Advanced Math Archive: Questions from October 05, 2022
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Determine whether -2x2y + y2 = 1 is an implicit solution of 2xydx =(x2 - y)dy = 0.
Determine si \( -2 \mathrm{x}^{2} \mathrm{y}+\mathrm{y}^{2}=1 \) es una solución implícita de \( 2 \mathrm{xydx}=\left(\mathrm{x}^{2}-\mathrm{y}\right) \mathrm{dy}=0 \)2 answers -
(2) Solve the following initial value problem: \[ \begin{aligned} \ddot{y} &=-y+\dot{y}+z \\ \dot{z} &=y-z-1 \\ y(0) &=1, \quad \dot{y}(0)=0, \quad z(0)=1 \end{aligned} \]2 answers -
\( \mathbf{f} 4\left[\begin{array}{cc}1 & x \\ -2 & 0\end{array}\right]+2\left[\begin{array}{cc}-2 & 0 \\ y & 0\end{array}\right]=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \)2 answers -
2 answers
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Determine which of the following functions is (are) the solution(s) of the equation differential xy”-y’=0 a. y=0 b. y=2 c. y= 2x d. y= 2x^2 e. None of the above Determine which of th
Determine cual o cuales de las siguientes funciones es (son) solución(es) de la ecuación diferencial \( x y^{\prime \prime}-y^{\prime}=0 \) a. \( y=0 \) b. \( y=2 \) c. \( y=2 x \) d. \( y=2 x^{2} \2 answers -
need explanation
11. Complete the following - Convert the double reflection over intersecting lines into a single rotation. a) \( r_{y \text { axis }} \circ r_{x \text { axis }}(x, y)=R_{O, 180}(x, y) \) b) \( r_{y \t2 answers -
oblems 19-21, solve the given initial value problem. \[ y^{\prime \prime \prime}-y^{\prime \prime}-4 y^{\prime}+4 y=0 \] \( y(0)=-4, \quad y^{\prime}(0)=-1, \quad y^{\prime \prime}(0)=-19 \)2 answers -
Let \( \mathbf{x}=\langle 1,-2\rangle, \mathbf{y}=\langle 1,5\rangle \), and \( \mathbf{z}=\langle-2,11\rangle \). If possible, find a nontrivial integer solution: \[ \langle 0,0\rangle=\quad \mathbf{2 answers -
solve problems 1,2,5
\( \# 1^{*}(10 \mathrm{pts}) y^{\prime \prime}-5 y^{\prime}+6 y=0 ; y(0)=3, y^{\prime}(0)=8 \) \( \# 2^{*}(10 \) pts \( ) y^{\prime \prime}+6 y^{\prime}+9 y=0 ; y(0)=6, y^{\prime}(0)=-15 \). \( \# 322 answers -
2. Solve the IVP \( \left\{\begin{array}{l}y^{\prime \prime}+y^{\prime}=0 \\ y(0)=0, y^{\prime}(0)=-10\end{array}\right. \)2 answers -
I need 33 please
29-33 Find the centroid of the region bounded by the given curves. 29. \( y=x^{2}, \quad x=y^{2} \) 30. \( y=2-x^{2}, \quad y=x \) 31. \( y=\sin 2 x, \quad y=\sin x, \quad 0 \leqslant x \leqslant \pi5 answers -
21 and 22;)
21. \( f(x, y)=4 \arctan (x y), \quad(1,1) \) 22. \( f(x, y)=y+\sin (x / y) \), \( (0,3) \)2 answers -
1. Consider the expansion of (x +1)^3. Use this expansion with x = 1, 2,...,n to obtain an simple expression of Sn. 2. Show using the Principle of Mathematical Induction that the expression obtained i
Para \( n \in \mathbb{N} \) sea \( S_{n}:=1+2^{2}+\cdots+n^{2} \). P-1.1 Considere el desarrollo de \( (x+1)^{3} \). Utilice este desarrollo con \( x=1,2, \ldots, n \) para obtener una expresión senc2 answers -
