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Question Number 186863    Answers: 0   Comments: 0

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Question Number 183293    Answers: 1   Comments: 0

Help! A beam being lifted by two forces where F1makes an angle of 23° degrees with the y axis acts in the second quadrant F2 acts in the first quadrant making an angle of 32° degrees with the y axis and the resultant force is 67 N, determine F1 and F2.

$$\: \\ $$$$\:\mathrm{Help}! \\ $$$$\: \\ $$$$\:\mathrm{A}\:\mathrm{beam}\:\mathrm{being}\:\mathrm{lifted}\:\mathrm{by}\:\mathrm{two}\:\mathrm{forces}\:\mathrm{where}\: \\ $$$$\:\mathrm{F1makes}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{23}°\:\mathrm{degrees}\:\mathrm{with}\:\mathrm{the}\:\mathrm{y} \\ $$$$\:\mathrm{axis}\:\mathrm{acts}\:\mathrm{in}\:\mathrm{the}\:\mathrm{second}\:\mathrm{quadrant}\:\mathrm{F2}\:\mathrm{acts}\:\mathrm{in} \\ $$$$\:\mathrm{the}\:\mathrm{first}\:\mathrm{quadrant}\:\mathrm{making}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{32}° \\ $$$$\:\mathrm{degrees}\:\mathrm{with}\:\mathrm{the}\:\mathrm{y}\:\mathrm{axis}\:\mathrm{and}\:\mathrm{the}\:\mathrm{resultant} \\ $$$$\:\mathrm{force}\:\mathrm{is}\:\mathrm{67}\:\mathrm{N},\:\mathrm{determine}\:\mathrm{F1}\:\mathrm{and}\:\mathrm{F2}. \\ $$$$\: \\ $$

Question Number 183165    Answers: 1   Comments: 0

Question Number 182438    Answers: 1   Comments: 0

[Help me!] The rate of change of w = x^3 y^2 z + y^3 z^2 − xz^4 at the point Q(0, 1, 2) in the direction V^→ = 2i + j + 2k is: a) −2 b) −3 c) −4 d) No alternative

$$\: \\ $$$$\:\left[\boldsymbol{\mathrm{Help}}\:\:\boldsymbol{\mathrm{me}}!\right] \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{The}}\:\:\boldsymbol{\mathrm{rate}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{change}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{w}}\:\:=\:\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} \boldsymbol{\mathrm{y}}^{\mathrm{2}} \boldsymbol{\mathrm{z}}\:\:+\:\boldsymbol{\mathrm{y}}^{\mathrm{3}} \boldsymbol{\mathrm{z}}^{\mathrm{2}} \:−\:\boldsymbol{\mathrm{xz}}^{\mathrm{4}} \:\:\boldsymbol{\mathrm{at}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{point}}\:\:\boldsymbol{\mathrm{Q}}\left(\mathrm{0},\:\mathrm{1},\:\mathrm{2}\right) \\ $$$$\:\boldsymbol{\mathrm{in}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{direction}}\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{V}}}\:\:=\:\:\mathrm{2}\boldsymbol{\mathrm{i}}\:\:+\:\:\boldsymbol{\mathrm{j}}\:\:+\:\:\mathrm{2}\boldsymbol{\mathrm{k}}\:\:\boldsymbol{\mathrm{is}}: \\ $$$$\: \\ $$$$\left.\:\boldsymbol{\mathrm{a}}\right)\:−\mathrm{2} \\ $$$$\left.\:\boldsymbol{\mathrm{b}}\right)\:−\mathrm{3} \\ $$$$\left.\:\boldsymbol{\mathrm{c}}\right)\:−\mathrm{4} \\ $$$$\left.\:\boldsymbol{\mathrm{d}}\right)\:\boldsymbol{\mathrm{No}}\:\:\boldsymbol{\mathrm{alternative}} \\ $$$$\: \\ $$

Question Number 182348    Answers: 1   Comments: 0

∫_0 ^2 ∫_0 ^3 ∫_0 ^4 e^(x+y+z) dx dy dz=?

$$\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{3}} \int_{\mathrm{0}} ^{\mathrm{4}} {e}^{{x}+{y}+{z}} {dx}\:{dy}\:{dz}=? \\ $$

Question Number 181730    Answers: 0   Comments: 2

Question Number 181707    Answers: 1   Comments: 0

if 2x+(1/( (√x)))=(1/2) find the value 8x+(1/( (√x)))=?

$$\boldsymbol{{if}}\:\:\:\:\:\mathrm{2}\boldsymbol{{x}}+\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\:\:\mathrm{8}\boldsymbol{{x}}+\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}}}=? \\ $$

Question Number 181025    Answers: 0   Comments: 1

Send you solutions to [email protected]

$$\mathrm{Send}\:\mathrm{you}\:\mathrm{solutions}\:\mathrm{to}\:\boldsymbol{\mathrm{kinmatics}}@\boldsymbol{\mathrm{gmail}}.\boldsymbol{\mathrm{com}} \\ $$

Question Number 180254    Answers: 1   Comments: 0

Question Number 181567    Answers: 0   Comments: 0

Question Number 174489    Answers: 0   Comments: 0

The points A, B and C have position vectors a, b and c respectively reffrred to an origin O. i. Given that the point X lie on AB produced so that AB : BX=2:1, find x, the position vector of X in terms of b and c. ii. if Y lies on BC, between B and C so that BY : YC = 1:3, find y, the position vector of Y in terms of b and c. iii. Given that Z is the mid point of AC, show that X, Y and Z are collinear.

