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AllQuestion and Answers: Page 1822

Question Number 27579 Answers: 1 Comments: 0

A circle with center (−3,1) passes through the point (3,1). Find it′s equation

$$\mathrm{A}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{center}\:\left(−\mathrm{3},\mathrm{1}\right) \\ $$$$\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\: \\ $$$$\left(\mathrm{3},\mathrm{1}\right).\:\mathrm{Find}\:\mathrm{it}'\mathrm{s}\:\mathrm{equation} \\ $$

Question Number 27578 Answers: 0 Comments: 1

if f(x)=((2x−3)/((x^2 −1)(x+2))) 1. Find the value for which f(x) is undefied. 2.Express f(x) in partial fraction

$$\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{2x}−\mathrm{3}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{x}+\mathrm{2}\right)} \\ $$$$\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{for}\:\mathrm{which}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{undefied}. \\ $$$$\mathrm{2}.\mathrm{Express}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fraction} \\ $$

Question Number 27577 Answers: 0 Comments: 0

find the equation of the line of the stationary point y=x^2 (x−3) and the distance between them

$$\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{stationary}\:\mathrm{point}\: \\ $$$$\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{x}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}−\mathrm{3}\right)\: \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{them} \\ $$

Question Number 27594 Answers: 0 Comments: 1

solve the differencial equation (1−x^2 )y^′ −xy =1 .

$${solve}\:{the}\:\:{differencial}\:{equation} \\ $$$$\left(\mathrm{1}−{x}^{\mathrm{2}} \right){y}^{'} \:−{xy}\:=\mathrm{1}\:\:\:. \\ $$

Question Number 27568 Answers: 1 Comments: 0

carol is 6 times as old as her nephew Hondo.Baby is 22 years yonger than her aunt carol.In four years carol′s age will be twice the sum of Hondo′s and Baby′s age.How old is each perso n now?

$${carol}\:{is}\:\mathrm{6}\:{times}\:{as}\:{old}\:{as}\:{her}\:{nephew} \\ $$$${Hondo}.{Baby}\:{is}\:\mathrm{22}\:{years}\:{yonger}\:{than} \\ $$$${her}\:{aunt}\:{carol}.{In}\:{four}\:{years}\:{carol}'{s} \\ $$$${age}\:{will}\:{be}\:{twice}\:{the}\:{sum}\:{of}\:{Hondo}'{s} \\ $$$${and}\:{Baby}'{s}\:{age}.{How}\:{old}\:{is}\:{each}\:{perso} \\ $$$${n}\:{now}? \\ $$

Question Number 27567 Answers: 0 Comments: 0

f(x)=3x^2 (a)Find the critical number (b)Find the interval on which f increase and decrese (c)Find the local extrem value of f (d)using the 2^(nd) derivative, find local extrem

$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3x}^{\mathrm{2}} \\ $$$$\left(\mathrm{a}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{critical}\:\mathrm{number} \\ $$$$\left(\mathrm{b}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{interval}\:\mathrm{on}\:\mathrm{which}\:\mathrm{f} \\ $$$$\mathrm{increase}\:\mathrm{and}\:\mathrm{decrese} \\ $$$$\left(\mathrm{c}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{local}\:\mathrm{extrem}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f} \\ $$$$\left(\mathrm{d}\right)\mathrm{using}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{derivative}, \\ $$$$\mathrm{find}\:\mathrm{local}\:\mathrm{extrem} \\ $$

Question Number 27564 Answers: 0 Comments: 4

Question Number 27563 Answers: 0 Comments: 0

The absolute value of ∫_(10) ^(19) ((cos x)/(1+x^8 )) dx is

$$\mathrm{The}\:\mathrm{absolute}\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{10}} {\overset{\mathrm{19}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\mathrm{1}+{x}^{\mathrm{8}} }\:{dx}\:\:\mathrm{is} \\ $$

