Algebra Archive: Questions from October 24, 2023
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Problem \#2: Identify which equations are linear and nonlinear. Note that \( y^{\prime}=d y / d x \) and \( y^{\prime \prime}=d^{2} y / d x^{2} \). a) \( y^{\prime \prime}-y^{\prime}=x^{2} \) b) \( \f1 answer -
Factorize the following expressions: a. \( \quad 567 x^{3}-1183 x y^{2} \) b. \( (4 x-1)^{2}-(3 x+2)^{2} \) c. \( \quad 3 x^{2}-4 y^{2}-3 z^{2}-4 x y+8 y z+8 z x \)1 answer -
3. Prove the following identities. Assume all trigonometric functions are well defined. (a) \( \frac{1+\cos x}{1-\cos x}-\frac{1-\cos x}{1+\cos x}=4 \cot x \csc x \); (b) \( \frac{\csc x}{\cot x}-\fra1 answer -
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OBJECTIVE: \( G=2 A+3 B \) CONSTRAINTS: \[ \begin{array}{l} A+B \geq 3 \\ 20 A+10 B \leq 80 \\ B \leq 2 A \end{array} \]0 answers -
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Question 1 Rescriba la ecuación de la función cuadrática f(x) = x² + 4x + 5 en la forma estándar f(x) = a(x-h)² + k O a. f(x) = (x - 2)² +1 O b. f(x) = (x + 2)² +1 C. Oc. f(x) = (x + 2)2² +2
Rescriba la ecuación de la función cuadrática \( f(x)=x^{2}+4 x+5 \) en la forma estándar \( f(x)=a(x-h)^{2}+k \) a. \( f(x)=(x-2)^{2}+1 \) b. \( f(x)=(x+2)^{2}+1 \) c. \( f(x)=(x+2)^{2}+2 \) d. \1 answer -
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(1 point) Let \( \vec{x}=\left[\begin{array}{c}-1 \\ 0 \\ -3\end{array}\right] \) and \( y=\left[\begin{array}{c}-3 \\ 2 \\ -4\end{array}\right] \). Find the vectors \( \vec{v}=6 \vec{x}, \vec{u}=\vec1 answer