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Home Question Bank Math Archive 2024 December 29

Math Questions from Dec 29,2024

Browse the Math Q&A Archive for Dec 29,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Exercice1: Simplifier les expressions suivantes: \( \begin{array}{l}A=\ln (2-\sqrt{3})+\ln (2+\sqrt{3}) \quad ; \quad B=\frac{1}{4} \ln 9-\ln \sqrt{3}+\ln \frac{1}{27} \\ C=2 \ln \sqrt{e}+\ln \sqrt[3]{e}-\ln \frac{1}{e} \quad ; \quad D=4 \ln (e \sqrt{e})+5 \ln \frac{1}{e}\end{array} \) Solve the simultaneous equations. You must show all your working. \( \begin{array}{l}4 x-3 y=26 \\ 5 x+6 y=13\end{array} \) Hallar y' de \( y=4 x^{7} \) \( \begin{array}{l}\text { a. } y^{\prime}=24 x^{6} \\ \text { b. } y^{\prime}=28 x^{7} \\ \text { c. } y^{\prime}=28 x^{6} \\ \text { d. } y^{\prime}=28 x^{8}\end{array} \) \( \int _ { 3 } ^ { 6 } ( 2 x ^ { 2 } + 3 x + 5 ) d \) 10 Solve the simultaneous equations. You must show all your working. \( \begin{array}{l}x-3 y=26 \\ 5 x+6 y=13\end{array} \) halle la ecuación de la recta tongente a la curva en el punto dado. \( \begin{array}{l}y=x+\text { senar, en el punto }(\pi, \pi) \\ \text { a. } y=\pi x \\ \text { b. } y=\pi x+3 \\ \text { a. } y=3 \pi x \\ \text { d. } y=\pi \text { La recta tangente es paralela al eje de las } x \text {. }\end{array} \) For the following quadratic function, tell whether the graph opens upward or downward and whether the graph is whder, narrower, or the same as \( f(x)=x^{2} \). \( F(x)=2 x^{2}+12 \) The graph opens A. downward. The graph is A. the same width as that of \( f(x)=x^{2} \) B. wider than \( f(x)=x^{2} \). Identify the vertex of the parabola. \( f(x)=(x+1)^{2}-1 \) The vertex of the parabola is the point (Type an ordered pair.) \( m^{-\frac{1}{4}}=27 m^{-1} \) Find the value of \( m \). 8 Simplify. \( y^{3} \div y^{5} \)
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