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Question Number 89878 Answers: 1 Comments: 1

A four_digit whole number is interesting if the number formed by the leftmost two digits is twice as large as the number formed by the rightmost two digits. (for example 2010 is interesting) 1 find the largest whole number B such that all interesting numbers are divisible by B 2 find the smallest whole number D such that D is divisible by all interesting numbers.

$$\boldsymbol{{A}}\:\boldsymbol{{four\_digit}}\:\boldsymbol{{whole}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{is}}\:\boldsymbol{{interesting}}\:\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{formed}}\:\boldsymbol{{by}}\:\boldsymbol{{the}}\:\boldsymbol{{leftmost}}\:\boldsymbol{{two}} \\ $$$$\boldsymbol{{digits}}\:\boldsymbol{{is}}\:\boldsymbol{{twice}}\:\boldsymbol{{as}}\:\boldsymbol{{large}}\:\boldsymbol{{as}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{number}}\:\boldsymbol{{formed}}\:\boldsymbol{{by}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{rightmost}}\:\boldsymbol{{two}}\:\boldsymbol{{digits}}. \\ $$$$\left(\boldsymbol{{for}}\:\boldsymbol{{example}}\:\mathrm{2010}\:\boldsymbol{{is}}\:\boldsymbol{{interesting}}\right) \\ $$$$\mathrm{1}\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{largest}}\:\boldsymbol{{whole}}\:\boldsymbol{{number}} \\ $$$$\mathbb{B}\:\boldsymbol{{such}}\:\boldsymbol{{that}}\:\boldsymbol{{all}}\:\boldsymbol{{interesting}} \\ $$$$\boldsymbol{{numbers}}\:\boldsymbol{{are}}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathbb{B} \\ $$$$\mathrm{2}\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{smallest}}\:\boldsymbol{{whole}} \\ $$$$\boldsymbol{{number}}\:\mathbb{D}\:\boldsymbol{{such}}\:\boldsymbol{{that}}\:\mathbb{D}\:\boldsymbol{{is}} \\ $$$$\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\boldsymbol{{all}}\:\boldsymbol{{interesting}} \\ $$$$\boldsymbol{{numbers}}. \\ $$

Question Number 89874 Answers: 0 Comments: 0

∫_(1/3) ^(2/3) ((ln(1+(√(x^2 −(1/3)))))/(x(√(x^2 −(1/3)))))dx

$$\int_{\frac{\mathrm{1}}{\mathrm{3}}} ^{\frac{\mathrm{2}}{\mathrm{3}}} \:\frac{{ln}\left(\mathrm{1}+\sqrt{{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{3}}}\right)}{{x}\sqrt{{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{3}}}}{dx} \\ $$

Question Number 89852 Answers: 1 Comments: 0

Question Number 89849 Answers: 3 Comments: 1

Question Number 89848 Answers: 0 Comments: 1

Q1. If sinθ=(3/5) then find the value of tanθ+cotθ

$${Q}\mathrm{1}.\:{If}\:{sin}\theta=\frac{\mathrm{3}}{\mathrm{5}}\:{then}\:{find}\:{the}\:{value}\:{of}\:{tan}\theta+{cot}\theta \\ $$

Question Number 89846 Answers: 1 Comments: 3

∫_(−1) ^1 x cosh(x) ln(1+e^x ) dx

$$\int_{−\mathrm{1}} ^{\mathrm{1}} \:{x}\:{cosh}\left({x}\right)\:{ln}\left(\mathrm{1}+{e}^{{x}} \right)\:{dx} \\ $$

Question Number 89835 Answers: 2 Comments: 0

x^2 (d^2 y/dx^2 ) + 4x (dy/dx) + 2y = e^x

$${x}^{\mathrm{2}} \:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{4}{x}\:\frac{{dy}}{{dx}}\:+\:\mathrm{2}{y}\:=\:{e}^{{x}} \\ $$

Question Number 89834 Answers: 1 Comments: 1

Find x e^x = x^2 −1 anyother method apart from Newton′s

$${Find}\:{x}\: \\ $$$$\boldsymbol{{e}}^{\boldsymbol{{x}}} =\:\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{1} \\ $$$$\boldsymbol{{anyother}}\:\boldsymbol{{method}}\:\boldsymbol{{apart}}\:\boldsymbol{{from}}\:\boldsymbol{{N}}{ewton}'{s} \\ $$

Question Number 89829 Answers: 0 Comments: 9

Question Number 89826 Answers: 0 Comments: 0

Solve the equation: x^2 + xy + y^2 = 7 ...... (i) y^2 + yz + z^2 = 3 ...... (ii) z^2 + xz + x^2 = 1 ..... (iii)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{xy}\:\:+\:\:\mathrm{y}^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{7}\:\:\:\:\:\:\:\:\:......\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\mathrm{y}^{\mathrm{2}} \:\:+\:\:\mathrm{yz}\:\:+\:\:\mathrm{z}^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{3}\:\:\:\:\:\:\:\:\:\:......\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\mathrm{z}^{\mathrm{2}} \:\:+\:\:\mathrm{xz}\:\:+\:\:\mathrm{x}^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:.....\:\left(\mathrm{iii}\right) \\ $$

