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Question Number 13735 Answers: 2 Comments: 6

Question Number 13731 Answers: 0 Comments: 1

Prove that if p>q>0 and x≥0 (1/p)((x^p /(p+1))−1)≥(1/q)((x^q /(q+1))−1).

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:{p}>{q}>\mathrm{0}\:\mathrm{and}\:{x}\geqslant\mathrm{0} \\ $$$$\frac{\mathrm{1}}{{p}}\left(\frac{{x}^{{p}} }{{p}+\mathrm{1}}−\mathrm{1}\right)\geqslant\frac{\mathrm{1}}{{q}}\left(\frac{{x}^{{q}} }{{q}+\mathrm{1}}−\mathrm{1}\right).\: \\ $$

Question Number 13733 Answers: 0 Comments: 4

Question continuing from mrW1 post on p^2 mod n≡1. Find a number n such that for all m<n such that HCF(m,n)=1 m^2 mod n =1 e.g. for 12 possible value of m are 1,5,7,11.

$$\mathrm{Question}\:\mathrm{continuing}\:\mathrm{from} \\ $$$$\mathrm{mrW1}\:\mathrm{post}\:\mathrm{on}\:{p}^{\mathrm{2}} \:\mathrm{mod}\:\mathrm{n}\equiv\mathrm{1}. \\ $$$$\mathrm{Find}\:\mathrm{a}\:\mathrm{number}\:{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{for}\:\mathrm{all}\:{m}<{n}\:\mathrm{such}\:\mathrm{that}\:\mathrm{HCF}\left({m},{n}\right)=\mathrm{1} \\ $$$${m}^{\mathrm{2}} \:\mathrm{mod}\:{n}\:=\mathrm{1} \\ $$$${e}.{g}.\:\mathrm{for}\:\mathrm{12}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{m} \\ $$$$\mathrm{are}\:\mathrm{1},\mathrm{5},\mathrm{7},\mathrm{11}. \\ $$

Question Number 13728 Answers: 1 Comments: 0

Prove that n!>((n/3))^n

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{n}!>\left(\frac{{n}}{\mathrm{3}}\right)^{{n}} \\ $$

Question Number 13727 Answers: 1 Comments: 1

A light wire which obeys hooke′s law hangs vertically on a fixed support. The wire has an unstretched lenght of 15cm. The lenght of the wire however increase to 20cm when a load of 0.5kg is attached to it lower end . What is the tension in the wire when the load is at rest ?. If the load is pulled down until the lenght of the wire is 22cm. What is the new tension in the wire (g = 9.8 m/s).

Question Number 13725 Answers: 0 Comments: 2

(1/7)=.142857^(−) (1/7) is a recurring decimal of period 6. What will be the period of (1/7^(20) )?

$$\frac{\mathrm{1}}{\mathrm{7}}=.\overline {\mathrm{142857}} \\ $$$$\frac{\mathrm{1}}{\mathrm{7}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{recurring}\:\mathrm{decimal}\:\mathrm{of}\:\mathrm{period}\:\mathrm{6}. \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{period}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{20}} }? \\ $$

Question Number 13724 Answers: 2 Comments: 3

Expansion of 1000! has 249, 0′s at the end Find the first non−zero digit from right. 1000!=......d000...00 What is the value of d?

$$\mathrm{Expansion}\:\mathrm{of}\:\mathrm{1000}!\:\mathrm{has}\:\mathrm{249},\:\mathrm{0}'{s}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{non}−\mathrm{zero}\:\mathrm{digit}\:\mathrm{from} \\ $$$$\mathrm{right}. \\ $$$$\mathrm{1000}!=......{d}\mathrm{000}...\mathrm{00} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{d}? \\ $$

Question Number 13721 Answers: 0 Comments: 0

what is NBS?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{NBS}? \\ $$

Question Number 13706 Answers: 1 Comments: 0

The volume of a right circular cone is 5 litres . Calculate the volumes of the two parts into which the cone is divided by a plane parallel to the base , One third of the way down from the vertex to the base. Give your answer to the nearest ml.

Question Number 13705 Answers: 1 Comments: 3

Assuming no air resistance, and angle of projection α=(π/4) , find the ratio of the length of trajectory L of a projectile motion (by the time it hits the ground) to its horizontal range R on ground. (L/R)=?

$${Assuming}\:{no}\:{air}\:{resistance}, \\ $$$${and}\:{angle}\:{of}\:{projection}\:\alpha=\frac{\pi}{\mathrm{4}}\:, \\ $$$${find}\:{the}\:{ratio}\:{of}\:{the}\:{length}\:{of} \\ $$$${trajectory}\:\boldsymbol{{L}}\:{of}\:{a}\:{projectile}\:{motion}\: \\ $$$$\left({by}\:{the}\:{time}\:{it}\:{hits}\:{the}\:{ground}\right) \\ $$$${to}\:{its}\:{horizontal}\:{range}\:\boldsymbol{{R}}\:{on}\: \\ $$$${ground}.\:\:\:\:\:\:\frac{\boldsymbol{{L}}}{\boldsymbol{{R}}}=? \\ $$

