:{form}\:{S}\:{if}\:{we}\:{join}\:{them}, \\ $$$${order}\:{of}\:{operation}\:{does}\:{not}\:{matter} \\ $$$$\:\left(\left\{{a},{b},{c},{d}\right\},\left\{{d},{e},{f}\right\}\right)\:{is}\:{the}\:{same}\:{as} \\ $$$$\:\left(\left\{{d},{e},{f}\right\},\left\{{a},{b},{c},{d}\right\}\right) \\ $$$$\:{how}\:{many}\:{ways}\:{can}\:{we}\:{choose}? \\ $$$$\: \\ $$$$ \\ $$

Question Number 190644 Answers: 1 Comments: 0