Question Number 89809 Answers: 3 Comments: 0

(dy/dx) = (y^2 /(xy−x^2 ))

$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{xy}−\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 89805 Answers: 1 Comments: 3

find minimum and maximum value of f(x,y) = x^2 −y^2 with constraint x^2 +y^2 = 1 with Lagrange method

$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{with}\:\mathrm{constraint}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{1} \\ $$$$\mathrm{with}\:\mathrm{Lagrange}\:\mathrm{method} \\ $$

Question Number 89804 Answers: 1 Comments: 0

Question Number 89816 Answers: 0 Comments: 3

Question Number 89817 Answers: 0 Comments: 0

Question Number 89795 Answers: 1 Comments: 0

Question Number 89794 Answers: 0 Comments: 1

true or false (1+(1/1^3 ))(1+(1/2^3 ))(1+(1/3^3 )).....(1+(1/n^3 ))<3

$${true}\:{or}\:{false} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }\right).....\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{3}} }\right)<\mathrm{3} \\ $$

Question Number 89781 Answers: 0 Comments: 8

Question Number 89776 Answers: 0 Comments: 2

what is the stability of the following function (dy/dt) = y^3 −2y^2 + y

$${what}\:{is}\:{the}\:{stability}\:{of}\:{the}\: \\ $$$${following}\:{function}\: \\ $$$$\frac{{dy}}{{dt}}\:=\:{y}^{\mathrm{3}} \:−\mathrm{2}{y}^{\mathrm{2}} \:+\:{y}\: \\ $$

Question Number 89768 Answers: 2 Comments: 0

t(n) − t(n−1) = n for n > 0 and t(0) = 1 find t(n)

$${t}\left({n}\right)\:−\:{t}\left({n}−\mathrm{1}\right)\:=\:{n}\:\: \\ $$$${for}\:{n}\:>\:\mathrm{0}\:{and}\:{t}\left(\mathrm{0}\right)\:=\:\mathrm{1}\: \\ $$$${find}\:{t}\left({n}\right)\: \\ $$

Question Number 89755 Answers: 1 Comments: 1

Question Number 89753 Answers: 1 Comments: 6

(d/dx) (Π_(k = 1) ^(16) (x+(1/k)))∣_( x = 0) = ?

$$\frac{\mathrm{d}}{\mathrm{dx}}\:\left(\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\mathrm{16}} {\prod}}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{k}}\right)\right)\underset{\:\mathrm{x}\:=\:\mathrm{0}} {\mid}\:=\:? \\ $$

Question Number 89749 Answers: 0 Comments: 4

Question Number 89748 Answers: 0 Comments: 4

dx = (1+2xtan y) dy

$$\mathrm{dx}\:=\:\left(\mathrm{1}+\mathrm{2xtan}\:\mathrm{y}\right)\:\mathrm{dy}\: \\ $$

Question Number 89745 Answers: 0 Comments: 2

f(x) = f(x+((3π)/8)) , ∀x∈ R if ∫_0 ^(3π/8) f(x) dx = t , then ∫_π ^(5π/2) f(x−π) dx = A. 2t B. 3t C. 4t D. 6t E. 8t

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{f}\left(\mathrm{x}+\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\:,\:\forall\mathrm{x}\in\:\mathbb{R} \\ $$$$\mathrm{if}\:\underset{\mathrm{0}} {\overset{\mathrm{3}\pi/\mathrm{8}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{t}\:,\:\mathrm{then}\: \\ $$$$\underset{\pi} {\overset{\mathrm{5}\pi/\mathrm{2}} {\int}}\mathrm{f}\left(\mathrm{x}−\pi\right)\:\mathrm{dx}\:=\: \\ $$$$\mathrm{A}.\:\mathrm{2t}\:\:\:\:\:\:\:\mathrm{B}.\:\mathrm{3t}\:\:\:\:\:\:\:\mathrm{C}.\:\mathrm{4t}\:\:\:\:\:\:\:\mathrm{D}.\:\mathrm{6t} \\ $$$$\mathrm{E}.\:\mathrm{8t}\: \\ $$

Question Number 89920 Answers: 0 Comments: 1

x=(1/(1+(1/(1+x)))) and y=(2/(2+(1/(1+y )))) find x+y

$${x}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+{x}}}\:{and}\:{y}=\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{1}+{y}\:}}\:{find}\:{x}+{y} \\ $$

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