Advanced Math Archive: Questions from April 27, 2023
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for the vector field F(X,y) =yî+ x j (i) Give a table of values and graph several vectors that give a good idea of the field. (ii) The flow curves can be obtained using the differential equatio
1. Para el campo vectorial \[ F(x, y)=y \hat{\imath}+x \hat{\jmath} \] (i) De una tabla de valores y grafique varios vectores que den una buena idea lel campo. (ii) Las curvas de flujo se pueden obten0 answers -
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2 answers
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Solve the following I.V.P. Y y = +3 y(1) = 1 X O a. 2 y = x(ln(x) + 1) 3 O b. y=x(−ln(x)+1)³ O c. O d. X O e. 2 y=x(_ln(x) − 1) 3 2 y = (- ln(x) + 4) 3 2 9 y=(−ln(x) +2) 3
Solve the following I.V.P. \[ y^{\prime}=\frac{y}{x}+3 \sqrt{\frac{x}{y}}, y(1)=1 \] a. \( y=x\left(\frac{9}{2} \ln (x)+1\right)^{\frac{2}{3}} \) b. \( y=x\left(\frac{9}{2} \ln (x)+1\right)^{3} \) c.2 answers -
resolve it
\[ 25^{\log _{5}(x-3)}-3^{\log _{3}(5 x)}+10^{\log _{6} 6}=0 \] Deje constancia de su procedimiento en forma ordenada en el archivo que suba como respuesta. Para calificar esta2 answers -
5. Considere el campo vectorial \( \mathbf{F}(x, y)=\left(4 x^{3} y^{3}+\frac{1}{x}\right) \mathbf{i}+\left(3 x^{4} y^{2}-\frac{1}{y}\right) \mathbf{j} \) : a. ¿Es \( \mathbf{F} \) conservativo? Si l2 answers -
excercises: 1, 2, 3, 4, 5, 11, 15, 17, 23, 24
Answers to Odd-Numbered Problems Begin on Page AN-101. In Problens 1-6, find \( f_{x}, f_{7}, f_{x}(2,-1) \), and \( f_{y}(-2,3) \). \( f(x, y)=3 x-2 y+3 y^{3} \) 2. \( f(x, y)=2 x^{3}-3 y+x^{2} \) 3.2 answers -
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Seleccionar la solución general de la siguiente ecuación diferencial \[ y^{\prime \prime}-4 y=12 t \] a) \( y=3 e^{2 t}+e^{-2 t}-3 t \) b) \( y=3 e^{2 t}+e^{-2 t}+3 t \) c) \( y=3 e^{2 t}-e^{-2 t}-32 answers -
Seleccionar la solución homogénea de la siguiente ecuación diferencial \[ y^{\prime \prime}+y^{\prime}+2 y=e^{t} \] a) \( y=e^{-\frac{t}{2}}\left(A \operatorname{Cos} \frac{\sqrt{7} t}{2}+B \operat2 answers -
Consider the vector field F whose third component is secant squared (i) Find the work done by the force F when it goes from the point P = (0, 0, 0) to L = (−5, 7, π/4 ) for one segment and then fr
\( F=x^{3} y^{4} \hat{i}+x^{4} y^{3} \hat{j}+\sec ^{2}(z) \hat{k} \) 5. Considerar el campo vectorial \( F \) cuya tercera componente es secante al cuadrado \[ F=x^{3} y^{4} \hat{i}+x^{4} y^{3} \hat{2 answers -
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Solve the following equations. (a) \( y^{\prime \prime \prime}+4 y^{\prime \prime}=0 \) (b) \( y^{\prime \prime}+2 y^{\prime}+5 y=0 \) (c) \( y^{\prime \prime}-3 y^{\prime}-10 y=0 \)2 answers -
#20 please help
In Problems 15-22, solve the given integral equation o integro-differential equation for \( y(t) \). 15. \( y(t)+3 \int_{0}^{t} y(v) \sin (t-v) d v=t \) 16. \( y(t)+\int_{0}^{t} e^{t-v} y(v) d v=\sin2 answers -
Hint. Find \( y=m x+b \) 1. (1) \( x+y=6 \) \[ m=\quad b= \] (2) \( x-y=2 \) \[ m=\quad b= \] System: Solutions:2 answers -
(b) \( y^{i v}+2 y^{\prime \prime}+y=3 t+4 \quad y(0)=y^{\prime}(0)=0 \quad, \quad y^{\prime \prime}(0)=y^{\prime \prime \prime}(0)=1 \) Solve the intize velue problem:2 answers -
Identify the equation for the graph. \[ y=(x-1)(x-3)^{3}(x \] B. \( y=(x-1)(x-3)^{2}(x \) -5) \[ y=(x-1)^{2}(x-3)(x \] D. \( y=(x-1)^{3}(x-3)(x \)2 answers -
2. Cuando uno levanta una pesa todo el trabajo realizado se disipa en Calor-¿Cuantas veces tienes que levantar una pesa de \( 50 \mathrm{~kg} \) para bajar \( 1 \mathrm{~kg} \) de peso? (supanga que2 answers -
1. Dos subsistemas satisfacen \( \frac{1}{T_{1}}=\frac{3}{2} \frac{N_{1} K}{U_{1}} \) y \( \frac{1}{T_{2}}=\frac{5}{2} \frac{N_{2} K}{U_{2}} \) con \( N_{1}=2 \mathrm{~mol} \) y \( N_{2}=3 \mathrm{~mo2 answers -
