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AllQuestion and Answers: Page 1895

Question Number 19986    Answers: 1   Comments: 0

An aeroplane has to go from a point A to point B, 500 km away due 30° east of north. A wind is blowing due north at a speed of 20 ms^(−1) . The air speed of the plane is 150 ms^(−1) . Find the direction in which the pilot should head the plane to reach point B.

$$\mathrm{An}\:\mathrm{aeroplane}\:\mathrm{has}\:\mathrm{to}\:\mathrm{go}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:{A} \\ $$$$\mathrm{to}\:\mathrm{point}\:{B},\:\mathrm{500}\:\mathrm{km}\:\mathrm{away}\:\mathrm{due}\:\mathrm{30}°\:\mathrm{east} \\ $$$$\mathrm{of}\:\mathrm{north}.\:\mathrm{A}\:\mathrm{wind}\:\mathrm{is}\:\mathrm{blowing}\:\mathrm{due}\:\mathrm{north} \\ $$$$\mathrm{at}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{20}\:\mathrm{ms}^{−\mathrm{1}} .\:\mathrm{The}\:\mathrm{air}\:\mathrm{speed}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{150}\:\mathrm{ms}^{−\mathrm{1}} .\:\mathrm{Find}\:\mathrm{the}\:\mathrm{direction} \\ $$$$\mathrm{in}\:\mathrm{which}\:\mathrm{the}\:\mathrm{pilot}\:\mathrm{should}\:\mathrm{head}\:\mathrm{the} \\ $$$$\mathrm{plane}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{point}\:{B}. \\ $$

Question Number 19982    Answers: 1   Comments: 1

What is the number of ordered pairs (A, B) where A and B are subsets of {1, 2, ..., 5} such that neither A ⊆ B nor B ⊆ A?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ordered}\:\mathrm{pairs} \\ $$$$\left({A},\:{B}\right)\:\mathrm{where}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{subsets}\:\mathrm{of} \\ $$$$\left\{\mathrm{1},\:\mathrm{2},\:...,\:\mathrm{5}\right\}\:\mathrm{such}\:\mathrm{that}\:\mathrm{neither}\:{A}\:\subseteq\:{B} \\ $$$$\mathrm{nor}\:{B}\:\subseteq\:{A}? \\ $$

Question Number 19970    Answers: 0   Comments: 4

The velocity-time graph of a body is shown in figure. The displacement covered by the body in 8 seconds is

$$\mathrm{The}\:\mathrm{velocity}-\mathrm{time}\:\mathrm{graph}\:\mathrm{of}\:\mathrm{a}\:\mathrm{body}\:\mathrm{is} \\ $$$$\mathrm{shown}\:\mathrm{in}\:\mathrm{figure}.\:\mathrm{The}\:\mathrm{displacement} \\ $$$$\mathrm{covered}\:\mathrm{by}\:\mathrm{the}\:\mathrm{body}\:\mathrm{in}\:\mathrm{8}\:\mathrm{seconds}\:\mathrm{is} \\ $$

Question Number 19976    Answers: 1   Comments: 0

Three vectors A^(→) , B^(→) and C^(→) add up to zero. Find which is false. (a) (A^(→) ×B^(→) )×C^(→) is not zero unless B^(→) , C^(→) are parallel (b) (A^(→) ×B^(→) )∙C^(→) is not zero unless B^(→) , C^(→) are parallel (c) If A^(→) , B^(→) , C^(→) define a plane, (A^(→) ×B^(→) ×C^(→) ) is in that plane (d) (A^(→) ×B^(→) ).C^(→) = ∣A^(→) ∣∣B^(→) ∣∣C^(→) ∣ → C^2 = A^2 + B^2

