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Question Number 69847 Answers: 1 Comments: 0

A plane is travelling at 500km/hr eastward. wind blows at 90km/hr southward. find the velocity and direction if the plane rlative to the ground.

$${A}\:{plane}\:{is}\:{travelling}\:{at}\:\mathrm{500}{km}/{hr}\:{eastward}. \\ $$$${wind}\:{blows}\:{at}\:\mathrm{90}{km}/{hr}\:{southward}. \\ $$$${find}\:{the}\:{velocity}\:{and}\:{direction}\:{if}\:{the}\:{plane}\:{rlative}\:{to}\:{the}\:{ground}. \\ $$

Question Number 69846 Answers: 1 Comments: 0

Find the x−component and y−component of a 25N force acting at 210° angle

$${Find}\:{the}\:{x}−{component}\:{and}\:{y}−{component}\:{of}\:{a}\:\mathrm{25}{N}\:{force}\:{acting}\:{at}\:\mathrm{210}°\:{angle} \\ $$

Question Number 69836 Answers: 1 Comments: 2

Question Number 69829 Answers: 2 Comments: 2

Question Number 69827 Answers: 2 Comments: 0

The acceleration of a particle moving in a straight line is defined as a=6t−20 m/s^2 , where t is in seconds. Knowing that s=0m when t=3s and that t=5sec when v=2m/s. Determine the total distance travelled when t=11s.

$${The}\:{acceleration}\:{of}\:{a}\:{particle}\:{moving} \\ $$$${in}\:{a}\:{straight}\:{line}\:{is}\:{defined}\:{as}\:{a}=\mathrm{6}{t}−\mathrm{20} \\ $$$${m}/{s}^{\mathrm{2}} ,\:{where}\:{t}\:{is}\:{in}\:{seconds}.\:{Knowing} \\ $$$${that}\:{s}=\mathrm{0}{m}\:{when}\:{t}=\mathrm{3}{s}\:{and}\:{that}\:{t}=\mathrm{5}{sec} \\ $$$${when}\:{v}=\mathrm{2}{m}/{s}.\:{Determine}\:{the}\:{total} \\ $$$${distance}\:{travelled}\:{when}\:{t}=\mathrm{11}{s}. \\ $$

Question Number 69809 Answers: 2 Comments: 2

lim_(x→∞) xsin (π/x)

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\mathrm{sin}\:\frac{\pi}{{x}} \\ $$

Question Number 69803 Answers: 0 Comments: 2

1)find f(α) =∫_0 ^∞ ((cos(αx))/((x^4 +1)^2 ))dx with α real 2) find the value of ∫_0 ^∞ ((cos(2x))/((x^4 +1)^2 ))dx 3) find nature of the serie Σf(n)

$$\left.\mathrm{1}\right){find}\:\:\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\alpha{x}\right)}{\left({x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma{f}\left({n}\right) \\ $$

Question Number 69795 Answers: 0 Comments: 1

let p(x)=(x+in)^n −n^n with n integr natural 1) find the roots of p(x) 2)factorize p(x) inside C[x] 3) decompose the fraction F(x)=(1/(p(x)))

$${let}\:{p}\left({x}\right)=\left({x}+{in}\right)^{{n}} −{n}^{{n}} \:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{p}\left({x}\right)} \\ $$

Question Number 69794 Answers: 1 Comments: 2

let p(x)=(x+1)^6 −e^(iα) with α real 1) find the roots of p(x) 2) factorize p(x)inside C[x] 3)factorize p(x)inside R[x]

$${let}\:{p}\left({x}\right)=\left({x}+\mathrm{1}\right)^{\mathrm{6}} \:−{e}^{{i}\alpha} \:\:\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right){inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right){factorize}\:{p}\left({x}\right){inside}\:{R}\left[{x}\right] \\ $$

Question Number 69792 Answers: 1 Comments: 1

find f(α) =∫ (dx/(x+α+(√(x^2 +3)))) and g(α)=∫ (dx/((x+α+(√(x^2 +3)))^2 )) with α real

$${find}\:{f}\left(\alpha\right)\:=\int\:\:\:\frac{{dx}}{{x}+\alpha+\sqrt{{x}^{\mathrm{2}} \:+\mathrm{3}}} \\ $$$${and}\:{g}\left(\alpha\right)=\int\:\:\:\frac{{dx}}{\left({x}+\alpha+\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}\right)^{\mathrm{2}} }\:\:\:\:{with}\:\alpha\:{real} \\ $$

Question Number 69790 Answers: 0 Comments: 1

sove (x^2 −3x)y^(′′) +2x y^′ =(2x+1)e^(−x^2 )

$${sove}\:\left({x}^{\mathrm{2}} −\mathrm{3}{x}\right){y}^{''} \:\:+\mathrm{2}{x}\:{y}^{'} \:=\left(\mathrm{2}{x}+\mathrm{1}\right){e}^{−{x}^{\mathrm{2}} } \\ $$

Question Number 69789 Answers: 0 Comments: 0

solve sin(2x)y^′ −3(cosx)y =xe^(−x)

$${solve}\:{sin}\left(\mathrm{2}{x}\right){y}^{'} \:−\mathrm{3}\left({cosx}\right){y}\:={xe}^{−{x}} \\ $$

Question Number 69786 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ (((2n+1)(−1)^n )/(n^2 (n+1)(n+2)^2 ))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)^{\mathrm{2}} } \\ $$

Question Number 69784 Answers: 0 Comments: 0

calculate f(a) =∫_0 ^∞ e^(−(x^2 +(a/x^2 ))) dx with a>0

$${calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left({x}^{\mathrm{2}} \:+\frac{{a}}{{x}^{\mathrm{2}} }\right)} {dx}\:\:{with}\:{a}>\mathrm{0} \\ $$

