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Question Number 171046 Answers: 2 Comments: 0

Question Number 171044 Answers: 1 Comments: 3

Is the Light a matter?

$${Is}\:{the}\:{Light}\:{a}\:{matter}? \\ $$

Question Number 171043 Answers: 1 Comments: 0

A∈R A=(((√(x−2))+x+3)/( (√(4−2x))+x−1)) faind A=?

$${A}\in{R} \\ $$$${A}=\frac{\sqrt{{x}−\mathrm{2}}+{x}+\mathrm{3}}{\:\sqrt{\mathrm{4}−\mathrm{2}{x}}+{x}−\mathrm{1}}\:\:\:\:\:\:\:\:\:\:{faind}\:{A}=? \\ $$

Question Number 171034 Answers: 0 Comments: 2

Question Number 171033 Answers: 2 Comments: 1

lim_(x→0) (1/x) [ ((((1−(√(1−x)))/( (√(1+x))−1)) ))^(1/3) −1 ]=?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}}\:\left[\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}−\sqrt{\mathrm{1}−{x}}}{\:\sqrt{\mathrm{1}+{x}}−\mathrm{1}}\:}−\mathrm{1}\:\right]=? \\ $$

Question Number 171032 Answers: 1 Comments: 0

Find the domain and range of the function, f(x)=((x^2 +2)/(2x+1)) Mastermind

$${Find}\:{the}\:{domain}\:{and}\:{range}\:{of}\:{the} \\ $$$${function},\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}+\mathrm{1}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171031 Answers: 1 Comments: 0

Question Number 171025 Answers: 2 Comments: 0

Question Number 171023 Answers: 0 Comments: 0

Question Number 171038 Answers: 2 Comments: 0

Question Number 171021 Answers: 0 Comments: 0

Question Number 171039 Answers: 1 Comments: 0

I_n =∫_0 ^1 (1−u)^n (√(ud(u))) Demonstrate that ∀n∈N, I_n ≥0

$${I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{u}\right)^{{n}} \sqrt{{ud}\left({u}\right)} \\ $$$${Demonstrate}\:{that}\:\forall{n}\in{N},\:{I}_{{n}} \geq\mathrm{0} \\ $$

Question Number 176906 Answers: 1 Comments: 3

Question Number 171014 Answers: 1 Comments: 0

Question Number 182219 Answers: 1 Comments: 0

Question Number 171012 Answers: 1 Comments: 1

The number of five digits can be made with the digits 1, 2, 3 each of which can be used atmost thrice in a number is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{five}\:\mathrm{digits}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3}\:\mathrm{each}\:\mathrm{of}\:\mathrm{which}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{used}\:\mathrm{atmost}\:\mathrm{thrice}\:\mathrm{in}\:\mathrm{a}\:\mathrm{number}\:\mathrm{is} \\ $$

Question Number 171011 Answers: 2 Comments: 0

How many 5-digit numbers from the digits {0, 1, ....., 9} have? (i) Strictly increasing digits (ii) Strictly increasing or decreasing digits (iii) Increasing digits (iv) Increasing or decreasing digits

$$\mathrm{How}\:\mathrm{many}\:\mathrm{5}-\mathrm{digit}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{digits}\:\left\{\mathrm{0},\:\mathrm{1},\:.....,\:\mathrm{9}\right\}\:\mathrm{have}? \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Strictly}\:\mathrm{increasing}\:\mathrm{digits} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Strictly}\:\mathrm{increasing}\:\mathrm{or}\:\mathrm{decreasing} \\ $$$$\mathrm{digits} \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{Increasing}\:\mathrm{digits} \\ $$$$\left(\mathrm{iv}\right)\:\mathrm{Increasing}\:\mathrm{or}\:\mathrm{decreasing}\:\mathrm{digits} \\ $$

Question Number 176748 Answers: 2 Comments: 0

log_4 (√(8−x))=1−log_4 x solve for x

$${log}_{\mathrm{4}} \sqrt{\mathrm{8}−{x}}=\mathrm{1}−{log}_{\mathrm{4}} {x} \\ $$$${solve}\:{for}\:{x} \\ $$

