Math Questions from Nov 26,2024

Browse the Math Q&A Archive for Nov 26,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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e. \( \frac{9}{18}+\frac{2}{14} \) \( \begin{array}{l}x=16 \cos t, y=1 \sin t, t=-\frac{-}{4} \\ \text { Find } \frac{d y}{d x} \\ \frac{d y}{d x}=\frac{4 \cos t}{-16 \sin t} \\ \text { Find the slope of the tangent line at } t=-\frac{\pi}{4} \text {. } \\ \text { The slope is } \frac{1}{4} \text {. } \\ \text { The equation } \square \text { represents the line tangent to the curve at } t=-\frac{\pi}{4} \text {. } \\ \text { (Type an exact answer, using radicals as needed.) }\end{array} \). Solve the system by elimination. \[ \begin{array}{l}5 x+2 y=10 \\ 10 x-3 y=55\end{array} \] The solution set is \( \} \). (Simplify your answer. Type an ordered pair.) Solve by the elimination method \( \begin{array}{l}7 x-y=0 \\ x+3 y=22\end{array} \) Solve the system by substitution. \[ \begin{array}{r}4 x+8 y=24 \\ -2 x+y=18\end{array} \] The solution set is \( \left\{\begin{array}{l}\text { (Simplify your answer. Type an ordered pair.) }\end{array}\right. \) ( a. Una cancha de baloncesto para adultos mide 26 m de largo por 14 m de ancho. Una cancha infantil mide 7.5 m menos de largo y 1.25 m menos de ancho. ¿Cuáles elárea de una cancha paraniños? Find an equation for the line tangent to the curve at the point defined by the given value of \( t \) Also, find the value of \( \frac{d^{2} y}{d x^{2}} \) at this point. \( x=16 \cos t, y=4 \sin t, t=-\frac{\pi}{4} \) \( \frac{d y}{d x}=\frac{d y}{d x} \). \( 16 \sin t \) Find the slope of the tangent line at \( t=-\frac{\pi}{4} \) The slope is Solve the system of equations using substitution. \( \begin{aligned} 5 x+y & =7 \\ y & =2 x\end{aligned} \) 6. Given \( f(x)=\frac{x-12}{x+24} \), find \( f(-12) \) Solve the logarthmic equation. \( \log _{2}(x+2)+\log _{2}(x-2)=5 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \{ \). Type an exact solution, using radicals as needed. Use a comma to separate answers as needed.) B. The solution is the empty set.
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