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Question Number 95262    Answers: 3   Comments: 0

3x^2 +5x^4 −7 plz help to solve this equation

$$\mathrm{3x}^{\mathrm{2}} +\mathrm{5x}^{\mathrm{4}} −\mathrm{7} \\ $$$$\mathrm{plz}\:\mathrm{help}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{equation} \\ $$

Question Number 95260    Answers: 1   Comments: 3

if the line 3x+2y−1=0 transformed by matrix A= (((1 a)),((b 2)) ) such that the image is the line 2x+8y+c=0 find the value of a×b×c

$$\mathrm{if}\:\mathrm{the}\:\mathrm{line}\:\mathrm{3x}+\mathrm{2y}−\mathrm{1}=\mathrm{0}\:\mathrm{transformed} \\ $$$$\mathrm{by}\:\mathrm{matrix}\:\mathrm{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{a}}\\{\mathrm{b}\:\:\:\mathrm{2}}\end{pmatrix}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{image}\:\mathrm{is}\:\mathrm{the}\:\mathrm{line}\:\mathrm{2x}+\mathrm{8y}+\mathrm{c}=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}×\mathrm{b}×\mathrm{c}\: \\ $$

Question Number 95259    Answers: 1   Comments: 1

find all roots ((√6) −(√2)i)^(1/3) by using demover theorem ?

$${find}\:{all}\:{roots}\:\left(\sqrt{\mathrm{6}}\:−\sqrt{\mathrm{2}}{i}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} {by}\:{using}\:{demover}\:{theorem}\:? \\ $$

Question Number 95246    Answers: 4   Comments: 0

Question Number 95232    Answers: 3   Comments: 6

Question Number 95230    Answers: 1   Comments: 0

lim_(x→0^+ ) ((7^(√x) −1)/(2^(√x) −1)) = ?

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{7}^{\sqrt{\mathrm{x}}} \:−\mathrm{1}}{\mathrm{2}^{\sqrt{\mathrm{x}}} \:−\mathrm{1}}\:=\:? \\ $$

Question Number 95339    Answers: 6   Comments: 0

f(x)=∣2x+3∣ f ′(x)=...?

$$\mathrm{f}\left(\mathrm{x}\right)=\mid\mathrm{2x}+\mathrm{3}\mid \\ $$$$\mathrm{f}\:'\left(\mathrm{x}\right)=...? \\ $$

Question Number 95227    Answers: 1   Comments: 0

∫_(−π) ^π ∣sin x + cos x ∣ dx =?

$$\underset{−\pi} {\overset{\pi} {\int}}\:\mid\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{cos}\:\mathrm{x}\:\mid\:\mathrm{dx}\:=?\: \\ $$

Question Number 95222    Answers: 1   Comments: 0

{ ((x^2 + x ((xy^2 ))^(1/(3 )) = 80 )),((y^2 + y ((x^2 y))^(1/(3 )) = 5 )) :} find x and y

$$\begin{cases}{{x}^{\mathrm{2}} \:+\:{x}\:\sqrt[{\mathrm{3}\:\:}]{{xy}^{\mathrm{2}} }\:=\:\mathrm{80}\:}\\{{y}^{\mathrm{2}} \:+\:{y}\:\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{2}} {y}}\:=\:\mathrm{5}\:}\end{cases} \\ $$$${find}\:{x}\:{and}\:{y}\: \\ $$

Question Number 95221    Answers: 1   Comments: 0

calculate ∫_0 ^π ln(2+cosθ)dθ

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \mathrm{ln}\left(\mathrm{2}+\mathrm{cos}\theta\right)\mathrm{d}\theta \\ $$

Question Number 95218    Answers: 0   Comments: 0

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^3 (n+1)^3 ))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} \left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 95217    Answers: 1   Comments: 0

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^2 (n+2)^3 ))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} \left(\mathrm{n}+\mathrm{2}\right)^{\mathrm{3}} } \\ $$

Question Number 95216    Answers: 1   Comments: 0

calculste Σ_(n=0) ^∞ (n/((2n+1)^2 (n+3)))

$$\mathrm{calculste}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{n}}{\left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{n}+\mathrm{3}\right)} \\ $$

