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Other Math Archive: Questions from December 07, 2022

• Using the Laplace transforms. Solve the following I.V.Ps a. y ′′ −4y ′ −12y = 0; y(0) = 8, y ′ (0) = 0 b. y ′′ + 3y ′ + 2y = t; y(0) = 1, y ′ (0) = 0 c. y ′′ −8y ′ + 25y =
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  (a) \( f(x)=\tan \left(e^{x}\right) \) (b) \( r(x)=e^{\tan (x)} \); (c) \( w(x)=\left(1-4 x^{2}\right)^{8} \cos (2 x) \).
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  Pragurta 1 Determina las caracteristicas de la función: Sinverponder \[ f(x)=4 x^{4} \text { más } 8 x^{3}+-52 x^{2}+-56 x+96 \] Grado \( = \) 100 F.Macar \( \quad \) Coefliente Principal = Comporta
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  HYPERBOLA VERTICES: \( (5,-2) \)
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  Pregunta 7 Sin responder aun Puntua como Determina el intercepto en \( y \) de Puntu \( f(x)=\frac{3 x^{2}+5 x+-4}{7 x^{2} \text { más } 2 x+1} \) P Marcar pregunta
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  6. Solve in integers \( x, y: 15 x+36 y=12 \)
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• Test FOR INDETERMiNacy using tree [(Paq) əP]EP
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  1. Determme si la funcion es una transtormacion lineal.. a. Sea \( \mathrm{M}_{2 \times 2} \) el espacio de las matrices \( 2 \times 2 \). Considere \( T: \mathbf{M}_{2 \times 2} \longrightarrow \math
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• #11 please
  In Problems 9-26, find a particular solution to the differential equation. 9. \( y^{\prime \prime}+3 y=-9 \) 10. \( y^{\prime \prime}+2 y^{\prime}-y=10 \) 11. \( y^{\prime \prime}(x)+y(x)=2^{x} \) 12.
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• #19
  In Problems 19-21, solve the given initial value problem. 19. \( y^{\prime \prime \prime}-y^{\prime \prime}-4 y^{\prime}+4 y=0 \); \[ y(0)=-4, \quad y^{\prime}(0)=-1, \quad y^{\prime \prime}(0)=-19 \]
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• Find the solution of this differential equation using the method of variation of parameters. y'' + a^2 y = bsec(ax)tan(ax) Using your parameter values a = 4 , b = 2 From the beginning. Write the ans
  Hallar la solución de esta ecuación diferencial usando el método de variación de parámetros. \[ y^{\prime \prime}+a^{2} y=b \sec (a x) \tan (a x) \] Usar tus valores de los parámetros \( a, b \)
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  Let \( U=\{q, r, s, t, u, v, w, x, y, z\} A=\{q, s, u, w, y\} B=\{q, s, y, z\} C=\{v, w, x, y, z\} \). List the elements in the set \( \left(A^{C} \cap B\right) \).
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  Let \( U=\{q, r, s, t, u, v, w, x, y, z\} A=\{q, s, u, w, y\} B=\{q, s, y, z\} C=\{v, w, x, y, z\} \). List the elements in the set. (No commas, just spaces.) \( A \cap(B \cup C) \)
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  Find \( \iint_{R} x^{2} d A \) where \( R=\left\{(x, y) \mid 9 x^{2}+16 y^{2} \leq 144\right\} \)
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  6. Solve in integers \( x, y: 15 x+36 y=12 \)
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  1. \( \frac{\cot \theta}{\tan \theta}=\frac{1-\sin ^{2} \theta}{1-\cos ^{2} \theta} \) 3. \( \cot ^{2} \theta=\frac{\cos ^{2} \theta}{1-\cos ^{2} \theta} \) 2. \( \frac{\tan \theta}{\cos \theta}=\frac
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  1. \( \sec ^{2} \theta+\csc ^{2} \theta=\sec ^{2} \theta \csc ^{2} \theta \) 3. \( \tan ^{2} \theta-\sin ^{2} \theta=\frac{\sin ^{2} \theta}{\cot ^{2} \theta} \) 2. \( \frac{\sin ^{2} \theta}{1-\cos \
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  \( \frac{(2 n+2) !}{(2 n-3) !} \)
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  1. DETERMINE WHETHER THE EQUATION DEFINES y AS A FUNCTION OF \( x \). a. \( y=x^{3} \) b. \( y=|x| \) c. \( x^{2}-4 y^{2}=1 \) d. \( y=\frac{3 x-1}{x+2} \)
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• 41, 43, 45
  In Problems 41-56, find the indicated derivative and simplify. 41. \( y^{\prime} \) if \( y=3\left(x^{2}-2\right)^{4} \) 42. \( y^{\prime} \) if \( y=2\left(x^{3}+6\right)^{5} \) 43. \( \frac{d}{d t}
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