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Question Number 11969 Answers: 2 Comments: 0

A gas occupies 30 dm^3 at s t p, what volume will it occupy at 91°C and 380 mmHg

$$\mathrm{A}\:\mathrm{gas}\:\mathrm{occupies}\:\mathrm{30}\:\mathrm{dm}^{\mathrm{3}} \:\mathrm{at}\:\mathrm{s}\:\mathrm{t}\:\mathrm{p},\:\:\mathrm{what}\:\mathrm{volume}\:\mathrm{will}\:\mathrm{it}\:\mathrm{occupy}\:\mathrm{at}\:\mathrm{91}°\mathrm{C}\: \\ $$$$\mathrm{and}\:\mathrm{380}\:\mathrm{mmHg} \\ $$

Question Number 11968 Answers: 0 Comments: 0

A motorcyclist, passing a road junction , moves due east for 8 seconds at a uniform speed of 5 m/s. He then moves due north for another 6 seconds with the same speed. At the end of 6 seconds his displacement from the road junction is 50 m in the diretion of A) 53°E (B) 37°E (C) 53°W (D) 37°W

$$\mathrm{A}\:\mathrm{motorcyclist},\:\mathrm{passing}\:\mathrm{a}\:\mathrm{road}\:\mathrm{junction}\:,\:\mathrm{moves}\:\mathrm{due}\:\mathrm{east}\:\mathrm{for}\:\mathrm{8}\:\mathrm{seconds}\:\mathrm{at} \\ $$$$\mathrm{a}\:\mathrm{uniform}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{5}\:\mathrm{m}/\mathrm{s}.\:\mathrm{He}\:\mathrm{then}\:\mathrm{moves}\:\mathrm{due}\:\mathrm{north}\:\mathrm{for}\:\mathrm{another}\:\mathrm{6}\:\mathrm{seconds} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{same}\:\mathrm{speed}.\:\mathrm{At}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{6}\:\mathrm{seconds}\:\mathrm{his}\:\mathrm{displacement}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{road}\:\mathrm{junction}\:\mathrm{is}\:\mathrm{50}\:\mathrm{m}\:\mathrm{in}\:\mathrm{the}\:\mathrm{diretion}\:\mathrm{of} \\ $$$$\left.\mathrm{A}\right)\:\mathrm{53}°\mathrm{E}\:\:\left(\mathrm{B}\right)\:\:\mathrm{37}°\mathrm{E}\:\:\left(\mathrm{C}\right)\:\:\mathrm{53}°\mathrm{W}\:\:\left(\mathrm{D}\right)\:\:\mathrm{37}°\mathrm{W} \\ $$

Question Number 11966 Answers: 0 Comments: 0

If a force of 200N is used to pull a block of mass 30 kg up a plane inclined at 60° to the horizontal at a steady speed . Calculate the percentage efficiency of the incline plane.

$$\mathrm{If}\:\mathrm{a}\:\mathrm{force}\:\mathrm{of}\:\mathrm{200N}\:\mathrm{is}\:\mathrm{used}\:\mathrm{to}\:\mathrm{pull}\:\mathrm{a}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{30}\:\mathrm{kg}\:\mathrm{up}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{inclined} \\ $$$$\mathrm{at}\:\mathrm{60}°\:\mathrm{to}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{at}\:\mathrm{a}\:\mathrm{steady}\:\mathrm{speed}\:.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{efficiency} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{incline}\:\mathrm{plane}. \\ $$

Question Number 11964 Answers: 0 Comments: 0

A load of 60 kg is pushed up a 400 m incline side of a platform 3 m high. what is the velocity ratio of the plane ?

$$\:\mathrm{A}\:\mathrm{load}\:\mathrm{of}\:\mathrm{60}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{pushed}\:\mathrm{up}\:\mathrm{a}\:\mathrm{400}\:\mathrm{m}\:\mathrm{incline}\:\mathrm{side}\:\mathrm{of}\:\mathrm{a}\:\mathrm{platform}\:\mathrm{3}\:\mathrm{m}\:\mathrm{high}.\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plane}\:? \\ $$