Question Number 27561 Answers: 0 Comments: 1

a penduum bob is operated by a thread of breadth 100cn and the bob is pulled aside untill the string makes an angle of 60°. calculate (i)the velocity of the bob when the string is vertiv

$${a}\:{penduum}\:{bob}\:{is}\:{operated}\:{by}\:{a}\: \\ $$$${thread}\:{of}\:{breadth}\:\mathrm{100}{cn}\:{and}\:{the} \\ $$$${bob}\:{is}\:{pulled}\:{aside}\:{untill}\:{the}\:{string} \\ $$$${makes}\:{an}\:{angle}\:{of}\:\mathrm{60}°.\:{calculate} \\ $$$$\left({i}\right){the}\:{velocity}\:{of}\:{the}\:{bob}\:{when} \\ $$$${the}\:{string}\:{is}\:{vertiv} \\ $$

Question Number 27559 Answers: 2 Comments: 1

Change in Q#27507 Solve simultaneously: 2(√x)+y=13 x+2(√y)=10

$$\mathrm{Change}\:\mathrm{in}\:\mathrm{Q}#\mathrm{27507} \\ $$$$\mathrm{Solve}\:\mathrm{simultaneously}: \\ $$$$\mathrm{2}\sqrt{\mathrm{x}}+\mathrm{y}=\mathrm{13} \\ $$$$\mathrm{x}+\mathrm{2}\sqrt{\mathrm{y}}=\mathrm{10} \\ $$

Question Number 27547 Answers: 0 Comments: 0

let give A=(_(1 −1) ^(1 1) ) find A^n and e^A .

$${let}\:{give}\:{A}=\left(_{\mathrm{1}\:\:\:\:\:\:\:\:\:−\mathrm{1}} ^{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{1}} \right)\:\:\:\:\:{find}\:{A}^{{n}} \:\:\:{and}\:\:{e}^{{A}} \:\:\:. \\ $$

Question Number 27538 Answers: 0 Comments: 0

Question Number 27536 Answers: 0 Comments: 0

m_1 s_1 (x−𝛉)=m_2 s_2 (𝛉−y) ; x=? ;y=? 𝛉=? solve it as an equation....

$$\boldsymbol{\mathrm{m}}_{\mathrm{1}} \boldsymbol{\mathrm{s}}_{\mathrm{1}} \left(\boldsymbol{\mathrm{x}}−\boldsymbol{\theta}\right)=\boldsymbol{\mathrm{m}}_{\mathrm{2}} \boldsymbol{\mathrm{s}}_{\mathrm{2}} \left(\boldsymbol{\theta}−\boldsymbol{\mathrm{y}}\right)\:\:\:;\:\boldsymbol{\mathrm{x}}=?\:;\boldsymbol{\mathrm{y}}=?\:\boldsymbol{\theta}=? \\ $$$$\mathrm{solve}\:\mathrm{it}\:\mathrm{as}\:\mathrm{an}\:\mathrm{equation}.... \\ $$

Question Number 27531 Answers: 0 Comments: 5

(√(1−cos θ/1+cos θ))=?

$$\sqrt{\mathrm{1}−\mathrm{cos}\:\theta/\mathrm{1}+\mathrm{cos}\:\theta}=? \\ $$

Question Number 27530 Answers: 0 Comments: 0

5/6.6/8.7/9.11/13.....asending order

$$\mathrm{5}/\mathrm{6}.\mathrm{6}/\mathrm{8}.\mathrm{7}/\mathrm{9}.\mathrm{11}/\mathrm{13}.....{asending}\:{order} \\ $$

Question Number 27525 Answers: 1 Comments: 1

x=7×4(√(3 ))thenx+1/x=?