Question Number 95215    Answers: 1   Comments: 0

calculate Σ_(n=0) ^∞ (((−1)^n )/(4n+1))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{4n}+\mathrm{1}} \\ $$

Question Number 95213    Answers: 0   Comments: 0

find ∫ ((√(x(x+1)))/(√(x+3)))dx

$$\mathrm{find}\:\int\:\frac{\sqrt{\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)}}{\sqrt{\mathrm{x}+\mathrm{3}}}\mathrm{dx} \\ $$

Question Number 95212    Answers: 1   Comments: 0

solve by Laplace transform y^(′′) +5y^′ +2y =x^2 cosx with y(o)=1 and y^′ (0) =2

$$\mathrm{solve}\:\mathrm{by}\:\mathrm{Laplace}\:\mathrm{transform} \\ $$$$\mathrm{y}^{''} \:+\mathrm{5y}^{'} \:+\mathrm{2y}\:=\mathrm{x}^{\mathrm{2}} \mathrm{cosx}\:\:\mathrm{with}\:\mathrm{y}\left(\mathrm{o}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\mathrm{2} \\ $$

Question Number 95211    Answers: 0   Comments: 0

solve by Laplace transform (x+1)y^′ −x^2 y =sin(2x)

$$\mathrm{solve}\:\mathrm{by}\:\mathrm{Laplace}\:\mathrm{transform} \\ $$$$\left(\mathrm{x}+\mathrm{1}\right)\mathrm{y}^{'} \:−\mathrm{x}^{\mathrm{2}} \mathrm{y}\:=\mathrm{sin}\left(\mathrm{2x}\right) \\ $$

Question Number 95209    Answers: 0   Comments: 0

∫(√(1+x^3 ))dx

$$\int\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\mathrm{dx} \\ $$

Question Number 95208    Answers: 0   Comments: 0

i\ ∫((sinx)/x)dx ii\ ∫((cosx)/x)dx iii\ ∫(1/(lnx))dx iv\ ∫(√(1−k^2 sin^2 x))dx v\ ∫(√(sinx))dx vi\ ∫sin(x^2 )dx vii\ ∫cos(x^2 )dx viii\ ∫xtanxdx ix\ ∫e^(−x^2 ) dx x\∫e^x^2 dx xi\ ∫(x^2 /(1+x^5 ))dx xii\ ∫((1+x^2 ))^(1/3) dx

$$\mathrm{i}\backslash\:\int\frac{\mathrm{sinx}}{\mathrm{x}}\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{ii}\backslash\:\int\frac{\mathrm{cosx}}{\mathrm{x}}\mathrm{dx} \\ $$$$\mathrm{iii}\backslash\:\int\frac{\mathrm{1}}{\mathrm{lnx}}\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{iv}\backslash\:\int\sqrt{\mathrm{1}−\mathrm{k}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$$$\mathrm{v}\backslash\:\int\sqrt{\mathrm{sinx}}\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{vi}\backslash\:\int\mathrm{sin}\left(\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$$$\mathrm{vii}\backslash\:\int\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}\:\:\:\:\:\:\mathrm{viii}\backslash\:\int\mathrm{xtanxdx} \\ $$$$\mathrm{ix}\backslash\:\int\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\backslash\int\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$$$\mathrm{xi}\backslash\:\int\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{5}} }\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{xii}\backslash\:\int\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 95206    Answers: 1   Comments: 1

find the equation of the straight line which passes through the point of intersertion of the lines 4x+3y+19=0 and 12x−5y+3=0 and has a y_intercept of 2

$${find}\:{the}\:{equation}\:{of}\:{the}\:{straight}\:{line}\:{which} \\ $$$${passes}\:{through}\:{the}\:{point}\:{of}\:{intersertion}\:{of} \\ $$$${the}\:{lines}\:\mathrm{4}{x}+\mathrm{3}{y}+\mathrm{19}=\mathrm{0}\:{and}\:\mathrm{12}{x}−\mathrm{5}{y}+\mathrm{3}=\mathrm{0} \\ $$$${and}\:{has}\:{a}\:{y\_intercept}\:{of}\:\mathrm{2} \\ $$

