Advanced Math Archive: Questions from October 28, 2022
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i) \( \frac{4}{2 x+3}=\frac{5}{6 x+9} \). ii) \( (y-3)^{7} \quad[ \) Expand. Bionomially] iii) \( 4 x^{2}-8 x+4=0 \quad \) [QUADRATIC FORMULA iv) \( 3 x+y+2 z=2 \) \( 3 x+y+2 z=2 \) \( 2 x+2 y+z=1 \)\2 answers -
Solve the following initial value problem. \[ y^{\prime \prime \prime}-4 y^{\prime \prime}+y^{\prime}+6 y=0 ; \quad y(0)=-1, \quad y^{\prime}(0)=3, \quad y^{\prime \prime}(0)=-3 \]2 answers -
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In Problems \( 1-8 \), find the general solution of the given equation. 1. \( t^{2} y^{\prime \prime}+5 t y^{\prime}-5 y=0 \) 2. \( 2 t^{2} y^{\prime \prime}+3 t y^{\prime}-y=0 \) 3. \( (t-1)^{2} y^{\2 answers -
i) \( \frac{4}{2 x+3}=\frac{5}{6 x+9} \). ii) \( (y-3)^{7} \quad[ \) Expand. Bionomially] iii) \( 4 x^{2}-8 x+4=0 \quad \) [QUADRATIC FORMULA iv) \( 3 x+y+2 z=2 \) \( 3 x+y+2 z=2 \) \( 2 x+2 y+z=1 \)\2 answers -
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2 answers
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Using the method of undetermined coefficients, find general solutions of the nonhomogeneous differential equations
\( y^{I V}+4 y^{\prime \prime}=8 e^{2 x}+8 x^{2} \) \( y^{I V}-y^{\prime \prime \prime}=\sin x+e^{x} \) \( y^{I V}-y=2 e^{x}+5 e^{x} \sin x \) \( y^{I V}+y^{\prime \prime \prime}-y^{\prime \prime}-y^{0 answers -
control system
\( x(z)=\frac{\sum_{n=1}^{n=4} b(n) \cdot z^{-n}}{\sum_{n=0}^{n=3} a(n) \cdot z^{-n}} \)2 answers -
Exercise 5.- Prove that if \( x^{2}+y^{2}=1 \) then a) \( |x+y| \leq \sqrt{2} \). b) \( |x-y| \leq \sqrt{2} \). c) \( |x|+|y| \leq \sqrt{2} \) d) ||\( x+y|-| x-y|| \leq \sqrt{2} \).2 answers -
2 answers
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2 answers
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Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, z=2 y \) and \( x^{2}=25-y \) 1. \( \int_{a}^2 answers -
Example 4: Solve the following system \( \left\{\begin{array}{l}(x, y, z)=(0,1,4)+s(2,1,6) \\ (x, y, z)=(-1,3,1)+t(5,2,0)\end{array}\right. \)2 answers -
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Hallar las siguientes transformadas de Laplace inversas: 1. \( L^{-1}\left\{\frac{1}{s^{4}}\right\} \) 2. \( L^{-1}\left\{\frac{1}{s^{2}}-\frac{48}{s^{5}}\right\} \) 3. \( L^{-1}\left\{\frac{1}{4 s+1}2 answers -
1. Identifique y represente en el plano complejo el conjunto de puntos que satisface las siguientes rel \[ |z-1|+|z+1| \leq 2, \quad|\operatorname{Re} z|2 answers -
2 answers
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Determina los coeficientes de la derivada. \[ f(x)=\left(-4 x^{2}+-7 x+-2\right) \text { por }\left(-4 x^{2}+1 x+6\right) \]2 answers -
determjne the characteristics of the graph vertical dialation vertical translation horizontal translation period= pi/
Determina las características de la gráfica. \( y=-6 \) cotangente \( -5(\theta+1)+2 \) Dilación vertical \( = \) Traslación vertical \( = \) Traslación horizontal = Periodo \( =\pi / \)2 answers -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, z=4 y \) and \( x^{2}=4-y \). 1. \( \int_{a}^2 answers