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AllQuestion and Answers: Page 1104

Question Number 107673 Answers: 3 Comments: 0

Question Number 107672 Answers: 1 Comments: 2

♠BeMath♠ ((4sin (((2π)/7))+sec ((π/(14))))/(cot ((π/7)))) ?

$$\:\:\:\:\:\spadesuit\mathcal{B}{e}\mathcal{M}{ath}\spadesuit \\ $$$$\:\:\:\:\frac{\mathrm{4sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{sec}\:\left(\frac{\pi}{\mathrm{14}}\right)}{\mathrm{cot}\:\left(\frac{\pi}{\mathrm{7}}\right)}\:? \\ $$

Question Number 107659 Answers: 1 Comments: 0

∮Bobhans∮ If all the letters of the word MISSISSIPPI are written down at random , the probability that all the four S appear consecutively is ___

$$\:\:\:\:\:\oint\mathbb{B}\mathrm{obhans}\oint \\ $$$$\mathrm{If}\:\mathrm{all}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{MISSISSIPPI}\:\mathrm{are}\:\mathrm{written}\:\mathrm{down}\: \\ $$$$\mathrm{at}\:\mathrm{random}\:,\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{all}\:\mathrm{the}\:\mathrm{four}\:\mathrm{S}\:\mathrm{appear}\:\mathrm{consecutively}\:\mathrm{is}\:\_\_\_ \\ $$

Question Number 107658 Answers: 1 Comments: 0

⋇JS⋇ A metal box (without top) is tobe contructed from a square sheet of metal that is 10 dm on the side by first cutting the square pieces of the same size from the corners of the sheet and folding up sides. what size squares should be cut in order to maximize the volume of the box.

$$\:\:\:\divideontimes\mathcal{JS}\divideontimes \\ $$$${A}\:{metal}\:{box}\:\left({without}\:{top}\right)\:{is}\:{tobe} \\ $$$${contructed}\:{from}\:{a}\:{square}\:{sheet} \\ $$$${of}\:{metal}\:{that}\:{is}\:\mathrm{10}\:{dm}\:{on}\:{the} \\ $$$${side}\:{by}\:{first}\:{cutting}\:{the}\:{square} \\ $$$${pieces}\:{of}\:{the}\:{same}\:{size}\:{from}\:{the} \\ $$$${corners}\:{of}\:{the}\:{sheet}\:{and}\:{folding} \\ $$$${up}\:{sides}.\:{what}\:{size}\:{squares} \\ $$$${should}\:{be}\:{cut}\:{in}\:{order}\:{to} \\ $$$${maximize}\:{the}\:{volume}\:{of}\:{the}\:{box}. \\ $$

Question Number 107656 Answers: 3 Comments: 0

Question Number 107650 Answers: 0 Comments: 0

Question Number 107647 Answers: 1 Comments: 0

≍BobHans≍ find the formula (d^3 /dx^3 )[g(f(x))]

$$\:\:\:\:\:\:\:\asymp\mathcal{B}\mathrm{ob}\mathcal{H}\mathrm{ans}\asymp \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{formula}\:\frac{\mathrm{d}^{\mathrm{3}} }{\mathrm{dx}^{\mathrm{3}} }\left[\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\right] \\ $$

Question Number 107654 Answers: 0 Comments: 0

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Question Number 107628 Answers: 0 Comments: 0

Question Number 107624 Answers: 0 Comments: 0

please prove: A,B,C are angles of triangle. Σ_(cylic) ((sinA+sinB)/(cosc))≥8cos(A/2)cos(B/2)cos(C/2)

$$\:\:\:\:\:\:\:{please}\:{prove}: \\ $$$$\:\mathrm{A},\mathrm{B},{C}\:\:{are}\:{angles}\:{of} \\ $$$${triangle}. \\ $$$$\underset{{cylic}} {\sum}\frac{{sinA}+{sinB}}{{cosc}}\geqslant\mathrm{8}{cos}\frac{{A}}{\mathrm{2}}{cos}\frac{{B}}{\mathrm{2}}{cos}\frac{{C}}{\mathrm{2}}\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 107621 Answers: 0 Comments: 1

Question Number 107618 Answers: 1 Comments: 0

Question Number 107617 Answers: 1 Comments: 0

Question Number 107609 Answers: 2 Comments: 0

Question Number 107598 Answers: 0 Comments: 3

Calculate: (√(1 + (√(2 + (√(3 + (√(4 + (√(5 + ...))))))))))

$$\:\:\:\:\mathrm{Calculate}:\:\:\sqrt{\mathrm{1}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{3}\:+\:\sqrt{\mathrm{4}\:+\:\sqrt{\mathrm{5}\:+\:...}}}}} \\ $$