$$\mathrm{The}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{have}\:\mathrm{position}\:\mathrm{vectors} \\ $$$$\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}\:\mathrm{respectively}\:\mathrm{reffrred}\:\mathrm{to}\:\mathrm{an}\:\mathrm{origin}\:\mathrm{O}. \\ $$$$\mathrm{i}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:\mathrm{X}\:\mathrm{lie}\:\mathrm{on}\:\mathrm{AB}\:\mathrm{produced} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{AB}\::\:\mathrm{BX}=\mathrm{2}:\mathrm{1},\:\mathrm{find}\:{x},\:\mathrm{the}\:\mathrm{position} \\ $$$$\mathrm{vector}\:\mathrm{of}\:\mathrm{X}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\boldsymbol{\mathrm{b}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}. \\ $$$$\mathrm{ii}.\:\mathrm{if}\:\mathrm{Y}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{BC},\:\mathrm{between}\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{BY}\::\:\mathrm{YC}\:=\:\mathrm{1}:\mathrm{3},\:\mathrm{find}\:{y},\:\mathrm{the}\:\mathrm{position}\:\mathrm{vector} \\ $$$$\mathrm{of}\:\mathrm{Y}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\boldsymbol{\mathrm{b}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}. \\ $$$$\mathrm{iii}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{Z}\:\:\mathrm{is}\:\mathrm{the}\:\mathrm{mid}\:\mathrm{point}\:\mathrm{of}\:\mathrm{AC},\: \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{X},\:\mathrm{Y}\:\mathrm{and}\:\mathrm{Z}\:\mathrm{are}\:\mathrm{collinear}. \\ $$

Question Number 173069    Answers: 2   Comments: 0

Θ =∫_0 ^( ∞) ∫_0 ^( ∞) xy e^( −(x+y)) cos(x+y )dxdy=(1/σ) find the value of ” σ ”.

$$ \\ $$$$ \\ $$$$\:\:\:\Theta\:=\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} {xy}\:{e}^{\:−\left({x}+{y}\right)} {cos}\left({x}+{y}\:\right){dxdy}=\frac{\mathrm{1}}{\sigma} \\ $$$$\:\:\:\:\:\:\:\:{find}\:{the}\:\:{value}\:{of}\:\:''\:\sigma\:\:''. \\ $$$$ \\ $$

Question Number 171033    Answers: 2   Comments: 1

lim_(x→0) (1/x) [ ((((1−(√(1−x)))/( (√(1+x))−1)) ))^(1/3) −1 ]=?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}}\:\left[\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}−\sqrt{\mathrm{1}−{x}}}{\:\sqrt{\mathrm{1}+{x}}−\mathrm{1}}\:}−\mathrm{1}\:\right]=? \\ $$

Question Number 170079    Answers: 2   Comments: 0

∣a^→ ∣=1 ∣b^→ ∣=2 ∢(a^→ , b^→ )=(π/3) ∣a^→ +b^→ ∣=?

$$\mid\overset{\rightarrow} {{a}}\mid=\mathrm{1} \\ $$$$\mid\overset{\rightarrow} {{b}}\mid=\mathrm{2} \\ $$$$\sphericalangle\left(\overset{\rightarrow} {{a}},\:\overset{\rightarrow} {{b}}\right)=\frac{\pi}{\mathrm{3}} \\ $$$$\mid\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid=? \\ $$

Question Number 169885    Answers: 1   Comments: 0

∣a^→ ∣=13 ∣b^→ ∣=19 ∣a^→ +b^→ ∣=24 ∣a^→ −b^→ ∣=?

$$\mid\overset{\rightarrow} {{a}}\mid=\mathrm{13} \\ $$$$\mid\overset{\rightarrow} {{b}}\mid=\mathrm{19} \\ $$$$\mid\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid=\mathrm{24} \\ $$$$\mid\overset{\rightarrow} {{a}}−\overset{\rightarrow} {{b}}\mid=? \\ $$

Question Number 169640    Answers: 0   Comments: 1

∫cos(x^7 )dx =

$$\int\mathrm{cos}\left({x}^{\mathrm{7}} \right){dx}\:= \\ $$

Question Number 169308    Answers: 0   Comments: 0

Question Number 168977    Answers: 0   Comments: 0

check that the function u(x,t) = exp{−((n^2 α^2 π^2 )/L^2 )t} sin((nπx)/L) n = 1,2,... satisfy the heat equation heat equation α^2 (∂^2 u/∂x^2 ) = (∂u/∂t), 0 < x < L

$$\mathrm{check}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function} \\ $$$${u}\left({x},{t}\right)\:=\:\mathrm{exp}\left\{−\frac{{n}^{\mathrm{2}} \alpha^{\mathrm{2}} \pi^{\mathrm{2}} }{{L}^{\mathrm{2}} }{t}\right\}\:\mathrm{sin}\frac{{n}\pi{x}}{{L}} \\ $$$${n}\:=\:\mathrm{1},\mathrm{2},...\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{heat}\:\mathrm{equation} \\ $$$$\boldsymbol{\mathrm{heat}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\alpha^{\mathrm{2}} \frac{\partial^{\mathrm{2}} {u}}{\partial{x}^{\mathrm{2}} }\:=\:\frac{\partial{u}}{\partial{t}},\:\mathrm{0}\:<\:{x}\:<\:{L} \\ $$

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