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Question Number 113185 Answers: 1 Comments: 0

Question Number 113160 Answers: 2 Comments: 4

Question Number 113159 Answers: 2 Comments: 0

∫_0 ^1 x^2 log(1−x)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} {log}\left(\mathrm{1}−{x}\right){dx} \\ $$

Question Number 113154 Answers: 1 Comments: 0

If ⌊x + (√5)⌋ = ⌊x⌋ + ⌊5⌋ then ⌊x⌋ − x would be greater than (a) (√5) − 2 (b) (√5) − 3 (c) (√5) (d) (√5) + 1 (e) (√5) − 1

$$\mathrm{If}\:\:\:\:\:\:\lfloor\mathrm{x}\:\:+\:\:\sqrt{\mathrm{5}}\rfloor\:\:\:=\:\:\:\lfloor\mathrm{x}\rfloor\:\:+\:\:\lfloor\mathrm{5}\rfloor \\ $$$$\mathrm{then}\:\:\:\:\:\lfloor\mathrm{x}\rfloor\:\:−\:\:\mathrm{x}\:\:\:\:\mathrm{would}\:\mathrm{be}\:\mathrm{greater}\:\mathrm{than} \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\sqrt{\mathrm{5}}\:\:−\:\:\mathrm{2}\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\:\:\:\sqrt{\mathrm{5}}\:\:−\:\:\mathrm{3}\:\:\:\:\:\:\left(\mathrm{c}\right)\:\:\:\:\sqrt{\mathrm{5}}\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\:\:\:\sqrt{\mathrm{5}}\:\:+\:\:\mathrm{1}\:\:\:\:\:\:\:\left(\mathrm{e}\right)\:\:\:\sqrt{\mathrm{5}}\:\:−\:\:\mathrm{1} \\ $$

Question Number 113151 Answers: 1 Comments: 4

Prove ((sin2A+cos2A+1)/(sin2A+cos2A−1))=((tan(A+45°))/(tanA)) Hence, prove that tan15°=2−(√3)

$$\mathrm{Prove}\:\frac{\mathrm{sin2A}+\mathrm{cos2A}+\mathrm{1}}{\mathrm{sin2A}+\mathrm{cos2A}−\mathrm{1}}=\frac{\mathrm{tan}\left(\mathrm{A}+\mathrm{45}°\right)}{\mathrm{tanA}} \\ $$$$\mathrm{Hence},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{tan15}°=\mathrm{2}−\sqrt{\mathrm{3}} \\ $$

Question Number 113368 Answers: 1 Comments: 0

There are 4 identical mathematics books, 3 identical physics books, 2 identical chemistry books. in how many ways can you compile the 9 books such that same books are not mutually adjacent.

$$\mathrm{There}\:\mathrm{are}\:\mathrm{4}\:\mathrm{identical}\:\mathrm{mathematics} \\ $$$$\mathrm{books},\:\mathrm{3}\:\mathrm{identical}\:\mathrm{physics}\:\mathrm{books},\:\mathrm{2} \\ $$$$\mathrm{identical}\:\mathrm{chemistry}\:\mathrm{books}. \\ $$$$\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\:\mathrm{can}\:\mathrm{you}\:\mathrm{compile} \\ $$$$\mathrm{the}\:\mathrm{9}\:\mathrm{books}\:\mathrm{such}\:\mathrm{that}\:\mathrm{same}\:\mathrm{books}\:\mathrm{are} \\ $$$$\mathrm{not}\:\mathrm{mutually}\:\mathrm{adjacent}. \\ $$

Question Number 113134 Answers: 3 Comments: 2

any one can explain me how to change decimal number to biner number. i′m forgot. example (315)_(10) = (...)_2 thank you

$$\mathrm{any}\:\mathrm{one}\:\mathrm{can}\:\mathrm{explain}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to} \\ $$$$\mathrm{change}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{to}\: \\ $$$$\mathrm{biner}\:\mathrm{number}.\:\mathrm{i}'\mathrm{m}\:\mathrm{forgot}. \\ $$$$\mathrm{example}\:\left(\mathrm{315}\right)_{\mathrm{10}} \:=\:\left(...\right)_{\mathrm{2}} \\ $$$$\mathrm{thank}\:\mathrm{you} \\ $$

