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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