$${x}=\mathrm{7}×\mathrm{4}\sqrt{\mathrm{3}\:}{thenx}+\mathrm{1}/{x}=? \\ $$

Question Number 27524 Answers: 1 Comments: 0

If x is real, the maximum value of ((3x^2 +9x+17)/(3x^2 +9x+7)) is

$$\mathrm{If}\:{x}\:\mathrm{is}\:\mathrm{real},\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{17}}{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{7}}\:\:\mathrm{is} \\ $$

Question Number 27520 Answers: 0 Comments: 0

Question Number 27539 Answers: 2 Comments: 1

Question Number 27517 Answers: 0 Comments: 0

Question Number 27557 Answers: 0 Comments: 1

proove that π = 3.142

$${proove}\:{that}\:\pi\:=\:\mathrm{3}.\mathrm{142} \\ $$

Question Number 27514 Answers: 1 Comments: 0

The president of a republic wishes to assign the premiership,the vice-premiership,and six other cabinet posts to a selected group of 8,comprising of 6 career diplomats and 2 business men.If none of the business men can be made premier or vice premier,in how many ways can the 8 posts be assigned to the 8 people?

$${The}\:{president}\:{of}\:{a}\:{republic}\:{wishes} \\ $$$${to}\:{assign}\:{the}\:{premiership},{the}\: \\ $$$${vice}-{premiership},{and}\:{six}\:{other} \\ $$$${cabinet}\:{posts}\:{to}\:{a}\:{selected}\:{group} \\ $$$${of}\:\mathrm{8},{comprising}\:{of}\:\mathrm{6}\:{career} \\ $$$${diplomats}\:{and}\:\mathrm{2}\:{business}\:{men}.{If} \\ $$$${none}\:{of}\:{the}\:{business}\:{men}\:{can}\:{be} \\ $$$${made}\:{premier}\:{or}\:{vice}\:{premier},{in} \\ $$$${how}\:{many}\:{ways}\:{can}\:{the}\:\mathrm{8}\:{posts} \\ $$$${be}\:{assigned}\:{to}\:{the}\:\mathrm{8}\:{people}? \\ $$

Question Number 27513 Answers: 1 Comments: 0

Using only the integers 4 to 8, how many even numbers can be formed if each must lie between 4000 and 9000?

$${Using}\:{only}\:{the}\:{integers}\:\mathrm{4}\:{to}\:\mathrm{8}, \\ $$$${how}\:{many}\:{even}\:{numbers}\:{can}\:{be} \\ $$$${formed}\:{if}\:{each}\:{must}\:{lie}\:{between} \\ $$$$\mathrm{4000}\:{and}\:\:\mathrm{9000}? \\ $$$$ \\ $$

Question Number 27555 Answers: 0 Comments: 0

Question Number 27507 Answers: 1 Comments: 4

2(√(x ))+y=9....(1) x+ 2(√y)=3....(2) solve the simultaneous equation

$$\mathrm{2}\sqrt{{x}\:}+{y}=\mathrm{9}....\left(\mathrm{1}\right) \\ $$$${x}+\:\mathrm{2}\sqrt{{y}}=\mathrm{3}....\left(\mathrm{2}\right) \\ $$$$ \\ $$$${solve}\:{the}\:{simultaneous}\:{equation} \\ $$

Question Number 27503 Answers: 1 Comments: 0

If x=cy+bz ,y=az+cx & z=bx+ay prove that(x^2 /(1−a^2 ))=(y^2 /(1−b^2 ))=(z^2 /(1−c^2 )) .

$$\mathrm{If}\:\mathrm{x}=\mathrm{cy}+\mathrm{bz}\:,\mathrm{y}=\mathrm{az}+\mathrm{cx}\:\&\:\mathrm{z}=\mathrm{bx}+\mathrm{ay} \\ $$$$\mathrm{prove}\:\mathrm{that}\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{a}^{\mathrm{2}} }=\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{1}−\mathrm{b}^{\mathrm{2}} }=\frac{\mathrm{z}^{\mathrm{2}} }{\mathrm{1}−\mathrm{c}^{\mathrm{2}} }\:. \\ $$

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