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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 ?

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

Question Number 104251 Answers: 1 Comments: 0

If x=8 and y=5 then what is the answer of ((x+y+6)/(x^2 −y^3 )) ?

$$\mathrm{If}\:{x}=\mathrm{8}\:\mathrm{and}\:{y}=\mathrm{5}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{answer}\:\mathrm{of}\:\:\frac{{x}+{y}+\mathrm{6}}{{x}^{\mathrm{2}} −{y}^{\mathrm{3}} }\:? \\ $$

Question Number 104246 Answers: 3 Comments: 0

(1−(1/3))(1−(1/4))(1−(1/5))....(1−(1/(99))) =?

$$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\right)....\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{99}}\right)\:=? \\ $$

Question Number 104243 Answers: 2 Comments: 0

prove that π=2×(2/(√2))×(2/(√(2+(√2))))×(2/(√(2+(√(2+(√2))))))×.....

$${prove}\:{that} \\ $$$$\pi=\mathrm{2}×\frac{\mathrm{2}}{\sqrt{\mathrm{2}}}×\frac{\mathrm{2}}{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}×\frac{\mathrm{2}}{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}}×..... \\ $$

Question Number 104270 Answers: 1 Comments: 0

sgn(∣x∣)=?

$${sgn}\left(\mid{x}\mid\right)=? \\ $$

Question Number 104265 Answers: 4 Comments: 0

(dy/dx)−y=sinx

$$\frac{{dy}}{{dx}}−{y}={sinx} \\ $$

Question Number 104240 Answers: 3 Comments: 1

(dy/dx) = 1+x^2 +y^2 +(xy)^2

$$\frac{{dy}}{{dx}}\:=\:\mathrm{1}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\left({xy}\right)^{\mathrm{2}} \\ $$

Question Number 104239 Answers: 0 Comments: 1

{3{2x}}=x x=?

$$\left\{\mathrm{3}\left\{\mathrm{2}{x}\right\}\right\}={x}\:\:\:{x}=? \\ $$

Question Number 104309 Answers: 1 Comments: 1

Question Number 104235 Answers: 1 Comments: 0

If you are given a triangle with side length 15 , 20 and 25. what is the triangle′s shortest altitude?

$${If}\:{you}\:{are}\:{given}\:{a}\:{triangle} \\ $$$${with}\:{side}\:{length}\:\mathrm{15}\:,\:\mathrm{20}\:{and} \\ $$$$\mathrm{25}.\:{what}\:{is}\:{the}\:{triangle}'{s} \\ $$$${shortest}\:{altitude}? \\ $$

Question Number 104231 Answers: 0 Comments: 2

Question Number 104221 Answers: 0 Comments: 1

The diagonals of a trapezoid ABCD intersect at point Q lies between the parallel line BC and AD such that ∠AQD = ∠CQB , line CD separates points P and Q . Prove that ∠BQP = ∠DAQ

$${The}\:{diagonals}\:{of}\:{a} \\ $$$${trapezoid}\:{ABCD}\:{intersect} \\ $$$${at}\:{point}\:{Q}\:{lies}\:{between}\:{the} \\ $$$${parallel}\:{line}\:{BC}\:{and}\:{AD} \\ $$$${such}\:{that}\:\angle{AQD}\:=\:\angle{CQB}\:, \\ $$$${line}\:{CD}\:{separates}\:{points}\:{P} \\ $$$${and}\:{Q}\:.\:{Prove}\:{that} \\ $$$$\angle{BQP}\:=\:\angle{DAQ}\: \\ $$

Question Number 104220 Answers: 3 Comments: 1

∫_0 ^π ((x^2 cos x)/((1+sin x)^2 )) dx ?

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{x}^{\mathrm{2}} \mathrm{cos}\:{x}}{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\mathrm{2}} }\:{dx}\:?\: \\ $$

Question Number 104218 Answers: 1 Comments: 1

lim_(x→1) [((ln (1+x)+Σ_(n = 1) ^∞ [(((1+x^2^n ))/((1−x^2^n )))]^2^(−n) )/(ln ((1/(1−x)))))]

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left[\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}\right)+\underset{{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\left[\frac{\left(\mathrm{1}+{x}^{\mathrm{2}^{{n}} } \right)}{\left(\mathrm{1}−{x}^{\mathrm{2}^{{n}} } \right)}\right]^{\mathrm{2}^{−{n}} } }{\mathrm{ln}\:\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)}\right] \\ $$$$ \\ $$

Question Number 104217 Answers: 2 Comments: 0

lim_(x→0) ((tan (x+3)^2 −tan (9))/x) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{tan}\:\left({x}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{tan}\:\left(\mathrm{9}\right)}{{x}}\:=\:? \\ $$

Question Number 104215 Answers: 1 Comments: 0

lim_(x→1) ((9^3^(2ln x) −9^2^(ln x) )/(ln x)) =?

