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Question Number 18884 Answers: 1 Comments: 0

Determine the smallest positive integer x, whose last digit is 6 and if we erase this 6 and put it in left most of the number so obtained, the number becomes 4x.

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{integer} \\ $$$$\mathrm{x},\:\mathrm{whose}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{6}\:\mathrm{and}\:\mathrm{if}\:\mathrm{we}\:\mathrm{erase} \\ $$$$\mathrm{this}\:\mathrm{6}\:\mathrm{and}\:\mathrm{put}\:\mathrm{it}\:\mathrm{in}\:\mathrm{left}\:\mathrm{most}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{so}\:\mathrm{obtained},\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{becomes}\:\mathrm{4x}. \\ $$

Question Number 18663 Answers: 1 Comments: 2

Find the product of 101 × 10001 × 100000001 × ... × (1000...01) where the last factor has 2^7 − 1 zeros between the ones. Find the number of ones in the product.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{101}\:×\:\mathrm{10001}\:× \\ $$$$\mathrm{100000001}\:×\:...\:×\:\left(\mathrm{1000}...\mathrm{01}\right)\:\mathrm{where}\:\mathrm{the} \\ $$$$\mathrm{last}\:\mathrm{factor}\:\mathrm{has}\:\mathrm{2}^{\mathrm{7}} \:−\:\mathrm{1}\:\mathrm{zeros}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{ones}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ones}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{product}. \\ $$

Question Number 18968 Answers: 1 Comments: 1

Find the side lengths of a triangle if side lengths are consecutive integers,and one of whose angles is twice as large as another.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{side}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{if}\:\mathrm{side}\:\mathrm{lengths}\:\mathrm{are}\:\mathrm{consecutive}\: \\ $$$$\mathrm{integers},\mathrm{and}\:\mathrm{one}\:\mathrm{of}\:\mathrm{whose}\:\mathrm{angles} \\ $$$$\mathrm{is}\:\mathrm{twice}\:\mathrm{as}\:\mathrm{large}\:\mathrm{as}\:\mathrm{another}. \\ $$

Question Number 18655 Answers: 0 Comments: 3

Find the number of odd integers between 30,000 and 80,000 in which no digit is repeated.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{odd}\:\mathrm{integers} \\ $$$$\mathrm{between}\:\mathrm{30},\mathrm{000}\:\mathrm{and}\:\mathrm{80},\mathrm{000}\:\mathrm{in}\:\mathrm{which}\:\mathrm{no} \\ $$$$\mathrm{digit}\:\mathrm{is}\:\mathrm{repeated}. \\ $$

Question Number 18653 Answers: 1 Comments: 0

Solve the inequality, ∣x − 1∣ + ∣x + 1∣ < 4

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{inequality},\:\mid{x}\:−\:\mathrm{1}\mid\:+\:\mid{x}\:+\:\mathrm{1}\mid\:<\:\mathrm{4} \\ $$

Question Number 18652 Answers: 1 Comments: 0

Show that for any natural number n, the fraction ((21n + 4)/(14n + 3)) is in its lowest term.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{natural}\:\mathrm{number}\:{n}, \\ $$$$\mathrm{the}\:\mathrm{fraction}\:\frac{\mathrm{21}{n}\:+\:\mathrm{4}}{\mathrm{14}{n}\:+\:\mathrm{3}}\:\mathrm{is}\:\mathrm{in}\:\mathrm{its}\:\mathrm{lowest}\:\mathrm{term}. \\ $$

Question Number 18650 Answers: 1 Comments: 0

∫dx/x(√(x^4 −1))

$$\int{dx}/{x}\sqrt{{x}^{\mathrm{4}} −\mathrm{1}} \\ $$

Question Number 18645 Answers: 0 Comments: 0

Question Number 18642 Answers: 1 Comments: 0

What is the area of the region bounded by coordinate axis and the line tangent to the graph, y = (1/8)x^2 + (1/2)x + 1, at the point (0, 1)

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{coordinate}\:\mathrm{axis}\:\mathrm{and}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{graph},\:\:\mathrm{y}\:=\:\frac{\mathrm{1}}{\mathrm{8}}\mathrm{x}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\:+\:\mathrm{1},\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\:\left(\mathrm{0},\:\mathrm{1}\right) \\ $$

Question Number 18640 Answers: 1 Comments: 1

Question Number 18639 Answers: 0 Comments: 0

∫(√(1+x^4 )) dx please solve this question.

$$\int\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx} \\ $$$${please}\:{solve}\:{this}\:{question}. \\ $$

Question Number 18632 Answers: 0 Comments: 0

x − 5x + 3 = 7 −4x = 4 x = −1

$${x}\:−\:\mathrm{5}{x}\:+\:\mathrm{3}\:=\:\mathrm{7} \\ $$$$−\mathrm{4}{x}\:=\:\mathrm{4} \\ $$$${x}\:=\:−\mathrm{1} \\ $$

Question Number 18625 Answers: 1 Comments: 1

x−5×+3=7

$$\mathrm{x}−\mathrm{5}×+\mathrm{3}=\mathrm{7} \\ $$

Question Number 18624 Answers: 1 Comments: 0

Argon diffuses through a hole under prescribed condition of temperature and pressure at the rate of 3cm^3 per velocity. At what velocity will helium diffuse through the same hole under the same condition (Ar = 29.94 g, He = 4g).

