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AllQuestion and Answers: Page 1139

Question Number 104357    Answers: 2   Comments: 0

(x+y+1) (dy/dx) = 1

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

Question Number 104852    Answers: 0   Comments: 0

if g∈C(R,R) and. ∫_0 ^1 g(x)dx=(1/3)+∫_0 ^1 g^2 (x^2 )dx then ∫_0 ^1 g(x)dx=(2/3) and ∫_0 ^1 g^2 (x)dx=(1/2)

$$\:\:{if}\:\:{g}\in{C}\left(\mathbb{R},\mathbb{R}\right)\:{and}.\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{g}\left({x}\right){dx}=\frac{\mathrm{1}}{\mathrm{3}}+\int_{\mathrm{0}} ^{\mathrm{1}} {g}^{\mathrm{2}} \left({x}^{\mathrm{2}} \right){dx}\: \\ $$$${then}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {g}\left({x}\right){dx}=\frac{\mathrm{2}}{\mathrm{3}}\:{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {g}^{\mathrm{2}} \left({x}\right){dx}=\frac{\mathrm{1}}{\mathrm{2}}\:\: \\ $$

Question Number 104851    Answers: 4   Comments: 0

∫ ((√(x^2 −9))/x^3 ) dx

$$\int\:\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{9}}}{{x}^{\mathrm{3}} }\:{dx}\: \\ $$

Question Number 104850    Answers: 0   Comments: 0

Let E be a no empty set with card=n≥1 Find in term of n Σ_(A,B⊆E) Card(A−B)=Σ_(A,B⊆E) Card(A∩B)=(1/3)Σ_(A,B⊆E) Card (A∪B)=n4^(n−1)

$${Let}\:\:{E}\:{be}\:{a}\:{no}\:{empty}\:{set}\:{with}\:{card}={n}\geqslant\mathrm{1} \\ $$$$\:{Find}\:{in}\:{term}\:{of}\:\:{n}\:\:\:\:\:\:\underset{{A},{B}\subseteq{E}} {\sum}{Card}\left({A}−{B}\right)=\underset{{A},{B}\subseteq{E}} {\sum}{Card}\left({A}\cap{B}\right)=\frac{\mathrm{1}}{\mathrm{3}}\underset{{A},{B}\subseteq{E}} {\sum}{Card}\:\left({A}\cup{B}\right)={n}\mathrm{4}^{{n}−\mathrm{1}} \:\:\:\: \\ $$

Question Number 104350    Answers: 1   Comments: 0

lim_(△x→0) ((sin ((α+△x)^n )−sin (α^n ))/(cos ((α+△x)^n )sin (α+△x)−cos (α^n )sin (α)))

$$\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\left(\alpha+\bigtriangleup{x}\right)^{{n}} \right)−\mathrm{sin}\:\left(\alpha^{{n}} \right)}{\mathrm{cos}\:\left(\left(\alpha+\bigtriangleup{x}\right)^{{n}} \right)\mathrm{sin}\:\left(\alpha+\bigtriangleup{x}\right)−\mathrm{cos}\:\left(\alpha^{{n}} \right)\mathrm{sin}\:\left(\alpha\right)} \\ $$

Question Number 104348    Answers: 3   Comments: 0

lim_(x→0) (((arc tan (x)−arc sin (x))/(x(1−cos (x)))))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{arc}\:\mathrm{tan}\:\left({x}\right)−\mathrm{arc}\:\mathrm{sin}\:\left({x}\right)}{{x}\left(\mathrm{1}−\mathrm{cos}\:\left({x}\right)\right)}\right) \\ $$

Question Number 104342    Answers: 1   Comments: 0

solve x (d^2 y/dx^2 )−(dy/dx)−4x^3 y = 8x^3 sin(x^2 )

$${solve}\:{x}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\frac{{dy}}{{dx}}−\mathrm{4}{x}^{\mathrm{3}} {y}\:=\:\mathrm{8}{x}^{\mathrm{3}} \mathrm{sin}\left({x}^{\mathrm{2}} \right) \\ $$

