Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1936

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).

$$\mathrm{A}\:\mathrm{light}\:\mathrm{wire}\:\mathrm{which}\:\mathrm{obeys}\:\mathrm{hooke}'\mathrm{s}\:\mathrm{law}\:\mathrm{hangs}\:\mathrm{vertically}\:\mathrm{on}\:\mathrm{a}\:\mathrm{fixed}\:\mathrm{support}. \\ $$$$\mathrm{The}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{an}\:\mathrm{unstretched}\:\mathrm{lenght}\:\mathrm{of}\:\mathrm{15cm}.\:\:\mathrm{The}\:\mathrm{lenght}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{however} \\ $$$$\mathrm{increase}\:\mathrm{to}\:\mathrm{20cm}\:\mathrm{when}\:\mathrm{a}\:\mathrm{load}\:\mathrm{of}\:\mathrm{0}.\mathrm{5kg}\:\mathrm{is}\:\mathrm{attached}\:\mathrm{to}\:\mathrm{it}\:\mathrm{lower}\:\mathrm{end}\:.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{tension}\:\mathrm{in}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{when}\:\mathrm{the}\:\mathrm{load}\:\mathrm{is}\:\mathrm{at}\:\mathrm{rest}\:?.\: \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{load}\:\mathrm{is}\:\mathrm{pulled}\:\mathrm{down}\:\mathrm{until}\:\mathrm{the}\:\mathrm{lenght}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{is}\:\mathrm{22cm}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{new} \\ $$$$\mathrm{tension}\:\mathrm{in}\:\mathrm{the}\:\mathrm{wire}\:\left(\mathrm{g}\:=\:\mathrm{9}.\mathrm{8}\:\mathrm{m}/\mathrm{s}\right). \\ $$

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.

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

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.

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

Question Number 13627    Answers: 1   Comments: 0

Question Number 13626    Answers: 1   Comments: 0

Prove that cosech^(−1) (x) = sinh^(−1) ((1/x))

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{cosech}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=\:\mathrm{sinh}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right) \\ $$

Question Number 13609    Answers: 1   Comments: 0

Question Number 13608    Answers: 0   Comments: 2

if distance is given by x(t)=2t+5 then ,the acceleration at 4s is............

$$\mathrm{if}\:\mathrm{distance}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\mathrm{x}\left(\mathrm{t}\right)=\mathrm{2t}+\mathrm{5}\:\mathrm{then}\:,\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{at}\:\mathrm{4s}\:\mathrm{is}............ \\ $$

Question Number 13606    Answers: 1   Comments: 0

Show that 19^(93) − 13^(99) is a positive integer divisible by 162.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{19}^{\mathrm{93}} \:−\:\mathrm{13}^{\mathrm{99}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{positive} \\ $$$$\mathrm{integer}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{162}. \\ $$

Question Number 13732    Answers: 1   Comments: 3

Sum the following: tan x+2tan 2x+2^2 tan 2^2 x+...+2^n tan 2^n x

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{following}: \\ $$$$\mathrm{tan}\:{x}+\mathrm{2tan}\:\mathrm{2}{x}+\mathrm{2}^{\mathrm{2}} \mathrm{tan}\:\mathrm{2}^{\mathrm{2}} {x}+...+\mathrm{2}^{{n}} \mathrm{tan}\:\mathrm{2}^{{n}} {x} \\ $$

Question Number 13601    Answers: 1   Comments: 0

Let f : R − {(3/5)} → R be defined by f(x) = ((3x + 2)/(5x − 3)) . Then, (a) f^(−1) (x) = x (b) f^(−1) (x) = −f(x) (c) fof(x) = −x (d) f^(−1) (x) = (1/(19))f(x)

$$\mathrm{Let}\:{f}\::\:\mathbb{R}\:−\:\left\{\frac{\mathrm{3}}{\mathrm{5}}\right\}\:\rightarrow\:\mathbb{R}\:\mathrm{be}\:\mathrm{defined}\:\mathrm{by} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{3}{x}\:+\:\mathrm{2}}{\mathrm{5}{x}\:−\:\mathrm{3}}\:.\:\mathrm{Then}, \\ $$$$\left(\mathrm{a}\right)\:{f}^{−\mathrm{1}} \left({x}\right)\:=\:{x} \\ $$$$\left(\mathrm{b}\right)\:{f}^{−\mathrm{1}} \left({x}\right)\:=\:−{f}\left({x}\right) \\ $$$$\left(\mathrm{c}\right)\:{fof}\left({x}\right)\:=\:−{x} \\ $$$$\left(\mathrm{d}\right)\:{f}^{−\mathrm{1}} \left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{19}}{f}\left({x}\right) \\ $$

Question Number 13622    Answers: 1   Comments: 0

Evaluate: ∫_0 ^(2π) e^(x/2) sin ((x/2) + (π/4))dx

$$\mathrm{Evaluate}:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {e}^{\frac{{x}}{\mathrm{2}}} \mathrm{sin}\:\left(\frac{{x}}{\mathrm{2}}\:+\:\frac{\pi}{\mathrm{4}}\right){dx} \\ $$

Question Number 13623    Answers: 1   Comments: 0

Evaluate: ∫_0 ^(2π) e^x cos ((π/4) + (x/2))dx

$$\mathrm{Evaluate}:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {e}^{{x}} \:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{4}}\:+\:\frac{{x}}{\mathrm{2}}\right){dx} \\ $$

Question Number 13598    Answers: 0   Comments: 1

If g(x) = x^2 + x − 2 and (1/2) gof(x) = 2x^2 − 5x + 2, then prove that f(x) = 2x − 3.

$$\mathrm{If}\:{g}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:+\:{x}\:−\:\mathrm{2}\:\mathrm{and} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:{gof}\left({x}\right)\:=\:\mathrm{2}{x}^{\mathrm{2}} \:−\:\mathrm{5}{x}\:+\:\mathrm{2},\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:−\:\mathrm{3}. \\ $$

  Pg 1931      Pg 1932      Pg 1933      Pg 1934      Pg 1935      Pg 1936      Pg 1937      Pg 1938      Pg 1939      Pg 1940   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com