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Question Number 72634 Answers: 1 Comments: 4

help me with the conditions please for a function f to be continuous at a point a

$${help}\:{me}\:{with}\:{the}\:{conditions}\:{please}\: \\ $$$${for}\:{a}\:{function}\:{f}\:{to}\:{be}\:{continuous}\:{at}\:{a}\:{point}\:{a} \\ $$

Question Number 72633 Answers: 0 Comments: 0

prove using th sandwich or Squeez theorem that for any a > 0 lim_(x→a) (√x) = (√a)

$${prove}\:{using}\:{th}\:{sandwich}\:{or}\:{Squeez}\:{theorem}\:{that} \\ $$$${for}\:{any}\:\:{a}\:>\:\mathrm{0} \\ $$$$\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\sqrt{{x}}\:=\:\sqrt{{a}}\: \\ $$

Question Number 72666 Answers: 1 Comments: 0

Question Number 72628 Answers: 0 Comments: 2

solve the inequality log_3 (2x^2 + 9x + 9) < 0

$${solve}\:{the}\:{inequality}\: \\ $$$$\:\:{log}_{\mathrm{3}} \left(\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{9}{x}\:+\:\mathrm{9}\right)\:<\:\mathrm{0} \\ $$

Question Number 72608 Answers: 1 Comments: 0

Question Number 72606 Answers: 2 Comments: 0

Question Number 72603 Answers: 1 Comments: 0

Question Number 72595 Answers: 1 Comments: 3

(α+β)^2 = α^2 + 2αβ + β^(2 )

$$\left(\alpha+\beta\right)^{\mathrm{2}} \:=\:\alpha^{\mathrm{2}} \:+\:\mathrm{2}\alpha\beta\:+\:\beta^{\mathrm{2}\:} \\ $$

Question Number 72593 Answers: 2 Comments: 0

If the length of a square is increased by 25% while its width is decrease by 15% to form a rectangle. What is the ratio of the area of the rectangle to the area of the square

$$\mathrm{If}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{is}\:\mathrm{increased}\:\mathrm{by}\:\:\mathrm{25\%}\:\mathrm{while}\:\mathrm{its} \\ $$$$\mathrm{width}\:\mathrm{is}\:\mathrm{decrease}\:\mathrm{by}\:\:\:\mathrm{15\%}\:\:\:\mathrm{to}\:\mathrm{form}\:\mathrm{a}\:\mathrm{rectangle}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square} \\ $$

Question Number 72589 Answers: 0 Comments: 2

Solve for x: ((√x))^x = 27x^(√x)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\:\left(\sqrt{\boldsymbol{\mathrm{x}}}\right)^{\boldsymbol{\mathrm{x}}} \:\:=\:\:\mathrm{27}\boldsymbol{\mathrm{x}}^{\sqrt{\boldsymbol{\mathrm{x}}}} \\ $$

Question Number 72577 Answers: 0 Comments: 3

solve the equation z(x+z)(∂z/∂x) − y(y+z)(∂z/∂y) = 0 where z=(√y) when x=1

$${solve}\:{the}\:{equation} \\ $$$$ \\ $$$${z}\left({x}+{z}\right)\frac{\partial{z}}{\partial{x}}\:−\:{y}\left({y}+{z}\right)\frac{\partial{z}}{\partial{y}}\:=\:\mathrm{0} \\ $$$$ \\ $$$${where}\:{z}=\sqrt{{y}}\:{when}\:{x}=\mathrm{1} \\ $$

Question Number 72579 Answers: 1 Comments: 0

Question Number 72569 Answers: 3 Comments: 0

2x−y+3z =1 4x+2y−z = −8 3x+y+2z = −1

$$\mathrm{2x}−\mathrm{y}+\mathrm{3z}\:=\mathrm{1} \\ $$$$\mathrm{4x}+\mathrm{2y}−\mathrm{z}\:=\:−\mathrm{8} \\ $$$$\mathrm{3x}+\mathrm{y}+\mathrm{2z}\:=\:−\mathrm{1} \\ $$

Question Number 72563 Answers: 1 Comments: 1

Question Number 72560 Answers: 0 Comments: 5

Question Number 72526 Answers: 2 Comments: 1

if the lcm and gcf of three numbers are 360 and 6,other numbers are 18 and 60.Find the third number. ... I need help plz...

$${if}\:{the}\:{lcm}\:{and}\:{gcf}\:{of}\:{three}\:{numbers} \\ $$$$\:{are}\:\mathrm{360}\:{and}\:\mathrm{6},{other}\:{numbers}\:{are}\:\mathrm{18}\: \\ $$$$\:{and}\:\mathrm{60}.{Find}\:{the}\:{third}\:{number}. \\ $$$$\:\:\:\:\:\:\:\:...\:{I}\:{need}\:{help}\:{plz}... \\ $$

Question Number 72519 Answers: 1 Comments: 1

Question Number 72507 Answers: 0 Comments: 0

Question Number 72499 Answers: 3 Comments: 0

Find the ratio of; x:y if 10x^2 −9xy +2y^2 =0

$${Find}\:{the}\:{ratio}\:{of};\:{x}:{y}\:{if}\:\mathrm{10}{x}^{\mathrm{2}} −\mathrm{9}{xy} \\ $$$$+\mathrm{2}{y}^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 72498 Answers: 1 Comments: 0

Karanja and Ouma can do a certain job in 6 days. Karanja alone can do the work in 5 days more than Ouma. How many days can Karanja take to do the job alone?

$${Karanja}\:{and}\:{Ouma}\:{can}\:{do}\:{a}\: \\ $$$${certain}\:{job}\:{in}\:\mathrm{6}\:{days}.\:{Karanja}\: \\ $$$${alone}\:{can}\:{do}\:{the}\:{work}\:{in}\:\mathrm{5}\:{days} \\ $$$${more}\:{than}\:{Ouma}.\:{How}\:{many}\: \\ $$$${days}\:{can}\:{Karanja}\:{take}\:{to}\:{do}\:{the} \\ $$$${job}\:{alone}? \\ $$

Question Number 72497 Answers: 3 Comments: 0

if, cot θ+cosec θ=(1/(√3)) then find the value of θ where 0<θ≤2π.

$$\mathrm{if},\:\mathrm{cot}\:\theta+\mathrm{cosec}\:\theta=\frac{\mathrm{1}}{\sqrt{\mathrm{3}}}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\theta\:\mathrm{where}\:\mathrm{0}<\theta\leqslant\mathrm{2}\pi. \\ $$

Question Number 72496 Answers: 2 Comments: 0

if a^x =b, b^y =c, c^z =a then prove that, xyz=0.

$$\mathrm{if}\:\mathrm{a}^{\mathrm{x}} =\mathrm{b},\:\mathrm{b}^{\mathrm{y}} =\mathrm{c},\:\mathrm{c}^{\mathrm{z}} =\mathrm{a}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}, \\ $$$$\mathrm{xyz}=\mathrm{0}. \\ $$

Question Number 72495 Answers: 0 Comments: 3

lim_(x→∞) (((lnx)/x))^((lnx)/x) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{lnx}}{{x}}\right)^{\frac{{lnx}}{{x}}} =? \\ $$

Question Number 72494 Answers: 1 Comments: 1

((∫x(√(x^2 +5)) dx−3∫(x/(√(x^2 +5)))dx)/(∫((x(x^2 +2))/(√(x^2 +5))) dx))