Question Number 171009 Answers: 1 Comments: 0

Find the inverse, y^(−1) of the function y=x^3 +4. Mastermind

$${Find}\:{the}\:{inverse},\:{y}^{−\mathrm{1}} \:{of}\:{the}\:{function} \\ $$$${y}={x}^{\mathrm{3}} +\mathrm{4}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171008 Answers: 0 Comments: 1

Find the maximum and minimum values of h(x)=(4/3)x^3 +(9/2)x^2 +5x+8. Mastermind

$${Find}\:{the}\:{maximum}\:{and}\:{minimum} \\ $$$${values}\:{of}\:{h}\left({x}\right)=\frac{\mathrm{4}}{\mathrm{3}}{x}^{\mathrm{3}} +\frac{\mathrm{9}}{\mathrm{2}}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{8}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171006 Answers: 0 Comments: 1

Find the area enclosed by the curve y=4−3x^2 and the x−axis between x_1 =−1 and x_2 =1. Mastermind

$${Find}\:{the}\:{area}\:{enclosed}\:{by}\:{the}\:{curve} \\ $$$${y}=\mathrm{4}−\mathrm{3}{x}^{\mathrm{2}} \:{and}\:{the}\:{x}−{axis}\:{between} \\ $$$${x}_{\mathrm{1}} =−\mathrm{1}\:{and}\:{x}_{\mathrm{2}} =\mathrm{1}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171005 Answers: 0 Comments: 0

The distance S metre travelled in time t seconds by an object released from rest and allow to fall freely under the force of gravity is given by s(t)=4.5t^2 . find a) the average speed of the object during the time interval from 2 to 2.5 seconds. b) the instantaneous velocity of the object after 4 seconds. Mastermind

$${The}\:{distance}\:{S}\:{metre}\:{travelled}\:{in}\:{time} \\ $$$${t}\:{seconds}\:{by}\:{an}\:{object}\:{released}\:{from} \\ $$$${rest}\:{and}\:{allow}\:{to}\:{fall}\:{freely}\:{under}\:{the} \\ $$$${force}\:{of}\:{gravity}\:{is}\:{given}\:{by}\:{s}\left({t}\right)=\mathrm{4}.\mathrm{5}{t}^{\mathrm{2}} . \\ $$$${find}\: \\ $$$$\left.{a}\right)\:{the}\:{average}\:{speed}\:{of}\:{the}\:{object} \\ $$$${during}\:{the}\:{time}\:{interval}\:{from}\:\mathrm{2}\:{to} \\ $$$$\mathrm{2}.\mathrm{5}\:{seconds}. \\ $$$$\left.{b}\right)\:{the}\:{instantaneous}\:{velocity}\:{of}\:{the} \\ $$$${object}\:{after}\:\mathrm{4}\:{seconds}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170998 Answers: 1 Comments: 0

Question Number 170997 Answers: 1 Comments: 0

Find the equation of the tangent to the curve x^2 +y^2 −4x+6y−12=0 at the point (2, 3). Mastermind

$${Find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{to}\:{the} \\ $$$${curve}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{6}{y}−\mathrm{12}=\mathrm{0}\:{at}\:{the} \\ $$$${point}\:\left(\mathrm{2},\:\mathrm{3}\right). \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170996 Answers: 1 Comments: 0

Find the volume of the solid obtained by rotating about x−axis of the curve y=(√x) on the interval [0, 2]. Mastermind

$${Find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\:{obtained} \\ $$$${by}\:{rotating}\:{about}\:{x}−{axis}\:{of}\:{the}\:{curve} \\ $$$${y}=\sqrt{{x}}\:{on}\:{the}\:{interval}\:\left[\mathrm{0},\:\mathrm{2}\right]. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170995 Answers: 0 Comments: 1

Approximate sin46° by “differentials” Mastermind

$${Approximate}\:{sin}\mathrm{46}°\:{by}\:``{differentials}'' \\ $$$$ \\ $$$${Mastermind} \\ $$

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