$$\mathrm{Three}\:\mathrm{vectors}\:\overset{\rightarrow} {{A}},\:\overset{\rightarrow} {{B}}\:\mathrm{and}\:\overset{\rightarrow} {{C}}\:\mathrm{add}\:\mathrm{up}\:\mathrm{to} \\ $$$$\mathrm{zero}.\:\mathrm{Find}\:\mathrm{which}\:\mathrm{is}\:\mathrm{false}. \\ $$$$\left({a}\right)\:\left(\overset{\rightarrow} {{A}}×\overset{\rightarrow} {{B}}\right)×\overset{\rightarrow} {{C}}\:\mathrm{is}\:\mathrm{not}\:\mathrm{zero}\:\mathrm{unless}\:\overset{\rightarrow} {{B}},\:\overset{\rightarrow} {{C}} \\ $$$$\mathrm{are}\:\mathrm{parallel} \\ $$$$\left({b}\right)\:\left(\overset{\rightarrow} {{A}}×\overset{\rightarrow} {{B}}\right)\centerdot\overset{\rightarrow} {{C}}\:\mathrm{is}\:\mathrm{not}\:\mathrm{zero}\:\mathrm{unless}\:\overset{\rightarrow} {{B}},\:\overset{\rightarrow} {{C}} \\ $$$$\mathrm{are}\:\mathrm{parallel} \\ $$$$\left({c}\right)\:\mathrm{If}\:\overset{\rightarrow} {{A}},\:\overset{\rightarrow} {{B}},\:\overset{\rightarrow} {{C}}\:\mathrm{define}\:\mathrm{a}\:\mathrm{plane},\:\left(\overset{\rightarrow} {{A}}×\overset{\rightarrow} {{B}}×\overset{\rightarrow} {{C}}\right) \\ $$$$\mathrm{is}\:\mathrm{in}\:\mathrm{that}\:\mathrm{plane} \\ $$$$\left({d}\right)\:\left(\overset{\rightarrow} {{A}}×\overset{\rightarrow} {{B}}\right).\overset{\rightarrow} {{C}}\:=\:\mid\overset{\rightarrow} {{A}}\mid\mid\overset{\rightarrow} {{B}}\mid\mid\overset{\rightarrow} {{C}}\mid\:\rightarrow\:{C}^{\mathrm{2}} \:=\:{A}^{\mathrm{2}} \:+\:{B}^{\mathrm{2}} \\ $$

Question Number 19964    Answers: 1   Comments: 1

Question Number 19955    Answers: 1   Comments: 2

Question Number 19948    Answers: 0   Comments: 0

Question Number 19945    Answers: 1   Comments: 0

If α and β are the roots of equation x^2 + px + q = 0 and α^2 , β^2 are roots of the equation x^2 − rx + s = 0, show that the equation x^2 − 4qx + 2q^2 − r = 0 has real roots.

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{equation} \\ $$$${x}^{\mathrm{2}} \:+\:{px}\:+\:{q}\:=\:\mathrm{0}\:\mathrm{and}\:\alpha^{\mathrm{2}} ,\:\beta^{\mathrm{2}} \:\mathrm{are}\:\mathrm{roots}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} \:−\:{rx}\:+\:{s}\:=\:\mathrm{0},\:\mathrm{show} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} \:−\:\mathrm{4}{qx}\:+\:\mathrm{2}{q}^{\mathrm{2}} \:−\:{r}\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{real}\:\mathrm{roots}. \\ $$

Question Number 19940    Answers: 0   Comments: 2

A circle is inscribed in an isosceles trapezium. Prove that the ratio of the area of the circle to the area of the trapezium is equal to the ratio of the circum- ference of the circle to the perimeter of the trapezium.

$${A}\:{circle}\:{is}\:{inscribed}\:{in}\:{an} \\ $$$${isosceles}\:{trapezium}.\:{Prove}\:{that} \\ $$$${the}\:{ratio}\:{of}\:{the}\:{area}\:{of}\:{the}\:{circle} \\ $$$${to}\:{the}\:{area}\:{of}\:{the}\:{trapezium}\:{is} \\ $$$${equal}\:{to}\:{the}\:{ratio}\:{of}\:{the}\:{circum}- \\ $$$${ference}\:{of}\:{the}\:{circle}\:{to}\:{the}\: \\ $$$${perimeter}\:{of}\:{the}\:{trapezium}. \\ $$