Question Number 104339    Answers: 3   Comments: 1

Examine ∫_0 ^3 ((2x)/((1−x^2 )^(2/3) )) dx

$${Examine}\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\frac{\mathrm{2}{x}}{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}/\mathrm{3}} }\:{dx} \\ $$

Question Number 104338    Answers: 0   Comments: 0

∫((tdt)/((1+t^3 )((1+t^3 ))^(1/3) ))

$$\int\frac{\mathrm{tdt}}{\left(\mathrm{1}+\mathrm{t}^{\mathrm{3}} \right)\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{t}^{\mathrm{3}} }} \\ $$

Question Number 104326    Answers: 1   Comments: 2

Suppose you had x rupees. Your father gave you more 6 rupees. You gave y rupees to your brother. Now how many rupees you have? You will buy three shirts with the rupees that you have now. Write the cost of each shirt.

$$\boldsymbol{\mathrm{Suppose}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{had}}\:\boldsymbol{{x}}\:\boldsymbol{\mathrm{rupees}}.\:\boldsymbol{\mathrm{Your}} \\ $$$$\boldsymbol{\mathrm{father}}\:\boldsymbol{\mathrm{gave}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{more}}\:\mathrm{6}\:\boldsymbol{\mathrm{rupees}}.\:\boldsymbol{\mathrm{You}} \\ $$$$\boldsymbol{\mathrm{gave}}\:\boldsymbol{{y}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{brother}}.\:\boldsymbol{\mathrm{Now}} \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{many}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{have}}?\:\boldsymbol{\mathrm{You}}\:\boldsymbol{\mathrm{will}} \\ $$$$\boldsymbol{\mathrm{buy}}\:\boldsymbol{\mathrm{three}}\:\boldsymbol{\mathrm{shirts}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{that}} \\ $$$$\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{now}}.\:\boldsymbol{\mathrm{Write}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{cost}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{each}} \\ $$$$\boldsymbol{\mathrm{shirt}}. \\ $$

Question Number 104312    Answers: 1   Comments: 0

∫_0 ^(π/4) ((√(sin^2 θ+2))/(sinθ))dθ

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\sqrt{\mathrm{sin}^{\mathrm{2}} \theta+\mathrm{2}}}{\mathrm{sin}\theta}\mathrm{d}\theta \\ $$

Question Number 104302    Answers: 3   Comments: 2

Question Number 104301    Answers: 2   Comments: 2

a girl weighs 569.37N on the earth surfsce (a) what would she weigh at a height above the earth surface of one earth radius? what would her mass be?

$$\mathrm{a}\:\mathrm{girl}\:\mathrm{weighs}\:\mathrm{569}.\mathrm{37N}\:\mathrm{on}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{surfsce}\:\left(\mathrm{a}\right)\:\mathrm{what}\:\mathrm{would}\:\mathrm{she}\:\mathrm{weigh}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height}\:\mathrm{above}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{one}\:\mathrm{earth}\:\mathrm{radius}?\:\mathrm{what}\:\mathrm{would}\:\mathrm{her}\:\mathrm{mass}\:\mathrm{be}? \\ $$

Question Number 104299    Answers: 2   Comments: 0

an astraonaut weighs 3200N on a planet whose mass is the same as that of the earth but whose radius is half that of the earth. the astronsut weight on the earth is what?

$$\mathrm{an}\:\mathrm{astraonaut}\:\mathrm{weighs}\:\mathrm{3200N}\:\mathrm{on}\:\mathrm{a}\:\mathrm{planet}\:\mathrm{whose}\:\mathrm{mass}\:\mathrm{is}\:\mathrm{the}\:\mathrm{same}\:\mathrm{as}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{but}\:\mathrm{whose}\:\mathrm{radius}\:\mathrm{is}\:\mathrm{half}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}.\:\mathrm{the}\:\mathrm{astronsut}\:\mathrm{weight}\:\mathrm{on}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{is}\:\mathrm{what}? \\ $$