Question Number 113114 Answers: 1 Comments: 1

Question Number 113113 Answers: 0 Comments: 0

suppose that the quantity demanded Q_d =13−6p+2(dp/dt)+(dp^2 /dt^2 ) and quantity supplied Q_s =−3+2p where p is the price find the equilibrium price for market clearance

$${suppose}\:{that}\:{the}\:{quantity}\:{demanded}\:{Q}_{{d}} =\mathrm{13}−\mathrm{6}{p}+\mathrm{2}\frac{{dp}}{{dt}}+\frac{{dp}^{\mathrm{2}} }{{dt}^{\mathrm{2}} }\:{and}\:{quantity}\:{supplied}\:{Q}_{{s}} =−\mathrm{3}+\mathrm{2}{p}\:{where}\:{p}\:{is}\:{the}\:{price}\:{find}\:{the}\:{equilibrium}\:{price}\:{for}\:{market}\:{clearance} \\ $$

Question Number 113111 Answers: 1 Comments: 0

find the area bounded by the curve y^2 =x^3 and the lines x=0 y=1 and y=2

$${find}\:{the}\:{area}\:{bounded}\:{by}\:{the}\:{curve}\:{y}^{\mathrm{2}} ={x}^{\mathrm{3}} \:{and}\:{the}\:{lines}\:{x}=\mathrm{0}\:{y}=\mathrm{1}\:{and}\:{y}=\mathrm{2} \\ $$

Question Number 113110 Answers: 2 Comments: 2

∫_0 ^1 (√(x(x−1)dx))

$$\overset{\mathrm{1}} {\int}_{\mathrm{0}} \sqrt{{x}\left({x}−\mathrm{1}\right){dx}} \\ $$

Question Number 113109 Answers: 1 Comments: 2

Question Number 113107 Answers: 1 Comments: 0

Question Number 113101 Answers: 0 Comments: 2

Prove that GCD ((a,b),b)=(a,b)

$${Prove}\:{that}\:{GCD}\:\left(\left({a},{b}\right),{b}\right)=\left({a},{b}\right) \\ $$

Question Number 113097 Answers: 1 Comments: 0

If 4 women earn as much as 9 boys; 4 men as much as 15 boys; 27 girls as much as 20 women, how many girls will earn the same amount as 24 men?

$$\mathrm{If}\:\mathrm{4}\:\mathrm{women}\:\mathrm{earn}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{9}\:\mathrm{boys};\:\mathrm{4}\:\mathrm{men}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as} \\ $$$$\mathrm{15}\:\mathrm{boys};\:\mathrm{27}\:\mathrm{girls}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{20}\:\mathrm{women},\:\mathrm{how}\:\mathrm{many}\:\mathrm{girls} \\ $$$$\mathrm{will}\:\mathrm{earn}\:\mathrm{the}\:\mathrm{same}\:\mathrm{amount}\:\mathrm{as}\:\mathrm{24}\:\mathrm{men}? \\ $$

Question Number 113092 Answers: 2 Comments: 0

What is the area of a tringle where the sides of triangle are 91 cm, 98 cm, and 105 cm

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tringle}\:\mathrm{where}\:\mathrm{the} \\ $$$$\mathrm{sides}\:\mathrm{of}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{91}\:\mathrm{cm},\:\mathrm{98}\:\mathrm{cm},\:\mathrm{and}\:\mathrm{105}\:\mathrm{cm} \\ $$

Question Number 113080 Answers: 1 Comments: 0

The perimeter of a triangle is 84 cm and it′s area is 336 square cm. If the length of one side of triangle is 30 cm, then what is the lengths of the remaining two sides of triangle ?

$$\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{is} \\ $$$$\mathrm{84}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{it}'\mathrm{s}\:\mathrm{area}\:\mathrm{is}\:\mathrm{336}\:\mathrm{square}\:\mathrm{cm}.\:\mathrm{If}\:\mathrm{the}\: \\ $$$$\mathrm{length}\:\mathrm{of}\:\mathrm{one}\:\mathrm{side}\:\mathrm{of}\:\mathrm{triangle}\:\mathrm{is}\:\mathrm{30}\:\mathrm{cm},\:\mathrm{then} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{two} \\ $$$$\mathrm{sides}\:\mathrm{of}\:\mathrm{triangle}\:? \\ $$

Question Number 113091 Answers: 1 Comments: 0

What is the area bounded by the curves arg(z) = (π/3) ; arg(z)= ((2π)/3) and arg(z−2−2i(√3))=π on the complex plane?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curves} \\ $$$$\mathrm{arg}\left(\mathrm{z}\right)\:=\:\frac{\pi}{\mathrm{3}}\:;\:\mathrm{arg}\left(\mathrm{z}\right)=\:\frac{\mathrm{2}\pi}{\mathrm{3}}\:\mathrm{and}\:\mathrm{arg}\left(\mathrm{z}−\mathrm{2}−\mathrm{2i}\sqrt{\mathrm{3}}\right)=\pi \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{plane}? \\ $$