Question Number 19939    Answers: 0   Comments: 0

f(x)=lnx

$${f}\left({x}\right)={lnx} \\ $$

Question Number 19936    Answers: 1   Comments: 1

Find the pricipal value of (1−i)^(1+i) .

$${Find}\:{the}\:{pricipal}\:{value}\:{of}\: \\ $$$$\:\:\:\:\:\left(\mathrm{1}−{i}\right)^{\mathrm{1}+{i}} \:. \\ $$

Question Number 19935    Answers: 0   Comments: 0

Which of the following points is a convex combination of (2, − 5, 0) and and (− 4, 2, 4) in R^3 (a) (0, 6, 1) (b) (− 4, − 2, 5) (c) (− 1, 0, 4) (d) (− 2, − (1/3), (8/3)) (e) None of the above

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{points}\:\mathrm{is}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{combination}\:\mathrm{of}\:\left(\mathrm{2},\:−\:\mathrm{5},\:\mathrm{0}\right)\:\mathrm{and} \\ $$$$\mathrm{and}\:\left(−\:\mathrm{4},\:\mathrm{2},\:\mathrm{4}\right)\:\mathrm{in}\:\mathbb{R}^{\mathrm{3}} \\ $$$$\left(\mathrm{a}\right)\:\:\left(\mathrm{0},\:\mathrm{6},\:\mathrm{1}\right) \\ $$$$\left(\mathrm{b}\right)\:\left(−\:\mathrm{4},\:−\:\mathrm{2},\:\mathrm{5}\right) \\ $$$$\left(\mathrm{c}\right)\:\left(−\:\mathrm{1},\:\mathrm{0},\:\mathrm{4}\right) \\ $$$$\left(\mathrm{d}\right)\:\left(−\:\mathrm{2},\:−\:\frac{\mathrm{1}}{\mathrm{3}},\:\frac{\mathrm{8}}{\mathrm{3}}\right) \\ $$$$\left(\mathrm{e}\right)\:\mathrm{None}\:\mathrm{of}\:\mathrm{the}\:\mathrm{above} \\ $$

Question Number 20132    Answers: 1   Comments: 0

Question Number 19953    Answers: 0   Comments: 0

Question Number 19920    Answers: 0   Comments: 2

lim_(n→∞) n∫_0 ^∞ sin x^n dx

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{n}\int_{\mathrm{0}} ^{\infty} \mathrm{sin}\:{x}^{{n}} \mathrm{d}{x} \\ $$

Question Number 19914    Answers: 0   Comments: 0

Question Number 19912    Answers: 1   Comments: 1

Question Number 19905    Answers: 0   Comments: 2

am get a trou ble to decrea se the size of text! where c an i able to de crease the size of text?

$$\mathrm{am}\:\mathrm{get}\:\mathrm{a}\:\mathrm{trou} \\ $$$$\mathrm{ble}\:\mathrm{to}\:\mathrm{decrea} \\ $$$$\mathrm{se}\:\mathrm{the}\:\mathrm{size}\:\mathrm{of}\: \\ $$$$\mathrm{text}!\:\mathrm{where}\:\mathrm{c} \\ $$$$\mathrm{an}\:\mathrm{i}\:\mathrm{able}\:\mathrm{to}\:\mathrm{de} \\ $$$$\mathrm{crease}\:\mathrm{the}\:\mathrm{size} \\ $$$$\mathrm{of}\:\mathrm{text}? \\ $$

