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AllQuestion and Answers: Page 1921

Question Number 17983 Answers: 1 Comments: 0

Evaluate cos(20°)cos(40°)cos(80°). This question is just for fun and practice. Evryone who wants can answer this question.

$${Evaluate}\:{cos}\left(\mathrm{20}°\right){cos}\left(\mathrm{40}°\right){cos}\left(\mathrm{80}°\right). \\ $$$${This}\:{question}\:{is}\:{just}\:{for}\:{fun}\:{and}\:{practice}. \\ $$$${Evryone}\:{who}\:{wants}\:{can}\:{answer}\:{this}\:{question}. \\ $$

Question Number 17976 Answers: 1 Comments: 0

A driver is 5.2 below the surface of water of density 1000kg/m. if the atmospheric pressure is 1.02 × 10^5 Pa. calculate the pressure on the driver.

$$\mathrm{A}\:\mathrm{driver}\:\mathrm{is}\:\mathrm{5}.\mathrm{2}\:\mathrm{below}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{water}\:\mathrm{of}\:\mathrm{density}\:\mathrm{1000kg}/\mathrm{m}.\:\:\mathrm{if}\:\mathrm{the} \\ $$$$\mathrm{atmospheric}\:\mathrm{pressure}\:\mathrm{is}\:\mathrm{1}.\mathrm{02}\:×\:\mathrm{10}^{\mathrm{5}} \:\mathrm{Pa}.\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{pressure}\:\mathrm{on}\:\mathrm{the}\:\mathrm{driver}. \\ $$

Question Number 17970 Answers: 1 Comments: 0

Question Number 17969 Answers: 0 Comments: 0

Question Number 17963 Answers: 0 Comments: 4

Question Number 17961 Answers: 1 Comments: 0

Question Number 17959 Answers: 1 Comments: 0

Question Number 17957 Answers: 1 Comments: 0

prove that (1+(a/x))^n =(1+((an)/x)) , x≫a

$$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{1}+\frac{\mathrm{a}}{\mathrm{x}}\right)^{\mathrm{n}} =\left(\mathrm{1}+\frac{\mathrm{an}}{\mathrm{x}}\right)\:,\:\:\mathrm{x}\gg\mathrm{a} \\ $$

Question Number 17939 Answers: 1 Comments: 1

∫secxdx

$$\int{secxdx}\: \\ $$

Question Number 17938 Answers: 2 Comments: 2

If only downward motion along lines is allowed, what is the total number of paths from point P to point Q in the figure below?

$$\mathrm{If}\:\mathrm{only}\:\mathrm{downward}\:\mathrm{motion}\:\mathrm{along}\:\mathrm{lines}\:\mathrm{is} \\ $$$$\mathrm{allowed},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{paths}\:\mathrm{from}\:\mathrm{point}\:\mathrm{P}\:\mathrm{to}\:\mathrm{point}\:\mathrm{Q}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{figure}\:\mathrm{below}? \\ $$

Question Number 17936 Answers: 2 Comments: 1

Two particles start moving towards each other with constant acceleration of 1 m/s^2 . If their initial separation is 100 m, find after what time they will meet each other (A) 40s (B) 45s (C) 50 s (D)55s

$$\mathrm{Two}\:\mathrm{particles}\:\mathrm{start}\:\mathrm{moving}\:\mathrm{towards} \\ $$$$\mathrm{each}\:\mathrm{other}\:\mathrm{with}\:\mathrm{constant}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\:\mathrm{1}\:{m}/{s}^{\mathrm{2}} .\:\mathrm{If}\:\mathrm{their}\:\mathrm{initial}\:\mathrm{separation}\:\mathrm{is} \\ $$$$\mathrm{100}\:\mathrm{m},\:\mathrm{find}\:\mathrm{after}\:\mathrm{what}\:\mathrm{time}\:\mathrm{they}\:\mathrm{will} \\ $$$$\mathrm{meet}\:\mathrm{each}\:\mathrm{other} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{40}{s}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{45}{s}\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{50}\:{s}\:\left(\mathrm{D}\right)\mathrm{55}{s} \\ $$

Question Number 17919 Answers: 0 Comments: 0

How do the electronic configurations of the elements with Z = 107 − 109 differ from one another?

