Advanced Math Archive: Questions from November 21, 2022
-
Evalvate \( \int_{c} F \cdot d r \) along parametric curve \( x=2 u, y=\sqrt{u} \) from \( u=0 \) to \( u=1 \) if \( F=-y i+x^{2} j \)2 answers -
1. Solve the IVP \[ \vec{y}^{\prime}=\frac{1}{6}\left(\begin{array}{cc} 7 & 2 \\ -2 & 2 \end{array}\right) \vec{y}, \quad \vec{y}(0)=\left(\begin{array}{c} 0 \\ -3 \end{array}\right) \]2 answers -
2. Solve the IVP \[ \vec{y}^{\prime}=\frac{1}{6}\left(\begin{array}{cc} 4 & -2 \\ 5 & 2 \end{array}\right) \vec{y}, \quad \vec{y}(0)=\left(\begin{array}{c} 1 \\ -1 \end{array}\right) \]2 answers -
Find \( \frac{d y}{d x} \) when (a) \( y=\tan ^{-1}\left\{\frac{4 \sqrt{x}}{1-4 x}\right\} \) (b) \( y=\frac{\sin ^{-1}(x)}{\sqrt{1-x^{2}}} \)2 answers -
If possible, compute the following: (a) \( F D-3 B \) (b) \( A B-2 D \) (c) \( F^{\top} B+D \) (d) \( 2 F-3(A E) \) (e) \( B D+A E \)2 answers -
0 answers
-
2 answers
-
Solve the following linear differential equations using the Laplace transform.
\( y^{\prime \prime}-4 y^{\prime}+4 y=t^{3}, \quad y(0)=1, y^{\prime}(0)=0 \) 2. \( y^{\prime \prime}-4 y^{\prime}+4 y=t^{3} e^{2 t}, \quad y(0)=0, y^{\prime}(0)=0 \).2 answers -
True or False The differential equation dy/dx = xy^3 + 1 is a differential equation of Bernoulli.
3. La ecuación diferencial \( \frac{d y}{d x}=x y^{3}+1 \) es una ecuación diferencial de Bernoulli.2 answers -
1. A first order diferential equation that is not linear and not autonomous is 2. A region in the xy plane for which the diferential equation xdy/dx=y has a unique solution that passes through the po
1. Una ecuación diferencial de primer orden que es no-lineal y no-autónoma es: a) \( 2 \frac{d y}{d x}+y=0 \) b) \( \frac{d y}{d x}=(x-1)(1-2 x) \) c) \( \frac{d y}{d x}+\ln \left(x^{2}\right) y=e^{2 answers -
Problem 3. \( [1+1+1+1 \) pts \( ] \) Compute 1. \( (2+3 i)^{\frac{1}{2}} \) 2. \( \left(-2+3 i^{5}\right)^{\frac{3}{4}} \) 3. \( \left(-1+3 i^{8}\right)^{\frac{1}{3}} \) 4. \( \left(\frac{3+}{2-}\rig2 answers -
1. Resuelve los siguientes Problemas de Valor Inicial a) [7 pts.] \( x^{2} \frac{d y}{d x}=y(1-x) ; y(-1)=-1 \). b) [11 pts \( ] x \frac{d y}{d x}+y=4 x+1 ; y(1)=8 \).2 answers -
[9 pts.] Verifica si la E.D. \( \left(y^{2} \cos x-3 x^{2} y-2 x\right) d x+\left(2 y \sin x-x^{3}+\ln y\right) d y=0 \) es exacta, y de ser así resuélvela.2 answers -
3. [8 pts.] Halla la solución de las siguientes ecuación diferencial \( \frac{d y}{d x}=1+e^{y-x+5} \).2 answers -
Solve the following lincar systems. \( \mathrm{i} x^{\prime}=x-5 y, y^{\prime}=x-y \) ii \( x^{\prime}=2 x-5 y, y^{\prime}=4 x-2 y ; x(0)=2, y(0)=3 \) iii \( x^{\prime}=-3 x-2 y, y^{\prime}=9 x+3 y \)2 answers -
\( \left(\begin{array}{ccc}a & 3 & 2 \\ -4 & -4 & c \\ b & 6 & -3\end{array}\right)\left(\begin{array}{ccc}3 & -2 & 0 \\ a & -9 & d \\ b & 8 & 7\end{array}\right)+2\left(\begin{array}{ccc}a & 3 & 2 \\2 answers -
\[ \cos \left(\frac{\pi}{2}+\theta\right)=-\sin \theta \] Choose the sequence of steps below that verifies the identity. A. \[ \cos \left(\frac{\pi}{2}+\theta\right)=\cos \frac{3 \pi}{2} \cos \theta-\2 answers -
Maximize \( p=x-5 y \) subject to \[ \begin{array}{r} 2 x+y \geq 4 \\ y \leq 9 \\ x \geq 0, y \geq 0 \end{array} \]3 answers -
In problems 21 and 22, consider the plane that passes through points P and Q and that is perpendicular to the plane xy. Find the slope of the tangent at the point indicated to the intersection curve o
En los problemas 21 y 22 , considere el plano que pasa por los puntos \( P \) y \( Q \) y que es perpendicular al plano \( x y \). Encuentre la pendiente de la tangente en el punto indicado a la curva0 answers -
\( \left(\begin{array}{ccc}a & 3 & 2 \\ -4 & -4 & c \\ b & 6 & -3\end{array}\right)\left(\begin{array}{ccc}3 & -2 & 0 \\ a & -9 & d \\ b & 8 & 7\end{array}\right)+2\left(\begin{array}{ccc}a & 3 & 2 \\2 answers -
Maximize \( p=x+2 y \) subject to \[ \begin{array}{l} x+4 y \leq 23 \\ 3 x+y \leq 14 \\ x \geq 0, y \geq 0 \end{array} \]2 answers -
0 answers