Question Number 19915    Answers: 2   Comments: 3

Question Number 19903    Answers: 1   Comments: 0

by use the first principle,find dy/dx of y=cos(x−(Π/8))

$$\mathrm{by}\:\mathrm{use}\:\mathrm{the}\:\mathrm{first}\: \\ $$$$\mathrm{principle},\mathrm{find} \\ $$$$\mathrm{dy}/\mathrm{dx}\:\mathrm{of}\: \\ $$$$\mathrm{y}=\mathrm{cos}\left(\mathrm{x}−\frac{\Pi}{\mathrm{8}}\right) \\ $$

Question Number 19900    Answers: 2   Comments: 0

Prove that this is an identity in x: (((x−a)(x−b))/((c−a)(c−b)))+(((x−b)(x−c))/((a−b)(a−c)))+(((x−c)(x−a))/((b−c)(b−a)))=1

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{this}\:\mathrm{is}\:\mathrm{an}\:\mathrm{identity}\:\mathrm{in}\:{x}: \\ $$$$\frac{\left({x}−{a}\right)\left({x}−{b}\right)}{\left({c}−{a}\right)\left({c}−{b}\right)}+\frac{\left({x}−{b}\right)\left({x}−{c}\right)}{\left({a}−{b}\right)\left({a}−{c}\right)}+\frac{\left({x}−{c}\right)\left({x}−{a}\right)}{\left({b}−{c}\right)\left({b}−{a}\right)}=\mathrm{1} \\ $$

Question Number 19895    Answers: 1   Comments: 1

Question Number 19898    Answers: 2   Comments: 0

Simplify : i log (((x − i)/(x + i))).

$$\mathrm{Simplify}\::\:{i}\:\mathrm{log}\:\left(\frac{{x}\:−\:{i}}{{x}\:+\:{i}}\right). \\ $$

Question Number 19890    Answers: 1   Comments: 0

A man on top of a tower of height 35m throws a stone vertically upwards with a speed of 14m/s. Find: (i)the height above the ground, reached by the stone. (ii)the speed of the stone,when it reaches the ground.

$${A}\:{man}\:{on}\:{top}\:{of}\:{a}\:{tower}\:{of}\:{height} \\ $$$$\mathrm{35}{m}\:{throws}\:{a}\:{stone}\:{vertically} \\ $$$${upwards}\:{with}\:{a}\:{speed}\:{of}\:\mathrm{14}{m}/{s}. \\ $$$${Find}: \\ $$$$\left({i}\right){the}\:{height}\:{above}\:{the}\:{ground}, \\ $$$${reached}\:{by}\:{the}\:{stone}. \\ $$$$\left({ii}\right){the}\:{speed}\:{of}\:{the}\:{stone},{when} \\ $$$${it}\:{reaches}\:{the}\:{ground}. \\ $$

Question Number 19886    Answers: 0   Comments: 1

Good morning sirs.Please is there any site or pdf that really explains motion(from equation of motion to Newton′s laws of motion)? if there is pls mrw1 ,ajfour ,123456 ,Tinkutara, mr b.e.h.i ,joel and others please help out;i really need to learn it. Thanks.

$${Good}\:{morning}\:{sirs}.{Please}\:{is} \\ $$$${there}\:{any}\:{site}\:{or}\:{pdf}\:{that}\:{really} \\ $$$${explains}\:{motion}\left({from}\:{equation}\right. \\ $$$${of}\:{motion}\:{to}\:{Newton}'{s}\:{laws}\:{of} \\ $$$$\left.{motion}\right)?\: \\ $$$${if}\:{there}\:{is}\:{pls} \\ $$$${mrw}\mathrm{1}\:,{ajfour}\:,\mathrm{123456}\:,{Tinkutara}, \\ $$$${mr}\:{b}.{e}.{h}.{i}\:,{joel}\:{and}\:{others}\:{please} \\ $$$${help}\:{out};{i}\:{really}\:{need}\:{to}\:{learn}\:{it}. \\ $$$$ \\ $$$${Thanks}. \\ $$$$ \\ $$

Question Number 19884    Answers: 1   Comments: 1

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