Question Number 104297    Answers: 1   Comments: 0

((3a^2 b^3 c)/(5b^4 c))+((6xy^3 z^(16) )/(10x^2 y^2 z^(10) )) = ? Can you solve this?

$$\frac{\mathrm{3}{a}^{\mathrm{2}} {b}^{\mathrm{3}} {c}}{\mathrm{5}{b}^{\mathrm{4}} {c}}+\frac{\mathrm{6}{xy}^{\mathrm{3}} {z}^{\mathrm{16}} }{\mathrm{10}{x}^{\mathrm{2}} {y}^{\mathrm{2}} {z}^{\mathrm{10}} }\:=\:? \\ $$$$\boldsymbol{\mathrm{Can}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}? \\ $$

Question Number 104296    Answers: 0   Comments: 0

FUN TIME AGAIN! S_n =1+2+3+4+5+6+7+8+9+.. S_n =1+(2+3+4)+(5+6+7)+... S_n =1+9+18+27+... S_n =1+9(1+2+3+4+5+6+7.......) S_n =1+9S_n S_n =−(1/8) S_n =1−1+1−1+1−1+1−1+1−1+.. S=(1/2) S_n =1−2+4−8+16−32+..... S_n =(1/(1+2))=(1/3) S_n =1+2+4+8+16+... S_n =1+2(1+2+4+8+...) S_n =1+2(1+2(1+2+4+8+...) S_n =1+2(1+2S_n ) −3S_n =3⇒S_n =−1

$$ \\ $$$$ \\ $$$$\mathrm{FUN}\:\mathrm{TIME}\:\mathrm{AGAIN}! \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+.. \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}+\left(\mathrm{2}+\mathrm{3}+\mathrm{4}\right)+\left(\mathrm{5}+\mathrm{6}+\mathrm{7}\right)+... \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}+\mathrm{9}+\mathrm{18}+\mathrm{27}+... \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}+\mathrm{9}\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}.......\right) \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}+\mathrm{9S}_{\mathrm{n}} \\ $$$$\mathrm{S}_{\mathrm{n}} =−\frac{\mathrm{1}}{\mathrm{8}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+.. \\ $$$$\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+\mathrm{16}−\mathrm{32}+..... \\ $$$$\mathrm{S}_{\mathrm{n}} =\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}+\mathrm{2}+\mathrm{4}+\mathrm{8}+\mathrm{16}+... \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}+\mathrm{2}\left(\mathrm{1}+\mathrm{2}+\mathrm{4}+\mathrm{8}+...\right) \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}+\mathrm{2}\left(\mathrm{1}+\mathrm{2}\left(\mathrm{1}+\mathrm{2}+\mathrm{4}+\mathrm{8}+...\right)\right. \\ $$$$\mathrm{S}_{\mathrm{n}} =\mathrm{1}+\mathrm{2}\left(\mathrm{1}+\mathrm{2S}_{\mathrm{n}} \right) \\ $$$$−\mathrm{3S}_{\mathrm{n}} =\mathrm{3}\Rightarrow\mathrm{S}_{\mathrm{n}} =−\mathrm{1} \\ $$

Question Number 104294    Answers: 1   Comments: 0

1. ((1(1/2)+2(6/7))/(2(2/3)−3(4/5)))=? 2. 4×Π×Π=? 3. Transfer into fractions: 5.8^. 9^. , 9.6^. , 78.57^. 8^.

$$\mathrm{1}.\:\:\frac{\mathrm{1}\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{2}\frac{\mathrm{6}}{\mathrm{7}}}{\mathrm{2}\frac{\mathrm{2}}{\mathrm{3}}−\mathrm{3}\frac{\mathrm{4}}{\mathrm{5}}}=? \\ $$$$\mathrm{2}.\:\:\mathrm{4}×\Pi×\Pi=? \\ $$$$\mathrm{3}.\:\:\boldsymbol{\mathrm{Transfer}}\:\boldsymbol{\mathrm{into}}\:\boldsymbol{\mathrm{fractions}}: \\ $$$$\:\:\:\:\:\:\mathrm{5}.\overset{.} {\mathrm{8}}\overset{.} {\mathrm{9}},\:\mathrm{9}.\overset{.} {\mathrm{6}},\:\mathrm{78}.\mathrm{5}\overset{.} {\mathrm{7}}\overset{.} {\mathrm{8}} \\ $$

