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Other Math Archive: Questions from March 19, 2023

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  Given that \( \left|\begin{array}{lll}a & b & c \\ d & e & f \\ g & h & i\end{array}\right|=-4 \), find \( \left|\begin{array}{ccc}a & b & c \\ d & e & f \\ 9 a & 9 b & 9 c\end{array}\right| \). \[ \l
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  Suppose \( \sin x=\frac{1}{3}, \sin y=\frac{1}{4}, 0 \leq x \leq \frac{\pi}{2} \) and \( \frac{\pi}{2} \leq y \leq \pi \). Find exact values for (a) \( \sin (x+y) \)
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• List the elements in the set . 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}. B ∩ C
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• y′′′ + 14y′′ + 49y′ = 0, y(0) = 0, y′(0) = 1, y′′(0) = −10 y(x)=
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  (a) Let \( z=\cos y+f(2 \sin x-3 \cos y) \), where \( f(u) \) is a twice differentiable function. i. Find the value of \( 3 \sec x \frac{\partial z}{\partial x}-2 \csc y \frac{\partial z}{\partial y}
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• supposing
  \[ f(x)=-3 x^{2}-2 x+1 \] a) \( f(3)= \) b) \( f(a)= \) c) \( f\left(-\frac{1}{2}\right)= \) d) \( f(a-h)= \) e) \( \frac{f(a-h)-f(a)}{h}, h \neq 0 \) \[ g(x)=\left\{\begin{array}{c} 3 x \quad \text
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  (1 point) Supongamos que se aplica el método de la bisección a una ecuación \( f(x)=0 \) en el intervalo \( [a, b] \). En la primera iteración, denotemos por \( c_{1} \) al punto medio entre \( [a
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  (1 point) Considera el siguiente algoritmo del método de Newton-Raphson: Algoritmo NewtonRaphson Leer \( c, N, E_{t o l} \); Para \( i \) Desde 1 Hasta \( N \) Hacer \[ \begin{array}{l} c_{a n t}=c ;
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  (1 point) Se usa el algoritmo SolEc mostrado abajo con \( a=-4, b=-2 \) y \( n=3 \). ¿Cuál es el valor de \( c \) en la línea Escribir c? Funcion \( z
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  2 en el numero 1.286 el valor de las centenas expresado en unidades es: b. 20 a. 80 d. 200 c. 6 3. En el numero 3,567 el valor de las unidades de mil expresado en unidades es: b. 3.000 a. 1.000 d. 300
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• PLEASE SOLVE #15 and #16, Thank you!! :)
  Exercises 1-18: In each exercise, (a) Find the general solution of the differential equation. (b) If initial conditions are specified, solve the initial value problem. 1. \( y^{\prime \prime \prime}-4
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• List the elements in the set B ∩ C . 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}
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  \( \begin{aligned} 5 x-2 y+2 z & =-5 \\ 10 x-4 y+4 z & =-13 \\ -15 x+6 y-6 z & =17\end{aligned} \)
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  Given \( f(x, y)=2 x^{3}+5 x y^{5}-y^{2} \), find the following numerical values: \[ f_{x}(1,0)= \] \[ f_{y}(1,0)= \] Given \( f(x, y)=2 x^{2}-6 x y^{4}+6 y^{5} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)=
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• mike had 2 apples and ate 1, how many does he have left.
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