Question Number 13695 Answers: 1 Comments: 2

Volume of a bubble is 3 times larger when it reaches the surface from the bottom of the lake. What is the depth of the lake? (A) 10 m (D) 40 m (B) 20 m (E) 50 m (C) 30 m

$$\mathrm{Volume}\:\mathrm{of}\:\mathrm{a}\:\mathrm{bubble}\:\mathrm{is}\:\mathrm{3}\:\mathrm{times}\:\mathrm{larger} \\ $$$$\mathrm{when}\:\mathrm{it}\:\mathrm{reaches}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{from}\:\mathrm{the}\:\mathrm{bottom} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{lake}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{depth}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lake}? \\ $$$$ \\ $$$$\left(\mathrm{A}\right)\:\mathrm{10}\:\mathrm{m}\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{40}\:\mathrm{m} \\ $$$$\left(\mathrm{B}\right)\:\mathrm{20}\:\mathrm{m}\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{E}\right)\:\mathrm{50}\:\mathrm{m} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{30}\:\mathrm{m} \\ $$

Question Number 13688 Answers: 1 Comments: 0

Question Number 13687 Answers: 0 Comments: 4

Question Number 13681 Answers: 1 Comments: 3

Question Number 13658 Answers: 1 Comments: 0

Prove that cos^2 x + cos^2 3x + cos^2 5x + ... to n terms = (1/2)[n + ((sin4nx)/(2sin2x))]

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{cos}^{\mathrm{2}} \mathrm{3}{x}\:+\:\mathrm{cos}^{\mathrm{2}} \mathrm{5}{x}\:+\:...\:\mathrm{to}\:{n}\:\mathrm{terms} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\left[{n}\:+\:\frac{\mathrm{sin4}{nx}}{\mathrm{2sin2}{x}}\right] \\ $$

Question Number 13654 Answers: 1 Comments: 0

The sum of the series sinθ + sin(((n − 4)/(n − 2)))θ + sin(((n − 6)/(n − 2)))θ + ... n terms is equal to (1) sin(((nθ)/(2 − n))) (2) cos(((2nθ)/(2 − n))) (3) tannθ (4) cotnθ

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\mathrm{sin}\theta\:+\:\mathrm{sin}\left(\frac{{n}\:−\:\mathrm{4}}{{n}\:−\:\mathrm{2}}\right)\theta\:+\:\mathrm{sin}\left(\frac{{n}\:−\:\mathrm{6}}{{n}\:−\:\mathrm{2}}\right)\theta\:+\:...\:{n}\:\mathrm{terms} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{sin}\left(\frac{{n}\theta}{\mathrm{2}\:−\:{n}}\right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{cos}\left(\frac{\mathrm{2}{n}\theta}{\mathrm{2}\:−\:{n}}\right) \\ $$$$\left(\mathrm{3}\right)\:\mathrm{tan}{n}\theta \\ $$$$\left(\mathrm{4}\right)\:\mathrm{cot}{n}\theta \\ $$

Question Number 13649 Answers: 1 Comments: 0

2xyy′+(x−1)y^2 =x^2 e^x

$$\mathrm{2}{xyy}'+\left({x}−\mathrm{1}\right){y}^{\mathrm{2}} ={x}^{\mathrm{2}} {e}^{{x}} \\ $$

Question Number 13647 Answers: 0 Comments: 6

x^2 +y^2 =5.....(1) 3x^2 +xy+y^2 =1.....(2) please help find x and y

$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{5}.....\left(\mathrm{1}\right) \\ $$$$\mathrm{3x}^{\mathrm{2}} +\mathrm{xy}+\mathrm{y}^{\mathrm{2}} =\mathrm{1}.....\left(\mathrm{2}\right) \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$

Question Number 13645 Answers: 0 Comments: 0

please is factor theorem and error and trial the same? please help cause i think theres a difference but i cant explain it. Thankz.

$$\mathrm{please}\:\mathrm{is}\:\mathrm{factor}\:\mathrm{theorem}\:\mathrm{and}\:\mathrm{error} \\ $$$$\mathrm{and}\:\mathrm{trial}\:\mathrm{the}\:\mathrm{same}?\:\mathrm{please}\:\mathrm{help}\: \\ $$$$\mathrm{cause}\:\mathrm{i}\:\mathrm{think}\:\mathrm{theres}\:\mathrm{a}\:\mathrm{difference} \\ $$$$\mathrm{but}\:\mathrm{i}\:\mathrm{cant}\:\mathrm{explain}\:\mathrm{it}. \\ $$$$ \\ $$$$\mathrm{Thankz}. \\ $$

Question Number 13636 Answers: 1 Comments: 0

A steam envine of efficiency 70% burns 20g of coal to produce 10kJ of energy.If it burns 200g of coal per second,calculate its output power.