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{9}^{\mathrm{3}^{\mathrm{2ln}\:{x}} } −\mathrm{9}^{\mathrm{2}^{\mathrm{ln}\:{x}} } }{\mathrm{ln}\:{x}}\:=? \\ $$

Question Number 104964 Answers: 0 Comments: 0

Question Number 104207 Answers: 2 Comments: 0

Question Number 104199 Answers: 2 Comments: 0

solve for real values of x the equation 4(3^(2x+1) )+17(3^x )=7. if m and n are positive real numbers other than 1, show that the log_n m+log_(1/m) n=0

$${solve}\:{for}\:{real}\:{values}\:{of}\:{x}\:{the}\:{equation} \\ $$$$\mathrm{4}\left(\mathrm{3}^{\mathrm{2}{x}+\mathrm{1}} \right)+\mathrm{17}\left(\mathrm{3}^{{x}} \right)=\mathrm{7}. \\ $$$${if}\:{m}\:{and}\:{n}\:{are}\:{positive}\:{real}\:{numbers}\:{other} \\ $$$${than}\:\mathrm{1},\:{show}\:{that}\:{the}\:\mathrm{log}_{{n}} {m}+\mathrm{log}_{\frac{\mathrm{1}}{{m}}} {n}=\mathrm{0} \\ $$

Question Number 104197 Answers: 2 Comments: 0

calculate ∫_5 ^(+∞) (dx/((x^2 −9)^4 ))

$$\mathrm{calculate}\:\int_{\mathrm{5}} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{9}\right)^{\mathrm{4}} } \\ $$

Question Number 104201 Answers: 0 Comments: 0

If a^2 + b^2 + c^2 = 1 and b + ic = (1 + a)z, then show that ((a + ib)/(i + c)) = ((1 + iz)/(1 − iz))

$$\mathrm{If}\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{1}\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\mathrm{b}\:\:+\:\:\mathrm{ic}\:\:=\:\:\left(\mathrm{1}\:\:+\:\:\mathrm{a}\right)\mathrm{z}, \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\:\:\:\:\:\:\frac{\mathrm{a}\:\:+\:\:\mathrm{ib}}{\mathrm{i}\:\:+\:\:\mathrm{c}}\:\:\:=\:\:\:\frac{\mathrm{1}\:\:+\:\:\mathrm{iz}}{\mathrm{1}\:\:−\:\:\mathrm{iz}} \\ $$

Question Number 104191 Answers: 1 Comments: 0

Given (E):x^4 −10x^2 +q=0 U=x^2 so (E_((U)) )=U^2 −40U+q=0 . We suppose that E_((U)) has two roots such as r_1 <r_(2 ) . We give also that r_1 +r_2 =40 and r_1 ×r_2 =q. 1)The equation E has four positive solution. Determinate them such that these solutions form an arithmetical progression.

$${Given}\:\left({E}\right):{x}^{\mathrm{4}} −\mathrm{10}{x}^{\mathrm{2}} +{q}=\mathrm{0} \\ $$$${U}={x}^{\mathrm{2}} \:{so}\:\left({E}_{\left({U}\right)} \right)={U}^{\mathrm{2}} −\mathrm{40}{U}+{q}=\mathrm{0}\:. \\ $$$${We}\:{suppose}\:{that}\:{E}_{\left({U}\right)} {has}\:{two}\:{roots} \\ $$$${such}\:{as}\:{r}_{\mathrm{1}} <{r}_{\mathrm{2}\:} . \\ $$$${We}\:{give}\:{also}\:{that}\:{r}_{\mathrm{1}} +{r}_{\mathrm{2}} =\mathrm{40}\:{and} \\ $$$${r}_{\mathrm{1}} ×{r}_{\mathrm{2}} ={q}. \\ $$$$\left.\mathrm{1}\right){The}\:{equation}\:{E}\:{has}\:{four}\:{positive} \\ $$$${solution}.\:{Determinate}\:{them}\:{such} \\ $$$${that}\:{these}\:{solutions}\:{form}\:{an}\: \\ $$$${arithmetical}\:{progression}. \\ $$$$ \\ $$

Question Number 104190 Answers: 3 Comments: 1

integers x,y satisfy 2x+15y=2019. find the minimum of ∣y−x∣.

$${integers}\:{x},{y}\:{satisfy}\:\mathrm{2}{x}+\mathrm{15}{y}=\mathrm{2019}. \\ $$$${find}\:{the}\:{minimum}\:{of}\:\mid{y}−{x}\mid. \\ $$

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