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Question Number 171622    Answers: 0   Comments: 0

Question Number 171614    Answers: 0   Comments: 11

A particle is moving along a straight line such that it's position from a fixed point is S = ( 12 - 15t² + 5t³ )m where t is in seconds. Determine: A. Total distance travelled by the particle from t = 1sec to t = 3sec B. The average speed of the particle during this time.

A particle is moving along a straight line such that it's position from a fixed point is S = ( 12 - 15t² + 5t³ )m where t is in seconds. Determine: A. Total distance travelled by the particle from t = 1sec to t = 3sec B. The average speed of the particle during this time.

Question Number 171599    Answers: 0   Comments: 0

Ω=∫_0 ^1 Log(((Log^2 (x))/x^(x^5 −x^4 +x^3 −x^2 +x−1) ))dx Mastermind

$$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} {Log}\left(\frac{{Log}^{\mathrm{2}} \left({x}\right)}{{x}^{{x}^{\mathrm{5}} −{x}^{\mathrm{4}} +{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +{x}−\mathrm{1}} }\right){dx} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171575    Answers: 0   Comments: 3

Question Number 171518    Answers: 0   Comments: 2

Question Number 171502    Answers: 0   Comments: 1

Solve (dy/dx)(xcos y+asin 2y)=−1 (dy/dx)=(((y+2)/(x+y−1)))^2

$${Solve} \\ $$$$\frac{{dy}}{{dx}}\left({x}\mathrm{cos}\:{y}+{a}\mathrm{sin}\:\mathrm{2}{y}\right)=−\mathrm{1} \\ $$$$\frac{{dy}}{{dx}}=\left(\frac{{y}+\mathrm{2}}{{x}+{y}−\mathrm{1}}\right)^{\mathrm{2}} \\ $$

Question Number 171493    Answers: 1   Comments: 0

Question Number 171491    Answers: 0   Comments: 0

Question Number 171490    Answers: 0   Comments: 0

Question Number 171475    Answers: 1   Comments: 0

Question Number 171472    Answers: 0   Comments: 0

lim_(a→∞) Σ_(n=1) ^a ((e^(in) .ln∣(1/x)∣)/(πn^2 )).tan^(−1) (n(√π)) Mastermind

$${li}\underset{{a}\rightarrow\infty} {{m}}\:\underset{{n}=\mathrm{1}} {\overset{{a}} {\sum}}\frac{{e}^{{in}} .{ln}\mid\frac{\mathrm{1}}{{x}}\mid}{\pi{n}^{\mathrm{2}} }.{tan}^{−\mathrm{1}} \left({n}\sqrt{\pi}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171437    Answers: 2   Comments: 0

make r the subject of the formula y=(((pr)/m) − (p^3 /1))^(−3/2) find r if y=−8 , m=−1, p=3

$$\mathrm{make}\:\boldsymbol{\mathrm{r}}\:\:\:\mathrm{the}\:\mathrm{subject}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formula} \\ $$$$ \\ $$$$\boldsymbol{\mathrm{y}}=\left(\frac{\boldsymbol{\mathrm{pr}}}{\boldsymbol{\mathrm{m}}}\:\:−\:\frac{\boldsymbol{\mathrm{p}}^{\mathrm{3}} }{\mathrm{1}}\right)^{−\mathrm{3}/\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{r}}\:\mathrm{if}\:\mathrm{y}=−\mathrm{8}\:\:\:,\:\:\mathrm{m}=−\mathrm{1},\:\:\mathrm{p}=\mathrm{3} \\ $$

Question Number 171332    Answers: 0   Comments: 2

A bicycle has a constant velocity of 10 m/s. A person starts from rest and runs to catch up to the bicycle in 30 s. What is the acceleration of the person?

A bicycle has a constant velocity of 10 m/s. A person starts from rest and runs to catch up to the bicycle in 30 s. What is the acceleration of the person?