Question Number 11958 Answers: 0 Comments: 1

A∈M_(2016×2016) with the entries a_(ij) {_(0, if i+j≠2016) ^(1, if i+j=2016) find the determinant??

$${A}\in{M}_{\mathrm{2016}×\mathrm{2016}} \: \\ $$$${with}\:{the}\:{entries}\:{a}_{{ij}} \left\{_{\mathrm{0},\:{if}\:{i}+{j}\neq\mathrm{2016}} ^{\mathrm{1},\:{if}\:{i}+{j}=\mathrm{2016}} \right. \\ $$$${find}\:{the}\:{determinant}?? \\ $$

Question Number 11956 Answers: 0 Comments: 2

A , 2B ,3C ,4D are positive numbers forming a geometric series prov that : (A + 3C) (B + 2D) > 2

$${A}\:,\:\mathrm{2}{B}\:,\mathrm{3}{C}\:,\mathrm{4}{D}\: \\ $$$${are}\:{positive}\:{numbers}\:{forming}\:{a}\: \\ $$$${geometric}\:{series}\: \\ $$$${prov}\:{that}\:: \\ $$$$\left({A}\:+\:\mathrm{3}{C}\right)\:\left({B}\:+\:\mathrm{2}{D}\right)\:>\:\mathrm{2} \\ $$

Question Number 11943 Answers: 1 Comments: 0

The solution of the equation x^2 + x + 1 = 1 is

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$${x}^{\mathrm{2}} +\:{x}\:+\:\mathrm{1}\:=\:\mathrm{1}\:\:\:\mathrm{is} \\ $$

Question Number 11937 Answers: 1 Comments: 5

∫(dx/(√(5 + 4x − x^2 ))) is this answer correct ? −ln[1/4(x − 5) − ln6(− 1 − x)] + C

$$\int\frac{\mathrm{dx}}{\sqrt{\mathrm{5}\:+\:\mathrm{4x}\:−\:\mathrm{x}^{\mathrm{2}} }}\: \\ $$$$ \\ $$$$ \\ $$$$\mathrm{is}\:\mathrm{this}\:\mathrm{answer}\:\mathrm{correct}\:?\:\:\:\:\:\:\:\:\:\:\:−\mathrm{ln}\left[\mathrm{1}/\mathrm{4}\left(\mathrm{x}\:−\:\mathrm{5}\right)\:−\:\mathrm{ln6}\left(−\:\mathrm{1}\:−\:\mathrm{x}\right)\right]\:+\:\mathrm{C} \\ $$

Question Number 11935 Answers: 3 Comments: 0

((7!)/(6!))+((8!)/(7!))+((9!)/(8!))+...((n!)/((n−1)!))=84 ⇒n=?

$$\frac{\mathrm{7}!}{\mathrm{6}!}+\frac{\mathrm{8}!}{\mathrm{7}!}+\frac{\mathrm{9}!}{\mathrm{8}!}+...\frac{\mathrm{n}!}{\left(\mathrm{n}−\mathrm{1}\right)!}=\mathrm{84}\:\Rightarrow\mathrm{n}=? \\ $$

Question Number 11930 Answers: 1 Comments: 0

Let a and b be two numbers, x be the single arithmetic mean of a and b. Show that the sum of n arithmetic means between a and b is nx.

$$\mathrm{Let}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{be}\:\mathrm{two}\:\mathrm{numbers},\:\mathrm{x}\:\mathrm{be}\:\mathrm{the}\:\mathrm{single}\:\mathrm{arithmetic}\:\mathrm{mean}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{arithmetic}\:\mathrm{means}\:\mathrm{between}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{nx}. \\ $$

