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Egypt
9) \( \int \frac{e^{\sqrt{x}}}{\sqrt{x}} d x \)
Calculus Mar 03, 2025
The rate of change of the function \( f: f(x)=\frac{1}{x} \), at \( x=\sqrt{5} \) equals \( \ldots \)
Calculus Mar 03, 2025
Q24: Car A moves with velocity \( 60 \mathrm{~km} / \mathrm{h} \) towards car B. Car B moves with velocity \( .65 \mathrm{~km} / \mathrm{h} \) in the opposite direction to car A. The distance between two cars is 180 km . In order to safely stop, the driver of car A wants to calculate the time it would take for the two cars to meet if they continued at the same uniform velocity. Which of the following represents this time?
Physics Mar 02, 2025
If \( l_{1}=\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}, 2_{2}=\cos \frac{\pi}{6}+i \sin \frac{\pi}{6} \), then the amplitude of \( \left(\frac{1}{7}\right)^{7} \) is \( \begin{array}{lll}\text { (a) } \frac{\pi}{6} & \text { (b) } \pi & \text { (c) } \frac{-1}{2} \pi\end{array} \) \( \begin{array}{ll}\text { (a) } x=\cos 17^{\circ}+i \sin 17^{\circ}, y=\cos 11^{\circ}+i \sin 11^{\circ} \text {, then complex number } 1=x^{\circ} y^{\circ}+i \sin 30^{\circ} & \text { (b) } \cos 150^{\circ}+i \sin 150^{\circ} \\ \text { in the trigonometric form is } & \text { (d) } \cos -600^{\circ}+i \sin -60^{\circ}\end{array} \)
Trigonometry Mar 02, 2025
\( \left(\cos \frac{5 \pi}{3}+i \sin \frac{5 \pi}{3}\right)^{4}=c \) (a) \( \frac{2 \pi}{3} \) (b) \( -\frac{1}{3} \pi i \) (c) \( \frac{1}{3} \pi i \) (d) \( \frac{-5}{3} \pi i \) If \( z=2\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right) \), then \( \frac{1}{1}= \) (a) \( \frac{1}{2} c \frac{2 \pi}{2} \) i (b) \( \frac{1}{2} e^{\frac{\pi}{1}} \) (c) \( 2 e^{2 \pi} \) (d) \( 2 e^{-\pi} j^{3} \) If \( z_{1}=6\left(\cos 240^{\circ}+i \sin 240^{\circ}\right), y_{2}=2\left(\cos 300^{\circ}+i \sin 300^{\circ}\right) \), then \( z_{2}^{\prime}= \) (a) \( 3 \mathrm{e}^{-\pi} \) i (b) \( 3 \mathrm{c}^{\frac{-\pi}{1}} \) (c) \( \frac{1}{3} c \frac{\pi}{3} \) i (d) \( \frac{1}{3} e^{\frac{x}{3}} \)
Trigonometry Mar 02, 2025
\( 6\left(\cos 210^{\circ}+i \sin 210^{\circ}\right) \div 3\left(\cos 70^{\circ}+i \sin 70^{\circ}\right)= \) \( \begin{array}{ll}\text { (a) } 2\left(\cos 3{ }^{\circ}+i \sin 3^{\circ}\right) & \text { (b) } 3\left(\cos 30^{\circ}+i \sin 30^{\circ}\right) \\ \text { (c) } 3\left(\cos 140^{\circ}+i \sin 140^{\circ}\right) & \text { (d) } 2\left(\cos 140^{\circ}+i \sin 140^{\circ}\right) \\ {\left[5\left(\cos 10^{\circ}+i \sin 10^{\circ}\right)\right]^{2}=} \\ \begin{array}{ll}\text { (a) } 25\left(\cos 100^{\circ}+i \sin 100^{\circ}\right) & \text { (b) } 10\left(\cos 100^{\circ}+i \sin 100^{\circ}\right) \\ \text { (c) } 25\left(\cos 20^{\circ}+i \sin 20^{\circ}\right) & \text { (d) } 10\left(\cos 20^{\circ}+i \sin 20^{\circ}\right) \\ \text { (a) } \frac{2 \pi}{3} i & \text { (b) }-\frac{1}{3} \pi i\end{array} & \text { (c) } \frac{1}{3} \pi i\end{array} \)
Trigonometry Mar 02, 2025
\( \int ( \ln x + \frac { 1 } { \ln x } ) \)
Calculus Mar 02, 2025
Find the polar furm of: (i) \( z=-4+4 i \)
Pre Calculus Mar 02, 2025
\( \int _{}^{}(\csc (2x)+\cot (2x))^{2} d \)
Calculus Mar 02, 2025
b) \( (3-4 i)(2+5 i) \)
Algebra Mar 02, 2025
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