Question Number 107596 Answers: 2 Comments: 0

Given I_(m,n) = ∫_1 ^e x^m (ln x)^n dx where m,n ∈ N^∗ Show that (1 + m)I_(m,n) = e^(m+1) −nI_(m,n−1) for m >0 and n>0 also, evaluate I_(2,3)

$$\mathrm{Given}\: \\ $$$$\:{I}_{{m},{n}} \:=\:\underset{\mathrm{1}} {\overset{{e}} {\int}}{x}^{{m}} \:\left(\mathrm{ln}\:{x}\right)^{{n}} \:{dx}\:\mathrm{where}\:{m},{n}\:\in\:\mathbb{N}^{\ast} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{1}\:+\:{m}\right){I}_{{m},{n}} \:=\:{e}^{{m}+\mathrm{1}} −{nI}_{{m},{n}−\mathrm{1}} \:\mathrm{for}\:{m}\:>\mathrm{0}\:\mathrm{and}\:{n}>\mathrm{0} \\ $$$$\mathrm{also},\:\mathrm{evaluate}\:{I}_{\mathrm{2},\mathrm{3}} \\ $$

Question Number 107594 Answers: 2 Comments: 0

Find the greatest common divisor of 1122 and 1001 and express the greatest common divisor d in the form. d = 1122x + 1001y Using the above result solve the congruence equation 37x ≡ 11 (mod 33)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{common}\:\mathrm{divisor}\:\mathrm{of}\:\mathrm{1122}\:\mathrm{and}\:\mathrm{1001}\:\mathrm{and}\: \\ $$$$\mathrm{express}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{common}\:\mathrm{divisor}\:{d}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}. \\ $$$$\:\:{d}\:=\:\mathrm{1122}{x}\:+\:\mathrm{1001}{y} \\ $$$$\mathrm{Using}\:\mathrm{the}\:\mathrm{above}\:\mathrm{result}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{congruence}\:\mathrm{equation} \\ $$$$\:\mathrm{37}{x}\:\equiv\:\mathrm{11}\:\left(\mathrm{mod}\:\mathrm{33}\right) \\ $$

Question Number 107591 Answers: 2 Comments: 2

Question Number 107589 Answers: 2 Comments: 0

Question Number 107586 Answers: 0 Comments: 2

App Updates: v2.135 • fix for background color problems • new drawing tools added in build and edit menu add equality marker to line etc • A new drawling tool to draw smooth curves.

$$\mathrm{App}\:\mathrm{Updates}:\:\mathrm{v2}.\mathrm{135} \\ $$$$\bullet\:\mathrm{fix}\:\mathrm{for}\:\mathrm{background}\:\mathrm{color}\:\mathrm{problems} \\ $$$$\bullet\:\mathrm{new}\:\mathrm{drawing}\:\mathrm{tools}\:\mathrm{added}\:\mathrm{in} \\ $$$$\:\:\:\mathrm{build}\:\mathrm{and}\:\mathrm{edit}\:\mathrm{menu} \\ $$$$\:\:\:\mathrm{add}\:\mathrm{equality}\:\mathrm{marker}\:\mathrm{to}\:\mathrm{line}\:\mathrm{etc} \\ $$$$\bullet\:\mathrm{A}\:\mathrm{new}\:\mathrm{drawling}\:\mathrm{tool}\:\mathrm{to}\:\mathrm{draw} \\ $$$$\:\:\:\:\mathrm{smooth}\:\mathrm{curves}. \\ $$

Question Number 107572 Answers: 1 Comments: 1

Question Number 107571 Answers: 0 Comments: 0

Given 0<x≤(π/2), 0<y≤(π/2), Let z_1 =((cos x)/(sin y))+((cos y)/(sin x)) i ,and ∣z_1 ∣=2 ; If z_2 =(√x)+(√(y ))i ,then what is the maximum value of ∣z_1 −z_2 ∣.

$${G}\mathrm{iven}\:\mathrm{0}<\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}},\:\mathrm{0}<\mathrm{y}\leqslant\frac{\pi}{\mathrm{2}}, \\ $$$$\mathrm{Let}\:{z}_{\mathrm{1}} =\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{y}}+\frac{\mathrm{cos}\:{y}}{\mathrm{sin}\:{x}}\:{i}\:,\mathrm{and}\:\mid{z}_{\mathrm{1}} \mid=\mathrm{2}\:; \\ $$$$\mathrm{If}\:{z}_{\mathrm{2}} =\sqrt{{x}}+\sqrt{{y}\:}{i}\:,\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mid{z}_{\mathrm{1}} −{z}_{\mathrm{2}} \mid. \\ $$

Question Number 107567 Answers: 3 Comments: 0

∫(√(3x^2 −2x)) dx

$$\int\sqrt{\mathrm{3x}^{\mathrm{2}} −\mathrm{2x}}\:\mathrm{dx} \\ $$

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