Question Number 95202    Answers: 0   Comments: 4

Question Number 95342    Answers: 2   Comments: 0

determine the value of k such that the point A(4,−2,6) B(0,1,0) C(1,0,−5) and D(1,k,−2) lie on the same plane

$$\mathrm{determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{the}\:\mathrm{point}\:\mathrm{A}\left(\mathrm{4},−\mathrm{2},\mathrm{6}\right)\:\mathrm{B}\left(\mathrm{0},\mathrm{1},\mathrm{0}\right)\:\mathrm{C}\left(\mathrm{1},\mathrm{0},−\mathrm{5}\right) \\ $$$$\mathrm{and}\:\mathrm{D}\left(\mathrm{1},\mathrm{k},−\mathrm{2}\right)\:\mathrm{lie}\:\mathrm{on}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{plane}\: \\ $$

Question Number 95341    Answers: 0   Comments: 0

Q) A light falls on two slits 0.15 mm apart.An interference pattern is produced on a screen 60 cm from the slits, if the distance between the second and the fifth bright bands (frings) is 0.7 cm. Calculate the avelength of the used light. solution: Δy_(n=2→n=5) =0.7⇒Δy=0.7/3=0.233×10^(−2) m Δy=((sλ)/d) ⇒λ=((dΔy)/s)=((0.15×10^(−3) ×0.233×10^(−2) )/(60×10^(−2) )) =5.83×10^(−7) =583 nm

$$\left.\mathrm{Q}\right)\:\mathrm{A}\:\mathrm{light}\:\mathrm{falls}\:\mathrm{on}\:\mathrm{two}\:\mathrm{slits}\:\mathrm{0}.\mathrm{15}\:{mm}\:\mathrm{apart}.\mathrm{An}\:\mathrm{interference}\:\mathrm{pattern} \\ $$$$\mathrm{is}\:\mathrm{produced}\:\mathrm{on}\:\mathrm{a}\:\mathrm{screen}\:\mathrm{60}\:{cm}\:\mathrm{from}\:\mathrm{the}\:\mathrm{slits},\:\mathrm{if}\: \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{second}\:\mathrm{and}\:\mathrm{the}\:\mathrm{fifth}\: \\ $$$$\mathrm{bright}\:\mathrm{bands}\:\left(\mathrm{frings}\right)\:\mathrm{is}\:\mathrm{0}.\mathrm{7}\:{cm}.\:\mathrm{Calculate}\:\mathrm{the}\: \\ $$$$\mathrm{avelength}\:\mathrm{of}\:\mathrm{the}\:\mathrm{used}\:\mathrm{light}. \\ $$$$\boldsymbol{{solution}}: \\ $$$$\Delta{y}_{{n}=\mathrm{2}\rightarrow\mathrm{n}=\mathrm{5}} =\mathrm{0}.\mathrm{7}\Rightarrow\Delta{y}=\mathrm{0}.\mathrm{7}/\mathrm{3}=\mathrm{0}.\mathrm{233}×\mathrm{10}^{−\mathrm{2}} \:{m} \\ $$$$\Delta{y}=\frac{{s}\lambda}{{d}}\:\Rightarrow\lambda=\frac{{d}\Delta{y}}{{s}}=\frac{\mathrm{0}.\mathrm{15}×\mathrm{10}^{−\mathrm{3}} ×\mathrm{0}.\mathrm{233}×\mathrm{10}^{−\mathrm{2}} }{\mathrm{60}×\mathrm{10}^{−\mathrm{2}} } \\ $$$$=\mathrm{5}.\mathrm{83}×\mathrm{10}^{−\mathrm{7}} =\mathrm{583}\:{nm} \\ $$

Question Number 95199    Answers: 1   Comments: 0

∫_(−π) ^π cosxln((1+x)/(1−x)) dx=?

$$\int_{−\pi} ^{\pi} {cosxln}\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\:{dx}=? \\ $$

Question Number 95198    Answers: 1   Comments: 0

∫(√((x+2)/(x−3)))dx=?

$$\int\sqrt{\frac{{x}+\mathrm{2}}{{x}−\mathrm{3}}}{dx}=? \\ $$

Question Number 95182    Answers: 1   Comments: 0

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