Advanced Math Archive: Questions from October 23, 2022
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\( L\left(7 e^{3 t} t^{z}-4+\sin (3 t)^{-}\right),\left\{\begin{array}{l}\text { compute } \\ \text { 1) } L\left(e^{a t} f(t)\right)=F(s-a) \\ \text { 2) } L(+f(t))=-F^{\prime}(s) \\ \text { 3) } L(\0 answers -
\( y^{\prime \prime}+y=\csc (x) \) \( y^{\prime \prime}-4 \cdot y^{\prime}+4 \cdot y=x^{2} \cdot e^{x} \) \( x^{2} \cdot y^{\prime \prime}-2 \cdot x \cdot y^{\prime}+2 \cdot y=x^{3} \cdot \cos (x) \)2 answers -
1 answer
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1. Formulate an application problem that could be modeled mathematically through the graph of the function \( 2 \mathrm{c} \) from Discussion 1. Some examples are the cost functions (manufacturing, pr0 answers -
Negate the logical expressions below. \( \forall x \forall y(\mathrm{Q}(\mathrm{x}, \mathrm{y}) \leftrightarrow \mathrm{P}(\mathrm{x}, \mathrm{y})) \) \( \exists x \forall y P(x, y) \wedge \forall x \2 answers -
The expression \[ d f=\cos (x+y) d x+\cos (x+y) d y \] is a total differential. What is the function \( f(x, y) \) ? \[ \begin{array}{l} f(x, y)=\sin (x+y) \\ f(x, y)=2 \cos (x+y) \\ f(x, y)=\cos (x+y2 answers -
2 answers
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2 answers
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Find the general solutions of the following DEs. (a) \( y^{\prime \prime}+9 y^{\prime}+14 y=0 \), (b) \( y^{\prime \prime}+4 y^{\prime}+6 y=0 \), (c) \( \pi y^{\prime \prime}+e y^{\prime}=0 \).2 answers -
Question 1. Let \( (a, b) \in \mathbb{Z} \times \mathbb{Z} \) and \( a \equiv b(\bmod 10) \). Prove \( (a, b) \in\{(x, y) \in \mathbb{Z} \times \mathbb{Z} \mid x \equiv y(\bmod 5)\} \).2 answers -
2 answers
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Find \( u \cdot v \). \[ u=6 i-2 j, v=8 i+j \] \( -10 \) 0 50 46 Find \( \operatorname{proj}_{w} \mathrm{v} \). \[ v=(5,-5), w=(6,8) \] \[ (0.5,-0.5) \] \( (0.6,0.8) \) \[ \langle-0.6,-0.8) \] \[ \la2 answers -
Puente de Tacoma En el verano de 1940 se finalizó la construcción del puente colgante Tacoma, casi de inmediato algunos observadores notaron que a veces parecía que el viento originaba grandes osci0 answers -
2 answers
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Differentiate (a) \( y=x \cos x \sin x \) (b) \( y=\frac{1+\sin x}{x+\cos x} \) (c) \( y=(1+\cos 3 x)^{4} \)2 answers -
0 answers
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2 answers
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thank you in advance !
4. \( y^{\prime}=-x e^{x}, y(0)=1 \) 5. \( y^{\prime}=x \sin x^{2}, y(\sqrt{\pi / 2})=1 \) 6. \( y^{\prime}=\tan x, y(\pi / 4)=3 \)2 answers -
E.6 Demostrar que el conjunto \( S=\left\{x+1, x-1, x^{2}-1, x^{2}+1\right\} \) es un sistema generador de \( \mathbb{P}_{\mathbb{R}}^{2}[x] \). Encontrar un subconjunto \( S_{1} \) de \( S \) que sea2 answers -
differential
Find the general solution \( y^{\prime \prime}+5 y^{\prime}-6 y=22+18 x-18 x^{2} \) \( y^{\prime \prime}-4 y^{\prime}+5 y=1+5 x \) \( y^{\prime \prime}+8 y^{\prime}+7 y=-8-x+24 x^{2}+x^{3} \) \( y^{\p1 answer -
determine if the given group is base of the vectorial space.
4 Estudiar si los siguientes conjuntos son bases del espacio vectorial dado: (a) \( \left\{1, x+3,(x+3)^{2},(x+3)^{3}\right\} \) en \( \mathbb{P}_{\mathbb{R}}^{3}[x] \). (b) \( \left\{\left(\begin{arr1 answer