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Question Number 150263 Answers: 2 Comments: 2

Π_(k=1) ^n (1+(k^2 /n^2 ))^(1/n)

$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}+\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} }\right)^{\frac{\mathrm{1}}{{n}}} \\ $$

Question Number 149120 Answers: 0 Comments: 0

Question Number 148137 Answers: 1 Comments: 0

∫ ((3cos^2 (x)+1)/(sin^5 (x)))dx = ???

$$\int\:\:\frac{\mathrm{3}{cos}^{\mathrm{2}} \left({x}\right)+\mathrm{1}}{{sin}^{\mathrm{5}} \left({x}\right)}{dx}\:=\:??? \\ $$

Question Number 147905 Answers: 1 Comments: 0

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Question Number 147828 Answers: 1 Comments: 0

Σ_(p=0) ^n psh(a+bp)

$$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{psh}\left(\mathrm{a}+\mathrm{bp}\right) \\ $$

Question Number 147820 Answers: 1 Comments: 0

Σ_(p=0) ^n sh^2 (a+pb)

$$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{sh}^{\mathrm{2}} \left(\mathrm{a}+\mathrm{pb}\right) \\ $$

Question Number 147819 Answers: 1 Comments: 0

Σ_(p=0) ^n ch^2 (a+pb)

$$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{ch}^{\mathrm{2}} \left(\mathrm{a}+\mathrm{pb}\right) \\ $$

Question Number 147603 Answers: 1 Comments: 0

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Question Number 145652 Answers: 2 Comments: 0

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Question Number 140821 Answers: 0 Comments: 1

O is centre of circle and square. find yellow area in terms of radius of circle

$${O}\:{is}\:{centre}\:{of}\:{circle}\:{and}\:{square}. \\ $$$${find}\:{yellow}\:{area}\:{in}\:{terms}\:{of}\:{radius}\: \\ $$$${of}\:{circle} \\ $$

Question Number 140597 Answers: 1 Comments: 0

Find the equation of circle which passes through the point (2,0) and whose center is the limit of the point of intersection of the lines 3x+5y=1 and (2+c)x+5c^2 y=1 as c→1 .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{which} \\ $$$$\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},\mathrm{0}\right)\:\mathrm{and} \\ $$$$\mathrm{whose}\:\mathrm{center}\:\mathrm{is}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{point}\:\mathrm{of}\:\mathrm{intersection}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{lines}\:\mathrm{3x}+\mathrm{5y}=\mathrm{1}\:\mathrm{and}\:\left(\mathrm{2}+\mathrm{c}\right)\mathrm{x}+\mathrm{5c}^{\mathrm{2}} \mathrm{y}=\mathrm{1} \\ $$$$\mathrm{as}\:\mathrm{c}\rightarrow\mathrm{1}\:. \\ $$

Question Number 138388 Answers: 2 Comments: 0

Find maximum volume of a cylinder within a unit cube whose axis is along a diagonal of the cube.

$${Find}\:{maximum}\:{volume}\:{of}\:{a} \\ $$$${cylinder}\:{within}\:{a}\:{unit}\:{cube}\: \\ $$$${whose}\:{axis}\:{is}\:{along}\:{a}\:{diagonal} \\ $$$${of}\:{the}\:{cube}. \\ $$

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Question Number 134097 Answers: 2 Comments: 0

In a square ABCD , a triangle APQ inscribed in it. AP=4 cm, PQ=3 cm and AQ=5 cm. Point P is on the side BC and point Q is on side CD. Find the area of the square ABCD.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{square}\:\mathrm{ABCD}\:,\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{APQ}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{it}.\:\mathrm{AP}=\mathrm{4}\:\mathrm{cm}, \\ $$$$\mathrm{PQ}=\mathrm{3}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{AQ}=\mathrm{5}\:\mathrm{cm}.\:\mathrm{Point} \\ $$$$\mathrm{P}\:\mathrm{is}\:\mathrm{on}\:\mathrm{the}\:\mathrm{side}\:\mathrm{BC}\:\mathrm{and}\:\mathrm{point}\:\mathrm{Q} \\ $$$$\mathrm{is}\:\mathrm{on}\:\mathrm{side}\:\mathrm{CD}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{square}\:\mathrm{ABCD}. \\ $$

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