Question Number 11979 Answers: 1 Comments: 0

If the sum of first p terms, first q terms and first r terms of an AP be x, y and z respectively. Then (x/p)(q−r) + (y/q)(r−p) + (z/r)(p−q) is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:{p}\:\mathrm{terms},\:\mathrm{first}\:\:{q}\:\mathrm{terms}\:\mathrm{and} \\ $$$$\mathrm{first}\:{r}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}\:\mathrm{be}\:\:{x},\:{y}\:\:\mathrm{and}\:{z}\: \\ $$$$\mathrm{respectively}.\:\mathrm{Then} \\ $$$$\frac{{x}}{{p}}\left({q}−{r}\right)\:+\:\frac{{y}}{{q}}\left({r}−{p}\right)\:+\:\frac{{z}}{{r}}\left({p}−{q}\right)\:\:\mathrm{is} \\ $$

Question Number 11921 Answers: 1 Comments: 0

given that y=Acos5x + Bsin5x, show that (d^2 y/dx^2 )+25y=0

$${given}\:{that}\:{y}={Acos}\mathrm{5}{x}\:+\:{Bsin}\mathrm{5}{x}, \\ $$$${show}\:{that}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{25}{y}=\mathrm{0} \\ $$

Question Number 11920 Answers: 4 Comments: 0

differentiate each function from first principle 1)f (x) = 1+(1/x) 2)f(x) = (1/(2x+3)) 3) f(x)=sin2x 4)f(x)=co2x

$${differentiate}\:{each}\:{function}\:{from}\:{first}\:{principle} \\ $$$$\left.\mathrm{1}\right){f}\:\left({x}\right)\:=\:\mathrm{1}+\frac{\mathrm{1}}{{x}} \\ $$$$\left.\mathrm{2}\right){f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}{x}+\mathrm{3}}\: \\ $$$$\left.\mathrm{3}\right)\:{f}\left({x}\right)={sin}\mathrm{2}{x} \\ $$$$\left.\mathrm{4}\right){f}\left({x}\right)={co}\mathrm{2}{x} \\ $$$$ \\ $$

Question Number 11915 Answers: 2 Comments: 2

Question Number 11914 Answers: 0 Comments: 0

Turevlenebilir bir f fonksiyonu icin f(x+y)=f(x)+f(y)+2xy ve f′(0)=−3 old.gore f′(2)=? czm∵ f(x+y)=f(x)+f(y)+2xy y yi sabit kabul edersek f′(x+y)=f′(x)+2y x=0,y=2 icn f′(2)=f′(0)+2.2 f′(2)=−3+4=1

$${Turevlenebilir}\:{bir}\:{f}\:{fonksiyonu}\:{icin} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+\mathrm{2}{xy}\:{ve}\:{f}'\left(\mathrm{0}\right)=−\mathrm{3} \\ $$$${old}.{gore}\:{f}'\left(\mathrm{2}\right)=? \\ $$$${czm}\because\:\:{f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+\mathrm{2}{xy} \\ $$$${y}\:{yi}\:{sabit}\:{kabul}\:{edersek} \\ $$$${f}'\left({x}+{y}\right)={f}'\left({x}\right)+\mathrm{2}{y} \\ $$$${x}=\mathrm{0},{y}=\mathrm{2}\:{icn} \\ $$$${f}'\left(\mathrm{2}\right)={f}'\left(\mathrm{0}\right)+\mathrm{2}.\mathrm{2} \\ $$$${f}'\left(\mathrm{2}\right)=−\mathrm{3}+\mathrm{4}=\mathrm{1} \\ $$

Question Number 11913 Answers: 0 Comments: 0

∫x^(x^x ) dx

$$\int\mathrm{x}^{\mathrm{x}^{\mathrm{x}} \:\:} \:\mathrm{dx} \\ $$

Question Number 11902 Answers: 1 Comments: 1

Assuming it rained at a constant rate, and the rain fell at angle θ to the ground (see diagram), determine if walking or running causes you to get more/less wet, or of it makes no difference for: 1. θ=90° (downwards) 2. θ<90° (the rain is moving on the same direction as you) 3. θ>90° (the rain is moving/blowing into you)

