Numerade

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4. A charged particle with charge q moves in a uniform magnetic field B and a time dependent Electric field $$E = E_0 \cos \omega t$$ where $$E_0$$ is a constant vector. Both B and $$E_0$$ point along the z-axis. The total force on the particle is given by the Lorentz Force Law $$F = q(E + v \times B)$$ (2) (a) Write the equations of motion for the particle in component parts [2 points] (b) Solve the equations of motion for the particles position as a function of time [7 points] (c) Describe the motion in the x and y directions. [1 point].

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(3) Consider the function $f(x) = \begin{cases} x^{4/3} \sin(\frac{1}{x^2}), & \text{if } x \neq 0; \\ 0, & \text{if } x = 0. \end{cases}$ a) [7 pts] Find $f'(0)$ or show that it does not exist. b) [9 pts] Does $\lim_{x \to 0} f'(x)$ exist? Is the function $f'(x)$ continuous at $x = 0$? (Be sure to explain you answer.)

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provide 5 case study questions with answers and their rationale on mobility in nursing

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Show the movement of electrons OH OH O O H O<sup>-</sup> HO

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5. (II) A gas is at 30°C. To what temperature must it be raised to triple the rms speed of its molecules? 6. (II) (a) What is the average translational kinetic energy of a nitrogen molecule at STP?

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Question 2 0.19 / 0.25 pts Which of the following can be found in both prokaryotic and eukaryotic cells (choose all that apply)? nucleus ?ribosomes ?DNA membrane bound organelles mitochondria chloroplasts ?plasma membrane RNA

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What is more likely a side effect of meperidine than other opiates? Miosis Respiratory depression Less dopamine stimulation Seizures Sedation

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Determine the interquartile range (IQR) of the table given in question 3. 3. An incomplete frequency distribution is given as follows. Variable Frequency 10-20 20-30 30-40 40-50 50-60 60-70 70-80 12 30 ? 65 ? 25 18 Given that the median value is 46, and the total frequency is 229, calculate the missing frequencies using the median formula (N.B. Frequency can never be a fraction, round up).

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Find the derivative of the function: y = x^(-6) + x^(-3) - 2

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If A is compact, prove that every continuous function $f: A \to \mathbb{R}$ takes a maximum and a minimum value on A.

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