Let a,b ∈ R. Consider the sequence defined by un = au_n-1 + b for all n ≥ 1 and let u0 be the first term. P-2.1 Find a non-recursive expression, in terms of a, b, u0 and n for u_n (simplify as mu
Sean \( a, b \in \mathbb{R} \). Considere la sucesión definida por \( u_{n}=a u_{n-1}+b \) para todo \( n \geq 1 \) y sea \( u_{0} \) su primer término. P-2.1 Encuentre una expresión no recursiva,0 answers -
Let x0 and r be two real numbers, for all n ≥ 1, define x_n := r x_n−1. P-3.1 Find an explicit expression for x_n in terms of x_0, r, and n. P-3.2 Formally justify (using the Principle of Mathemat
Sean \( x_{0} \) y \( r \) dos números reales, para todo \( n \geq 1 \), se define \( x_{n}:=r x_{n-1} \). P-3.1 Encuentre una expresión explícita para \( x_{n} \) en función de \( x_{0}, r \) y \2 answers -
Consider the sequence defined recursively by un = sqrt(2-un-1) for n ≥ 1 and initial term u0. P-4.1 Show that the sequence un is undefined in R when u0 ≤ −2. P-4.2 Show that if u0 = 0 the sequen
Considere la sucesión definida recursivamente por \( u_{n}=\sqrt{2-u_{n-1}} \) para \( n \geq 1 \) y de término inicial P-4.1 Muestre que la sucesión \( u_{n} \) no está definida en \( \mathbb{R}2 answers -
2 answers
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Compruebe que la familia \( \mathrm{y}^{2}-2 \mathrm{y}=\mathrm{x}^{2}-\mathrm{x}+\mathrm{c} \) es una solución implícita de la ecuación diferencial \( (2 y-2) y^{\prime}=2 x-1 \)2 answers -
1. Find the equation of the wait that passes through the point (6, -2, 3) and has center at (-1, 2, 1) 2. Graph the vectors j + 2k and i – 2j + 3k 3. Determine if the vectors j + 2k and i
MUESTRE TODO SU TRABAJO: 1. Halle la ecuación de la espera que pasa por el punto \( (6,-2,3) \) y tiene centro en \( (-1,2,1) \) 2. Grafique los vectores \( \mathbf{j}+2 \mathbf{k} \quad \mathbf{y} \2 answers -
1 answer
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11. If \( y \propto \frac{1}{x^{3}} \), and when \( x=2, y=3 \) (i) Express \( y \) in terms of \( x \). (ii) Find \( x \) when \( y=192 \) \( (i) y=\frac{k}{x^{3}} \) (ii)2 answers -
6. Compruebe que \( y=x \operatorname{sen}(x)+x \cos (x) \) es una solución de la ecuación diferencial \( y^{\prime \prime}+y=2 \cos (x)-2 \)2 answers -
2 answers
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please
2] 3. Find and simplify an expression for \( d y / d x \). a) \( y=x^{-4} \ln (x) \) b) \( y=7^{\ln (x)}-2 \log _{8}\left(x^{3}\right) \) c) \( y=\left(1+x^{2}\right)^{\sin (x)} \)2 answers -
1 answer
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2 answers
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Despeje el valor de \( x \) en la ecuación: \( \ln (a)+\ln (2 x-a)-\ln (x)=\ln (x) \) Considere \( a=10 \) Exprese su respuesta con dos decimales2 answers -
2 answers
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(1 point) Match each function with one of the graphs below. A D 1. \( f(x, y)=\sqrt{4-4 x^{2}-y^{2}} \) 2. \( f(x, y)=1+2 x^{2}+2 y^{2} \) 3. \( f(x, y)=y^{2}+1 \) 4. \( f(x, y)=1+y \)1 answer