$$\mathrm{Assuming}\:\mathrm{it}\:\mathrm{rained}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{rate}, \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{rain}\:\mathrm{fell}\:\mathrm{at}\:\mathrm{angle}\:\theta\:\mathrm{to}\:\mathrm{the}\:\mathrm{ground} \\ $$$$\left(\mathrm{see}\:\mathrm{diagram}\right),\:\mathrm{determine}\:\mathrm{if}\:\mathrm{walking}\:\mathrm{or} \\ $$$$\mathrm{running}\:\mathrm{causes}\:\mathrm{you}\:\mathrm{to}\:\mathrm{get}\:\mathrm{more}/\mathrm{less}\:\mathrm{wet}, \\ $$$$\mathrm{or}\:\mathrm{of}\:\mathrm{it}\:\mathrm{makes}\:\mathrm{no}\:\mathrm{difference}\:\mathrm{for}: \\ $$$$\: \\ $$$$\mathrm{1}.\:\:\:\theta=\mathrm{90}°\:\:\left(\mathrm{downwards}\right) \\ $$$$\mathrm{2}.\:\theta<\mathrm{90}°\:\:\left(\mathrm{the}\:\mathrm{rain}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{on}\:\mathrm{the}\right. \\ $$$$\left.\:\:\:\:\:\:\:\:\:\mathrm{same}\:\mathrm{direction}\:\mathrm{as}\:\mathrm{you}\right) \\ $$$$\mathrm{3}.\:\theta>\mathrm{90}°\:\:\left(\mathrm{the}\:\mathrm{rain}\:\mathrm{is}\:\mathrm{moving}/\mathrm{blowing}\right. \\ $$$$\left.\:\:\:\:\:\:\:\:\:\mathrm{into}\:\mathrm{you}\right) \\ $$

Question Number 11901 Answers: 0 Comments: 0

((7cos^2 x+sin^2 x−3)/(2cos^2 x−sin^2 x))=? czm∵ ((7cos^2 x+1−cos^2 x−3)/(2cos^2 x−sin^2 x)) ((6cos^2 x−2)/(2cos^2 x−(1−cos^2 x)))=((6cos^2 x−2)/(3cos^2 x−1)) ((2(3cos^2 x−1))/(3cos^2 x−1))=2

Question Number 11900 Answers: 1 Comments: 0

Calculate. cos(𝛑/7)×cos((4𝛑)/7)×cos((5𝛑)/7).

$$\boldsymbol{\mathrm{Calculate}}. \\ $$$$\boldsymbol{\mathrm{cos}}\frac{\boldsymbol{\pi}}{\mathrm{7}}×\boldsymbol{\mathrm{cos}}\frac{\mathrm{4}\boldsymbol{\pi}}{\mathrm{7}}×\boldsymbol{\mathrm{cos}}\frac{\mathrm{5}\boldsymbol{\pi}}{\mathrm{7}}. \\ $$

Question Number 11899 Answers: 0 Comments: 0

f′(x)={_(3 ;x>2) ^(2x ; x≤2) f(2)=1 ise f(1)+f(3)=? czm∵ f(x)={_(3x+c_2 ; x>2) ^(x^2 +c_1 ;x≤2) f(2)=x^2 +c_1 dir 1=4+c_1 => c_1 =−3 1=2.3+c_2 => c_2 =−5 f(x)={_(3x−5 x>2) ^(x^2 −3 ;x≤2) f(1)=1^2 −3=−2, f(3)=3.3−5=4 f(1)+f(3)=−2+4=2