Question Number 104293    Answers: 1   Comments: 0

find the acceleration of gravity at an alitude of 1000k

$$\mathrm{find}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{gravity}\:\mathrm{at} \\ $$$$\:\mathrm{an}\:\mathrm{alitude}\:\mathrm{of}\:\mathrm{1000k} \\ $$

Question Number 104286    Answers: 0   Comments: 0

Question Number 104281    Answers: 1   Comments: 1

Question Number 104280    Answers: 1   Comments: 5

What is the GCD of (1/2), (3/4), ((16)/(30)) ?

$$\boldsymbol{\mathrm{What}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{GCD}}\:\boldsymbol{\mathrm{of}}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{3}}{\mathrm{4}},\:\frac{\mathrm{16}}{\mathrm{30}}\:? \\ $$

Question Number 104278    Answers: 1   Comments: 0

x−(−(−x+(−x+x)))= ?

$${x}−\left(−\left(−{x}+\left(−{x}+{x}\right)\right)\right)=\:? \\ $$

Question Number 104275    Answers: 1   Comments: 2

The HCF of (x−1)(x^2 −4) and (x^2 −1)(x+2) is

$$\mathrm{The}\:\mathrm{HCF}\:\mathrm{of}\:\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{4}\right)\:\mathrm{and}\: \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}+\mathrm{2}\right)\:\:\mathrm{is} \\ $$

Question Number 104264    Answers: 2   Comments: 0

∫_0 ^( (√2)) ∫_y ^( (√(4−y^2 ))) (1/(√(1+x^2 +y^2 )))dxdy

$$\int_{\mathrm{0}} ^{\:\sqrt{\mathrm{2}}} \:\int_{{y}} ^{\:\sqrt{\mathrm{4}−{y}^{\mathrm{2}} }} \frac{\mathrm{1}}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }}{dxdy} \\ $$

Question Number 104260    Answers: 0   Comments: 1

You bought 3g rice, 5g flour in a market. At first you had 500 rupees. Now you have 300 rupees. How much rupees you wasted? Suppose you distribute the 300 rupees among your 4 sons. Now how much rupees does your one son get?

$$\mathrm{You}\:\mathrm{bought}\:\mathrm{3g}\:\mathrm{rice},\:\mathrm{5g}\:\mathrm{flour}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{market}.\:\mathrm{At}\:\mathrm{first}\:\mathrm{you}\:\mathrm{had}\:\mathrm{500}\:\mathrm{rupees}. \\ $$$$\mathrm{Now}\:\mathrm{you}\:\mathrm{have}\:\mathrm{300}\:\mathrm{rupees}.\:\mathrm{How}\:\mathrm{much} \\ $$$$\mathrm{rupees}\:\mathrm{you}\:\mathrm{wasted}?\:\mathrm{Suppose}\:\mathrm{you} \\ $$$$\mathrm{distribute}\:\mathrm{the}\:\mathrm{300}\:\mathrm{rupees}\:\mathrm{among} \\ $$$$\mathrm{your}\:\mathrm{4}\:\mathrm{sons}.\:\mathrm{Now}\:\mathrm{how}\:\mathrm{much}\:\mathrm{rupees} \\ $$$$\mathrm{does}\:\mathrm{your}\:\mathrm{one}\:\mathrm{son}\:\mathrm{get}? \\ $$

Question Number 104253    Answers: 1   Comments: 1

When a∗b= ((a+b)/(a−b)) then what is the answer of 2∗3×9∗10 ?

$$\mathrm{When}\:{a}\ast{b}=\:\frac{{a}+{b}}{{a}−{b}}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{answer}\:\mathrm{of}\:\mathrm{2}\ast\mathrm{3}×\mathrm{9}\ast\mathrm{10}\:? \\ $$

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