Question Number 171314    Answers: 1   Comments: 0

If C_r , C_s are cyclic groups such that g.c.d(r,s)=1, then show that C_r ×C_s is a cyclic group. Mastermind

$${If}\:{C}_{{r}} ,\:{C}_{{s}} \:{are}\:{cyclic}\:{groups}\:{such}\:{that} \\ $$$${g}.{c}.{d}\left({r},{s}\right)=\mathrm{1},\:{then}\:{show}\:{that}\:{C}_{{r}} ×{C}_{{s}} \:{is} \\ $$$${a}\:{cyclic}\:{group}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171179    Answers: 1   Comments: 0

Question Number 171161    Answers: 1   Comments: 0

Question Number 171153    Answers: 1   Comments: 0

An aeroplane covers a certain distance at a speed of 240kmph in 5 hours. to cover the same distance in 1(2/3) hrs, it must travel at a speed of: A) 300kmph B) 360kmph C) 600kmph D) 700kmph Mastermind

$${An}\:{aeroplane}\:{covers}\:{a}\:{certain}\:{distance} \\ $$$${at}\:{a}\:{speed}\:{of}\:\mathrm{240}{kmph}\:{in}\:\mathrm{5}\:{hours}. \\ $$$${to}\:{cover}\:{the}\:{same}\:{distance}\:{in}\:\mathrm{1}\frac{\mathrm{2}}{\mathrm{3}}\:{hrs}, \\ $$$${it}\:{must}\:{travel}\:{at}\:{a}\:{speed}\:{of}: \\ $$$$\left.{A}\right)\:\mathrm{300}{kmph} \\ $$$$\left.{B}\right)\:\mathrm{360}{kmph} \\ $$$$\left.{C}\right)\:\mathrm{600}{kmph} \\ $$$$\left.{D}\right)\:\mathrm{700}{kmph} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171152    Answers: 1   Comments: 0

The average ages of three person is 27 years. Their ages are in the propor tion of 1:3:5. What is the age in years of the youngest one among them? Mastermind

$${The}\:{average}\:{ages}\:{of}\:{three}\:{person}\:{is} \\ $$$$\mathrm{27}\:{years}.\:{Their}\:{ages}\:{are}\:{in}\:{the}\:{propor} \\ $$$${tion}\:{of}\:\mathrm{1}:\mathrm{3}:\mathrm{5}.\:{What}\:{is}\:{the}\:{age}\:{in}\:{years} \\ $$$${of}\:{the}\:{youngest}\:{one}\:{among}\:{them}? \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171107    Answers: 0   Comments: 0

Please help lim_(x→−∞) (x−1)e^(x−1) −1=? lim_(x→+∞) (x−1)e^(x−1) −1=? g(x)=(x−1)e^(x−1) −1 g(x)′=?

$${Please}\:{help} \\ $$$${li}\underset{{x}\rightarrow−\infty} {{m}}\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1}=? \\ $$$${li}\underset{{x}\rightarrow+\infty} {{m}}\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1}=? \\ $$$${g}\left({x}\right)=\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1} \\ $$$${g}\left({x}\right)'=? \\ $$$$ \\ $$

Question Number 171094    Answers: 0   Comments: 0

prove that: 𝛀=Σ_(n=0) ^∞ ((((n!)^2 )/((2n)!)))^2 (2^(4n) /((2n+1)^3 ))=^? (7/2)𝛇(3)−πG G−Catalan′s constant

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}: \\ $$$$\boldsymbol{\Omega}=\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\left(\boldsymbol{\mathrm{n}}!\right)^{\mathrm{2}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}\right)!}\right)^{\mathrm{2}} \frac{\mathrm{2}^{\mathrm{4}\boldsymbol{\mathrm{n}}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} }\overset{?} {=}\frac{\mathrm{7}}{\mathrm{2}}\boldsymbol{\zeta}\left(\mathrm{3}\right)−\pi\boldsymbol{\mathrm{G}} \\ $$$$\boldsymbol{\mathrm{G}}−\boldsymbol{\mathrm{Catalan}}'\boldsymbol{\mathrm{s}}\:\:\boldsymbol{\mathrm{constant}} \\ $$

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 171025    Answers: 2   Comments: 0

Question Number 171038    Answers: 2   Comments: 0

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

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

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