$${f}'\left({x}\right)=\left\{_{\mathrm{3}\:\:\:\:\:;{x}>\mathrm{2}} ^{\mathrm{2}{x}\:\:;\:{x}\leqslant\mathrm{2}} \right. \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{1}\:{ise}\:{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{3}\right)=? \\ $$$${czm}\because\:{f}\left({x}\right)=\left\{_{\mathrm{3}{x}+{c}_{\mathrm{2}} \:;\:{x}>\mathrm{2}} ^{{x}^{\mathrm{2}} +{c}_{\mathrm{1}} \:;{x}\leqslant\mathrm{2}} \right. \\ $$$${f}\left(\mathrm{2}\right)={x}^{\mathrm{2}} +{c}_{\mathrm{1}} \:{dir} \\ $$$$\mathrm{1}=\mathrm{4}+{c}_{\mathrm{1}} \:=>\:{c}_{\mathrm{1}} =−\mathrm{3} \\ $$$$\mathrm{1}=\mathrm{2}.\mathrm{3}+{c}_{\mathrm{2}} \:=>\:{c}_{\mathrm{2}} =−\mathrm{5} \\ $$$${f}\left({x}\right)=\left\{_{\mathrm{3}{x}−\mathrm{5}\:\:\:\:{x}>\mathrm{2}} ^{{x}^{\mathrm{2}} −\mathrm{3}\:\:\:;{x}\leqslant\mathrm{2}} \right. \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1}^{\mathrm{2}} −\mathrm{3}=−\mathrm{2},\:{f}\left(\mathrm{3}\right)=\mathrm{3}.\mathrm{3}−\mathrm{5}=\mathrm{4} \\ $$$${f}\left(\mathrm{1}\right)+{f}\left(\mathrm{3}\right)=−\mathrm{2}+\mathrm{4}=\mathrm{2} \\ $$$$ \\ $$

Question Number 11889 Answers: 1 Comments: 0

The number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{8}\: \\ $$$$\mathrm{different}\:\mathrm{flowers}\:\mathrm{can}\:\mathrm{be}\:\mathrm{strung}\:\mathrm{to} \\ $$$$\mathrm{form}\:\mathrm{a}\:\mathrm{garland}\:\mathrm{so}\:\mathrm{that}\:\mathrm{4}\:\mathrm{particular} \\ $$$$\mathrm{flowers}\:\mathrm{are}\:\mathrm{never}\:\mathrm{separated}\:\mathrm{is} \\ $$

Question Number 11886 Answers: 0 Comments: 0

∫x^x^x dx

$$\int\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \:\mathrm{dx} \\ $$

Question Number 11887 Answers: 1 Comments: 0

(dy/dt) +3t^2 y = t^(2 ) , y(0) = 1 y(t) = ?

$$\frac{{dy}}{{dt}}\:+\mathrm{3}{t}^{\mathrm{2}} {y}\:=\:{t}^{\mathrm{2}\:} \:\:\:\:,\:{y}\left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$$${y}\left({t}\right)\:=\:? \\ $$

Question Number 11898 Answers: 1 Comments: 0

(a) You are listening to your favourite song on a CD. You note that the sound wave has a pleasant frequency of 12 Hertz. (i) What is the velovity of the sound wave (ii) What wavelenght are the wave moving at (iii) What is the period (b) 60 complete waves pass a particular point in 4 secs, if the distance between 3 successive troughs of the water is 15m. Calculate the speed of the wave.

Question Number 11883 Answers: 1 Comments: 0

Draw the structural formula of the compound 2,2,7 - trimethyl - 4 - (1 - methylpropyl) nonane

$$\mathrm{Draw}\:\mathrm{the}\:\mathrm{structural}\:\mathrm{formula}\:\mathrm{of}\:\mathrm{the}\:\mathrm{compound} \\ $$$$\mathrm{2},\mathrm{2},\mathrm{7}\:-\:\mathrm{trimethyl}\:-\:\mathrm{4}\:-\:\left(\mathrm{1}\:-\:\mathrm{methylpropyl}\right)\:\mathrm{nonane} \\ $$

Question Number 11880 Answers: 0 Comments: 0

S_(ABCD) =3+2(√2) ∠BAO=∠MAO=22,5° ∠BCM=∠DCM S_(AOB) =?

$$\boldsymbol{\mathrm{S}}_{\boldsymbol{\mathrm{ABCD}}} =\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\angle\boldsymbol{\mathrm{BAO}}=\angle\boldsymbol{\mathrm{MAO}}=\mathrm{22},\mathrm{5}° \\ $$$$\angle\boldsymbol{\mathrm{BCM}}=\angle\boldsymbol{\mathrm{DCM}} \\ $$$$\boldsymbol{\mathrm{S}}_{\boldsymbol{\mathrm{AOB}}} =? \\ $$

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