Question 5 : (August 2023 ) The function \( G(m) \) represents the amount of gasoline consumed by a car traveling \( m \) miles. An appropriate domain for this function would be (1) integers (2) rational numbers (3) nonnegative integers (4) nonnegative rational numbers

Mathematics Assignment for Grade 12. December 15/04/2017 E. C. Instructions: - Workout the following problems with the necessary steps with clear and legible handwriting. - Write your group number, full name with their Roll NO. 1. The number of terms in an arithmetic progression is even. The sum of the odd terms is 24. If the sum of even terms is 30 and the last term exceeds the first by \( \frac{21}{2} \), then find the number of terms. 2. If \( a^{2}+b^{2}, a b+b c \) and \( b^{2}+c^{2} \) are in geometric progression, prove that \( a, b, c \) are also in geometric progression. 3. Let \( f(x)=\left\{\begin{aligned} 4 x, & x \geq 3 \\ x^{2}+3, & x<3\end{aligned}\right. \), find the equation of the tangent line and the normal line to the graph of \( f \) at the point \( (4,16) \). 4. Find the maximum possible area of an isosceles triangle whose perimeter is 6 m . 5. Given \( f(x)=\sqrt{12-x-x^{2}},[-4,3] \) find: a) absolute maximum. b) dbsotute-minimum.

if the domain of \( y=f(x) \) is \( [-2,2] \), whatis the domain of fanction with the rule of \( y=f(\sqrt{x-1}) \)

15. which one of the following is the range of \( f(x)=x^{\frac{-2}{3}} \) ? \( \begin{array}{l}\text { A. IR } \backslash\{0\} \quad B .(0, \infty) \quad C .(-\infty, 0) \quad D . \mathbb{R}\end{array} \)

Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \). Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s).

25 exponentielle: \( \begin{array}{lll}\text { a. } 4 \sqrt{2} e^{i \frac{\pi}{4}} & \text { b. } 4 \sqrt{2} e^{i \frac{7 \pi}{4}} & \text { c. } 4 \sqrt{2} e^{i \frac{3 \pi}{4}} \\ \text { 2. Un argument du nombre complexe }-2 e^{i \frac{\pi}{5}} \text { est: } \\ \begin{array}{lll}\text { a. } \frac{7 \pi}{10} & \text { b. }-\frac{4 \pi}{5} & \text { c. }-\frac{3 \pi}{10}\end{array} \\ \begin{array}{lll}\text { 3. On pose } z=3-3 i . L a f o r m e ~ e x p o n e n t i e l l e ~ d e ~ \\ i\end{array} \\ \begin{array}{lll}\text { a. } 3 \sqrt{2} e^{-i \frac{\pi}{4}} & \text { b. } 3 \sqrt{2} e^{-i \frac{3 \pi}{4}} & \text { c. } 3 \sqrt{2} e^{i \frac{\pi}{4}} \\ \text { 4. On pose } z=3+i \sqrt{3} \text {. La forme exponentielle de }-4 z\end{array} \\ \text { est: } & \text { b. } 2 \sqrt{3} e^{i \frac{7 \pi}{6}} & \text { c. } 8 \sqrt{3} e^{-i \frac{5 \pi}{6}}\end{array} \)