Question Number 113073 Answers: 1 Comments: 0

Find all positive integers n for which 5^n +1 is divisible by 7

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{n}\:\mathrm{for}\: \\ $$$$\mathrm{which}\:\mathrm{5}^{\mathrm{n}} +\mathrm{1}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{7} \\ $$

Question Number 113070 Answers: 1 Comments: 0

If n∈Z^+ , prove that (1/(2(√1)))+(1/(3(√2)))+(1/(4(√3)))+...(1/((n+1)(√n)))<2

$$\mathrm{If}\:{n}\in\mathbb{Z}^{+} ,\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{1}}}+\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{3}}}+...\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\sqrt{{n}}}<\mathrm{2} \\ $$$$ \\ $$

Question Number 113063 Answers: 1 Comments: 0

Question Number 113060 Answers: 3 Comments: 0

(1) (√(dy/dx)) = ((d((√y)))/dx) (2) x^2 ≡ 73 (mod 216) (3) If 2^x_1 +2^x_2 +2^x_3 +...+2^x_n =80,000 where x_1 ,x_2 ,x_3 ,...,x_n are distinct whole number . find the value of n

$$\:\left(\mathrm{1}\right)\:\sqrt{\frac{\mathrm{dy}}{\mathrm{dx}}}\:=\:\frac{\mathrm{d}\left(\sqrt{\mathrm{y}}\right)}{\mathrm{dx}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{x}^{\mathrm{2}} \:\equiv\:\mathrm{73}\:\left(\mathrm{mod}\:\mathrm{216}\right) \\ $$$$\left(\mathrm{3}\right)\:\mathrm{If}\:\mathrm{2}^{\mathrm{x}_{\mathrm{1}} } +\mathrm{2}^{\mathrm{x}_{\mathrm{2}} } +\mathrm{2}^{\mathrm{x}_{\mathrm{3}} } +...+\mathrm{2}^{\mathrm{x}_{\mathrm{n}} } =\mathrm{80},\mathrm{000} \\ $$$$\:\mathrm{where}\:\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} ,\mathrm{x}_{\mathrm{3}} ,...,\mathrm{x}_{\mathrm{n}} \:\mathrm{are}\:\mathrm{distinct} \\ $$$$\mathrm{whole}\:\mathrm{number}\:.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n} \\ $$

Question Number 113059 Answers: 2 Comments: 0

Question Number 113015 Answers: 2 Comments: 0

Question Number 113006 Answers: 1 Comments: 0

a+(1/(b+(1/(c+(1/(d+...))))))=(2)^(1/3) If a,b,c,d,... are positive integers, then what is the value of ′b′?

$$\mathrm{a}+\frac{\mathrm{1}}{\mathrm{b}+\frac{\mathrm{1}}{\mathrm{c}+\frac{\mathrm{1}}{\mathrm{d}+...}}}=\sqrt[{\mathrm{3}}]{\mathrm{2}} \\ $$$$\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},...\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers},\:\mathrm{then} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:'\mathrm{b}'? \\ $$

Question Number 113005 Answers: 1 Comments: 0

Two different two−digit natural numbers are written beside each other such that the larger number is written on the left. When the absolute difference of the two numbers is subtracted from the four−digit number so formed, the number obtained is 5481. What is the sum of the two−digit numbers?

$$\mathrm{Two}\:\mathrm{different}\:\mathrm{two}−\mathrm{digit}\:\mathrm{natural} \\ $$$$\mathrm{numbers}\:\mathrm{are}\:\mathrm{written}\:\mathrm{beside}\:\mathrm{each} \\ $$$$\mathrm{other}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{larger}\:\mathrm{number} \\ $$$$\mathrm{is}\:\mathrm{written}\:\mathrm{on}\:\mathrm{the}\:\mathrm{left}.\:\mathrm{When}\:\mathrm{the} \\ $$$$\mathrm{absolute}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{numbers}\:\mathrm{is}\:\mathrm{subtracted}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{four}−\mathrm{digit}\:\mathrm{number}\:\mathrm{so}\:\mathrm{formed},\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{obtained}\:\mathrm{is}\:\mathrm{5481}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}−\mathrm{digit}\:\mathrm{numbers}? \\ $$

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