Advanced Math Archive: Questions from September 19, 2022
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Homework 2.7. Find the solution of the following initial value problems 1. \( y^{\prime \prime}-y^{\prime}-2 y=0, y(0)=y^{\prime}(0)=1 \) 2. \( y^{\prime \prime}-4 y^{\prime}-21 y=0, y(0)=y^{\prime}(01 answer -
Discrete math
Express the negation of the following statements i) \( \forall x \forall y[P(x, y) \rightarrow Q(x, y)] \) ii) \( \exists x \forall y P(x, y) \vee \forall x \exists y Q(x, y) \) iii) \( \quad \exists1 answer -
Solve: \[ \begin{array}{c} x_{1}+x_{2}+2 x_{3}=4 \\ 2 x_{1}+3 x_{2}+6 x_{3}=10 \\ 3 x_{1}+6 x_{2}+10 x_{3}=17 \end{array} \]2 answers -
1 answer
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Find the exact value of \[ \frac{\sin (x-y)}{\cos x \cos y}+\frac{\sin (y-w)}{\cos y \cos w}+\frac{\sin (w-x)}{\cos w \cos x} \]1 answer -
3. \( y^{\prime}=y+2 y^{5} \) for \( y>0 \). \( \left(\right. \) Hint: Let \( \left.u=y^{1-n} .\right) \)1 answer -
pls!
Sea \( y_{1}(x)=x^{2} \cos (\ln x) \) una solución de la ecuación diferencial \( x^{2} y^{\prime \prime}-3 x y^{\prime}+5 y=0 \). Encuentre una segunda solución. \[ y_{2}(x)=x^{2} \tan (\ln x) \] \2 answers -
match the following situations, graphs, and equations:
A) A plumber charges a fixed fee for coming to your house, then charges a fixed amount per hour on top of this. \( x= \) the time the job takes in hours. \( y= \) the total cost of the plumber's time2 answers -
1 answer
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1 answer
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Solve the following IVP: \[ \left\{\begin{array}{l} (\cos x) \frac{d y}{d x}+y \sin x=e^{x} \cos ^{2} x \\ y(0)=0 \end{array}\right. \] Solve the IVP: \[ \left\{\begin{array}{l} \frac{d y}{d x}=\frac1 answer -
Differentiate the following to \( x \) and simplify where possible: 2.1 \( y=x^{4} \tan 3 x \) 2.2 \( y=\ln \left(2 x^{2}+1\right) \) \( 2.3 y=\frac{e^{x}+1}{e^{x}-1} \) \( 2.4 y=\frac{2 \sin x}{1-\co2 answers -
Find the gradient of the following functions. a) \( f(x, y, z)=3 x^{2} \sqrt{y}+\cos (3 z) \) b) \( \quad g(x, y, z)=\sin (3 x) e^{2 y} \ln (4 z) \)1 answer -
Sea \( y_{1}(x)=x^{2} \cos (\ln x) \) una solución de la ecuación diferencial \( x^{2} y^{\prime \prime}-3 x y^{\prime}+5 y=0 \). Encuentre una segunda solución. \[ y_{2}(x)=x^{2} \tan (\ln x) \] \1 answer -
Encuentre la solución general de la ecuación diferencial \( 2 y^{\prime 6}+3 y^{\prime \prime}-16 y^{\prime \prime}+15 y^{\prime}-4 y=0 \) sujeto a \( y(0)=-2, y^{\prime}(0)=6, y^{\prime \prime}(0)=1 answer -
5. Please evaluate the integrals: (a) \( \int 2^{\theta} \sin (5 \theta) d \theta \) (b) \( \int \sin \left(\log _{5} 2 t\right) d t \) (c) \( \int \sin 7 \theta \cos 2 \theta d \theta \) (d) \( \int1 answer -
1 answer
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3. Consider the vector \( F(x, y, z)=\left(4 y^{2}+\frac{3 x^{2} y}{z^{2}}\right) i+\left(8 x y+\frac{x^{2}}{z^{2}}\right) j+\left(11-\frac{2 x^{3} y}{z^{3}}\right) k . \) Find the \( \operatorname{di1 answer -
1 answer
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2. Find the gradient of the following functions. a) \( f(x, y, z)=3 x^{2} \sqrt{y}+\cos (3 z) \) b) \( \quad g(x, y, z)=\sin (3 x) e^{2 y} \ln (4 z) \)1 answer -
Find the gradient of the following functions. a) \( \quad f(x, y, z)=3 x^{2} \sqrt{y}+\cos (3 z) \) b) \( \quad g(x, y, z)=\sin (3 x) e^{2 y} \ln (4 z) \)1 answer -
\( F(x, y, z)=\left(4 y^{2}+\frac{3 x^{2} y}{z^{2}}\right) i+\left(8 x y+\frac{x^{2}}{z^{2}}\right) j+\left(11-\frac{2 x^{2} y}{z^{2}}\right) k \)0 answers -
(t point) Match each function weth one of the graphs below. \( f(x, y)=1+y \) \( f(x, y)=e^{-y} \) \( f(x, y)=1+2 x^{2}+2 y^{2} \) \( f(x, y)=\sqrt{4 x^{2}+y^{2}} \)1 answer -
Find the gradient of the following functions. a) \( \quad f(x, y, z)=3 x^{2} \sqrt{y}+\cos (3 z) \) b) \( \quad g(x, y, z)=\sin (3 x) e^{2 y} \ln (4 z) \)1 answer -
3. Consider the vector \( F(x, y, z)=\left(4 y^{2}+\frac{3 x^{2} y}{z^{2}}\right) i+\left(8 x y+\frac{x^{2}}{z^{2}}\right) j+\left(11-\frac{2 x^{3} y}{z^{2}}\right) k \). Find the \( \operatorname{div2 answers -
Hardest question in the world (point "i)" is a photo but guilty(x)∧ guilty(y)∧ guilty(z) is part of i)) A crime. He has to solve a murder. You know that the killer is one of the following people:
Tiene que resolver un asesinato. Sabe que el asesino es una de las siguientes personas: Oscar, Estuardo, Diana, Patricia, David, Alberto, Martina, Matías, Tomás. El detective (CJ) encargado de inves1 answer -
2 answers
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If p,q are false and r is true, find the value of truth of (pVq) ---- -r
3. Si \( p, q \) son falsos y \( r \) es verdadero, encuentre el valor de verdad de \[ (p \vee q) \rightarrow-r \]1 answer -
1 answer
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solve the Differential Equation
\( \left(y+2 x y^{3}\right) d x+\left(1+3 x^{2} y^{2}+x\right) d y=0 \)1 answer