Question Number 69778 Answers: 2 Comments: 5

prove that the equation (b^2 −4ac)x^2 + 4(a + c)x −4 = 0 is always real.

$${prove}\:{that}\:{the}\:{equation}\: \\ $$$$\:\:\left({b}^{\mathrm{2}} −\mathrm{4}{ac}\right){x}^{\mathrm{2}} \:+\:\mathrm{4}\left({a}\:+\:{c}\right){x}\:−\mathrm{4}\:=\:\mathrm{0}\:{is}\:{always}\:{real}. \\ $$

Question Number 69766 Answers: 0 Comments: 4

find (dy/dx) at the point (0,3) when 2x^2 y + y + 4xy^2 = 2x + 3

$${find}\:\:\frac{{dy}}{{dx}}\:\:{at}\:{the}\:{point}\:\:\left(\mathrm{0},\mathrm{3}\right)\:\:{when}\:\:\mathrm{2}{x}^{\mathrm{2}} {y}\:+\:{y}\:+\:\mathrm{4}{xy}^{\mathrm{2}} \:=\:\mathrm{2}{x}\:+\:\mathrm{3}\: \\ $$

Question Number 69765 Answers: 1 Comments: 0

Given that y = (√(5x^2 + 3)) , show that when x^2 = (6/5) , (d^2 y/dx^(2 ) ) = ((125)/8)

$${Given}\:{that}\:\:{y}\:=\:\sqrt{\mathrm{5}{x}^{\mathrm{2}} \:+\:\mathrm{3}}\:,\:{show}\:{that}\:\:{when}\:{x}^{\mathrm{2}} \:=\:\frac{\mathrm{6}}{\mathrm{5}}\:,\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}\:} }\:=\:\frac{\mathrm{125}}{\mathrm{8}} \\ $$

Question Number 69764 Answers: 1 Comments: 1

find (dy/dx) if x = sin^2 t and y= tan t at t = (π/4)

$${find}\:\:\:\frac{{dy}}{{dx}}\:\:{if}\:\:{x}\:=\:{sin}^{\mathrm{2}} {t}\:\:{and}\:\:{y}=\:{tan}\:{t}\:{at}\:\:{t}\:=\:\frac{\pi}{\mathrm{4}} \\ $$

Question Number 69763 Answers: 1 Comments: 2

find (dy/dx) if y = 3^x e^(2x + 1) , at x =1

$${find}\:\frac{{dy}}{{dx}}\:\:{if}\:\:{y}\:=\:\mathrm{3}^{{x}} {e}^{\mathrm{2}{x}\:+\:\mathrm{1}} ,\:{at}\:{x}\:=\mathrm{1} \\ $$

Question Number 69762 Answers: 1 Comments: 1

prove by mathematical induction, that for all positive integers n, Σ_(r=1) ^n r(r + 1) = (n/3)(n + 1)( n + 2)

$${prove}\:{by}\:{mathematical}\:{induction},\:{that}\:{for}\:{all}\:{positive}\:{integers}\:{n}, \\ $$$$\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{r}\left({r}\:+\:\mathrm{1}\right)\:=\:\frac{{n}}{\mathrm{3}}\left({n}\:+\:\mathrm{1}\right)\left(\:{n}\:+\:\mathrm{2}\right) \\ $$

Question Number 69754 Answers: 0 Comments: 2

Question Number 69746 Answers: 1 Comments: 1

Question Number 69741 Answers: 2 Comments: 4

Question Number 69738 Answers: 1 Comments: 0

Sarah dances everyday of the week, including saturdays and sundays. In november 2018, Sarah had to miss a few days. To control her absences she marks the day she missed class with a x on the calendar. She marked the 5th, 21st and 27th of november. What percentage indicates Sarah′s absences in november?

$${Sarah}\:{dances}\:{everyday}\:{of}\:{the}\:{week}, \\ $$$${including}\:{saturdays}\:{and}\:{sundays}. \\ $$$${In}\:{november}\:\mathrm{2018},\:{Sarah}\:{had}\:{to}\:{miss} \\ $$$${a}\:{few}\:{days}.\:{To}\:{control}\:{her}\:{absences} \\ $$$${she}\:{marks}\:{the}\:{day}\:{she}\:{missed}\:{class} \\ $$$${with}\:{a}\:\boldsymbol{{x}}\:{on}\:{the}\:{calendar}. \\ $$$${She}\:{marked}\:{the}\:\mathrm{5}{th},\:\mathrm{21}{st}\:{and}\:\mathrm{27}{th} \\ $$$${of}\:{november}. \\ $$$${What}\:{percentage}\:{indicates}\:{Sarah}'{s} \\ $$$${absences}\:{in}\:{november}? \\ $$

Question Number 69735 Answers: 1 Comments: 1

∫_( 0) ^(π/4) ((sin x+cos x)/(3+sin 2x)) dx =

$$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{3}+\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\:= \\ $$

Question Number 69734 Answers: 0 Comments: 1

If I_n = ∫_(0 ) ^(π/4) tan^n x dx, n ∈ N, then I_(n+2) +I_n =

$$\mathrm{If}\:{I}_{{n}} =\:\underset{\mathrm{0}\:} {\overset{\pi/\mathrm{4}} {\int}}\mathrm{tan}^{{n}} {x}\:{dx},\:{n}\:\in\:{N},\:\mathrm{then}\:{I}_{{n}+\mathrm{2}} +{I}_{{n}} = \\ $$

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