Evalúa \( \iiint_{E}(x-y) d V \), donde \( E \) es la región entre los cilindros \( x^{2}+y^{2}=1, x^{2}+y^{2}=16 \), por encima del plano \( x y \) y debajo del plano \( z=y+4 \).2 answers -
\[ y^{\prime \prime}+2 y^{\prime}+y=\delta(t-3), \quad y(0)=1, \quad y^{\prime}(0)=-1 . \] 4. [26] Solve the initial value problem2 answers -
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porfavor contestar a mano paso a paso
6. Calcule \( \int_{C} z \ln (x+y) d s \), donde \( C \) está dada por la parametrización \[ \begin{array}{l} x=1+3 t \\ y=2+t^{2} \\ z=t^{4} \end{array} \] \[ \text { para }-1 \leq t \leq 1 \text {2 answers -
Find \( \int_{0}^{\sqrt{\frac{5 \pi}{6}}} \int_{0}^{\sqrt{\frac{2 \pi}{3}}} x y \sin \left(x^{2}+y^{2}\right) d x d y \)2 answers -
Calculate, see equation below, where C is given by the parameterization x= 1+3t y= 2+t^2 z= t^4 for -1<=t<=1
6. Calcule \( \int_{C} z \ln (x+y) d s \), donde \( C \) está dada por la parametrización \[ \begin{array}{l} x=1+3 t \\ y=2+t^{2} \\ z=t^{4} \end{array} \] \[ \text { para }-1 \leq t \leq 1 \]2 answers -
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. Determine the inverse function for y= g(t)=7¹-². (If necessary, use the natural log function.) (A) 8¹(y) = 7+2 (B)_g¯¹(y)=7²-y (C)_g¯`¹(y)= In(y + 2) In(7) (D)_g¯¹(y)=2+¹n (y) In (7) (E)
40. Determine the inverse function for \( y=g(t)=7^{t-2} \). (If necessary, use the natural log function.) (A) \( g^{-1}(y)=7^{y+2} \) (B) \( g^{-1}(y)=7^{2-y} \) (C) \( g^{-1}(y)=\frac{\ln (y+2)}{\ln2 answers -
3.- (6 puntos). La ecuación diferencial: \( x y^{\prime \prime}+\sqrt{x} y^{\prime}+5 y=0 \), ¿̇e puede garantizar que tiene solución y es única si \( y(-1)=2 ; y^{\prime}(-1)=0 \) ? a) Verdadero2 answers -
(1 point) Let \( f(x, y)=13 x^{7} y^{4} \). \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x}(3,3)= \\ f_{y}(3,3)= \end{array} \]2 answers -
Differential Equations. Every part of 3. Thanks
Find a formula for the solution of the initial value problem. (a) \( y^{\prime \prime}+3 y^{\prime}+y=f(t), \quad y(0)=0, \quad y^{\prime}(0)=0 \) (b) \( y^{\prime \prime}+4 y=f(t), \quad y(0)=0, \qua2 answers -
1,3 how would you start qestion 1
Lse the method of variation of parametars to find the general solution of exch of the following cquations. 1. 9. \( y^{n}+2 y+y=e^{-x} \log x \) 2. \( y^{2}=1+y=\cot x \), 10. \( y^{\prime \prime}+y=\2 answers -
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Wse the method of variation of parsmetars co find the gemera solution of eveh of the following couations. 1. \( y^{23}+y=\sec x \). 2. \( y^{\prime \prime}+y=\cot x \). 10. \( y+y=\cos x \). 3. \( y^{2 answers -
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Uee the method of variation of parameters to find the general solution of ench of the following equations. 9. \( y^{\prime \prime}+2 y+y=e^{-x} \log x \). 2. \( y^{\prime \prime}+y=\cot x \). 10. \( y2 answers -
(1 point) Let \( f(x, y)=3 y\left(3+x^{2}\right)^{-2} \). \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x}(2,2)= \\ f_{y}(2,2)= \end{array} \]2 answers -
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pls solve ques 6 distinct real roots
Solution: Rewriting the given D E. in operator form \[ \left(D^{2}-D-12\right) y=0 \] 9,4 - HIGHER ENGINEERING MATHEMATICS - III Ans. \( y=c_{1} e^{-2 x}+c_{2} e^{2} \) 6. \( y^{\prime \prime}-6 y^{\p2 answers -
pls solve ques 3
EXERCISE Equal (or repeated or double) root: secon Solve the following: 1. \( y^{\prime \prime}+8 y^{\prime}+16 y=0 \) Ans. \( y=\left(c_{1}+c_{2} x\right) e^{-4 x} \) 2. \( y^{\prime \prime}-6 y^{\pr2 answers -
cauchy's residue theorem
5. \( \int_{0}^{\infty} \frac{x^{2} d x}{\left(x^{2}+1\right)\left(x^{2}+4\right)}=\frac{\pi}{6} \).2 answers -
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