$$\mathrm{How}\:\mathrm{do}\:\mathrm{the}\:\mathrm{electronic}\:\mathrm{configurations}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{elements}\:\mathrm{with}\:\mathrm{Z}\:=\:\mathrm{107}\:−\:\mathrm{109}\:\mathrm{differ} \\ $$$$\mathrm{from}\:\mathrm{one}\:\mathrm{another}? \\ $$

Question Number 17918 Answers: 0 Comments: 0

Write the electronic configuration and the block to which an element with Z = 90 belongs.

$$\mathrm{Write}\:\mathrm{the}\:\mathrm{electronic}\:\mathrm{configuration}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{block}\:\mathrm{to}\:\mathrm{which}\:\mathrm{an}\:\mathrm{element}\:\mathrm{with} \\ $$$$\mathrm{Z}\:=\:\mathrm{90}\:\mathrm{belongs}. \\ $$

Question Number 17901 Answers: 1 Comments: 2

Question Number 17895 Answers: 0 Comments: 2

Question Number 17909 Answers: 0 Comments: 1

Please answer Q. 17525

$${Please}\:{answer}\:{Q}.\:\mathrm{17525} \\ $$

Question Number 17890 Answers: 0 Comments: 0

Question Number 17948 Answers: 1 Comments: 3

Question Number 17886 Answers: 0 Comments: 7

Question Number 17884 Answers: 1 Comments: 1

Question Number 17879 Answers: 0 Comments: 0

Question Number 17878 Answers: 0 Comments: 0

Question Number 17872 Answers: 2 Comments: 0

Solve : ∣x − 1∣ + ∣x∣ + ∣x + 1∣ = x + 2

$$\mathrm{Solve}\:: \\ $$$$\mid{x}\:−\:\mathrm{1}\mid\:+\:\mid{x}\mid\:+\:\mid{x}\:+\:\mathrm{1}\mid\:=\:{x}\:+\:\mathrm{2} \\ $$

Question Number 17867 Answers: 1 Comments: 0

prove that (2+(√3))^(2n) +(2−(√3))^(2n) is an even integer and that (2+(√3))^(2n) −(2−(√3))^(2n) =w(√3) for some integers w,for all integer n≥1.

$${prove}\:{that}\:\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} +\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} {is}\:{an} \\ $$$${even}\:{integer}\:{and}\:{that}\:\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} −\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} ={w}\sqrt{\mathrm{3}} \\ $$$${for}\:{some}\:{integers}\:{w},{for}\:{all}\:{integer}\:{n}\geqslant\mathrm{1}. \\ $$$$ \\ $$

Question Number 17866 Answers: 1 Comments: 0

Prove that sin 5A = 5 cos^4 A sin A − 10 cos^2 A sin^3 A + sin^5 A

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{sin}\:\mathrm{5}{A}\:=\:\mathrm{5}\:\mathrm{cos}^{\mathrm{4}} \:{A}\:\mathrm{sin}\:{A}\:− \\ $$$$\mathrm{10}\:\mathrm{cos}^{\mathrm{2}} \:{A}\:\mathrm{sin}^{\mathrm{3}} \:{A}\:+\:\mathrm{sin}^{\mathrm{5}} \:{A} \\ $$

Question Number 17852 Answers: 0 Comments: 1

A particle moves in a straight line (x-axis) with the velocity shown in the figure. Knowing that x = −16 m at t = 0, draw the a-t and x-t curves for the interval 0 < t < 40 s and determine (i) Maximum value of the position coordinate of the particle. (ii) The values of t for which the particle is at a distance of 50 m from the origin.

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\left({x}-\mathrm{axis}\right)\:\mathrm{with}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{figure}.\:\mathrm{Knowing}\:\mathrm{that}\:{x}\:=\:−\mathrm{16}\:\mathrm{m}\:\mathrm{at} \\ $$$${t}\:=\:\mathrm{0},\:\mathrm{draw}\:\mathrm{the}\:{a}-{t}\:\mathrm{and}\:{x}-{t}\:\mathrm{curves}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{interval}\:\mathrm{0}\:<\:{t}\:<\:\mathrm{40}\:\mathrm{s}\:\mathrm{and}\:\mathrm{determine} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{position} \\ $$$$\mathrm{coordinate}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{The}\:\mathrm{values}\:\mathrm{of}\:{t}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the} \\ $$$$\mathrm{particle}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{50}\:\mathrm{m}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{origin}. \\ $$

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