$$\mathrm{Argon}\:\mathrm{diffuses}\:\mathrm{through}\:\mathrm{a}\:\mathrm{hole}\:\mathrm{under}\:\mathrm{prescribed}\:\mathrm{condition}\:\mathrm{of}\:\mathrm{temperature} \\ $$$$\mathrm{and}\:\mathrm{pressure}\:\mathrm{at}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\:\mathrm{3cm}^{\mathrm{3}} \:\mathrm{per}\:\mathrm{velocity}.\:\mathrm{At}\:\mathrm{what}\:\mathrm{velocity}\:\mathrm{will}\:\mathrm{helium}\: \\ $$$$\mathrm{diffuse}\:\mathrm{through}\:\mathrm{the}\:\mathrm{same}\:\mathrm{hole}\:\mathrm{under}\:\mathrm{the}\:\mathrm{same}\:\mathrm{condition}\: \\ $$$$\left(\mathrm{Ar}\:=\:\mathrm{29}.\mathrm{94}\:\mathrm{g},\:\:\mathrm{He}\:=\:\mathrm{4g}\right). \\ $$

Question Number 18627 Answers: 1 Comments: 1

lim_(x→0) (((sin x)/x))^((sin x)/(x−sin x))

$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\right)^{\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}−\mathrm{sin}\:\mathrm{x}}} \\ $$

Question Number 18614 Answers: 0 Comments: 1

Question Number 18607 Answers: 1 Comments: 1

A block of mass M is pulled vertically upward through a rope of mass m by applying force F on-one end of the rope. What force does the rope exert on the block?

$$\mathrm{A}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:{M}\:\mathrm{is}\:\mathrm{pulled}\:\mathrm{vertically} \\ $$$$\mathrm{upward}\:\mathrm{through}\:\mathrm{a}\:\mathrm{rope}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{by} \\ $$$$\mathrm{applying}\:\mathrm{force}\:{F}\:\mathrm{on}-\mathrm{one}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rope}. \\ $$$$\mathrm{What}\:\mathrm{force}\:\mathrm{does}\:\mathrm{the}\:\mathrm{rope}\:\mathrm{exert}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{block}? \\ $$

Question Number 18606 Answers: 0 Comments: 0

(1/3)+(3/(3×7))+(5/(3×7×11))+(7/(3×7×11×15))+...n terms

$$\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{3}×\mathrm{7}}+\frac{\mathrm{5}}{\mathrm{3}×\mathrm{7}×\mathrm{11}}+\frac{\mathrm{7}}{\mathrm{3}×\mathrm{7}×\mathrm{11}×\mathrm{15}}+...{n}\: \\ $$$$\:{terms} \\ $$

Question Number 18604 Answers: 0 Comments: 0

Question Number 18603 Answers: 0 Comments: 0

The work function of a metal is 4 eV. If light of frequency 2.3 × 10^(15) Hz is incident on metal surface, then, (1) No photoelectron will be ejected (2) 2 photoelectron of zero kinetic energy are ejected (3) 1 photoelectron of zero kinetic energy is ejected (4) 1 photoelectron is ejected, which required the stopping potential of 5.52 volt

$$\mathrm{The}\:\mathrm{work}\:\mathrm{function}\:\mathrm{of}\:\mathrm{a}\:\mathrm{metal}\:\mathrm{is}\:\mathrm{4}\:\mathrm{eV}.\:\mathrm{If} \\ $$$$\mathrm{light}\:\mathrm{of}\:\mathrm{frequency}\:\mathrm{2}.\mathrm{3}\:×\:\mathrm{10}^{\mathrm{15}} \:\mathrm{Hz}\:\mathrm{is} \\ $$$$\mathrm{incident}\:\mathrm{on}\:\mathrm{metal}\:\mathrm{surface},\:\mathrm{then}, \\ $$$$\left(\mathrm{1}\right)\:\mathrm{No}\:\mathrm{photoelectron}\:\mathrm{will}\:\mathrm{be}\:\mathrm{ejected} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}\:\mathrm{photoelectron}\:\mathrm{of}\:\mathrm{zero}\:\mathrm{kinetic} \\ $$$$\mathrm{energy}\:\mathrm{are}\:\mathrm{ejected} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{1}\:\mathrm{photoelectron}\:\mathrm{of}\:\mathrm{zero}\:\mathrm{kinetic} \\ $$$$\mathrm{energy}\:\mathrm{is}\:\mathrm{ejected} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{1}\:\mathrm{photoelectron}\:\mathrm{is}\:\mathrm{ejected},\:\mathrm{which} \\ $$$$\mathrm{required}\:\mathrm{the}\:\mathrm{stopping}\:\mathrm{potential}\:\mathrm{of}\:\mathrm{5}.\mathrm{52} \\ $$$$\mathrm{volt} \\ $$

Question Number 18611 Answers: 1 Comments: 1

Without using L Hospital′s rule prove that lim_(x→0) ((sin x)/x)=1

$$\mathrm{Without}\:\mathrm{using}\:\mathrm{L}\:\mathrm{Hospital}'\mathrm{s} \\ $$$$\mathrm{rule}\:\mathrm{prove}\:\mathrm{that}\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}=\mathrm{1} \\ $$

Question Number 18593 Answers: 1 Comments: 0