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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