Numerade

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Problem 3: Two blocks of mass $m_1 = 2 \text{ kg}$ and $m_2 = 3 \text{ kg}$ are connected by a rope that goes over a frictionless pulley and provides a tension $T$. $m_1$ is accelerating downwards with an acceleration $a$ and $m_2$ is accelerating down an inclined plane with an acceleration $a$. $m_2$ is on an inclined plane with angle $\theta = 30^\circ$ and the surface has a kinetic friction coefficient $\mu_k = 0.6$. a) What is $a$, the acceleration of the system? Answer: $3.8 \text{ m/sec}^2$ b) What is $T$, the tension in the rope connecting $m_1$ and $m_2$? Answer: $12.0 \text{ N}$ $g = 9.8 \text{ m/sec}^2$ Problem 4: In the Figure we show a car ridding around in a circle in a banked highway. In this situation a car is basically driving around in an inclined plane. The radius the car is making is $50 \text{ m}$, the angle of the inclined plane is $30^\circ$, and the coefficient of static friction between the road and the tires of the car is $0.5$. What is the maximum speed a car can have so that it wont slide up the inclined plane as it is going around in a circle? Answer: $27.2 \text{ m/sec}$

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The primary care nurse practitioner is seeing a patient with a diagnosis of gout. The NP wants to prescribe colchicine to the patient. In which of the following would the NP not prescribe colchicine?

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Sunny Co. is a 100% equity-financed company (no debt or preferred stock); hence, its WACC equals its cost of common equity. Sunny Co.'s retained earnings will be sufficient to fund its capital budget in the foreseeable future. The company has a beta of 1.50, the risk-free rate is 5.0%, and the market return is 6.5% What is Sunny Co.'s cost of equity? 16.25% 24.13% 8.75% 7.25%

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Simplify. \[ 8 x \sqrt{2}-x \sqrt{2} \] $ \square $

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The empirical formula of a compound of phosphorus and oxygen was found to be P2O5. Experimentation shows that the molar mass of this compound is 283.89 g/mol. What is the compound’s molecular formula?

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25 year old Jorge has postponed marriage because prefers to cohabitate instead he can't find anyone to marry has finished college early because of the recession has lower wages and lives with his parents

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An ant walks due east at a constant speed of 1 mi/hr on a sheet of paper that rests on a table. Suddenly the sheet of paper starts moving southeast at $4\sqrt{2}$ mi/hr. Describe the motion of the insect relative to the table. Consider the diagram to the right. Let $v_p$ be the velocity of the ant relative to the paper, let $p$ be the velocity of the paper, and let $v_t$ be the velocity of the ant relative to the table. Note that the diagram is not to scale. Which of the following equations should stand? A. $v_t = p - v_p$ C. $v_t = v_p + p$ B. $v_t = v_p \cdot p$ D. $v_t = v_p - p$ The magnitude of the motion relative to the table is mi/hr. (Type an exact answer, using radicals as needed.) The direction of the motion relative to the table is south of east. (Round to the nearest hundredth as needed.)

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Two specimens of the same brass material were heat treated at 600°C for times of 10 min and 50 min. After cooling to room temperature, average grain size and yield strength of each specimen were measured. The results of these tests are presented in the table below. On the basis of the information, determine the yield strength achieved after a heat treatment of 5.0 min at 600°C. Assume a value of 2.0 for the grain diameter exponent of Equation 8.9. Heating Time (min) Average Grain Yield Strength Diameter (mm) (MPa) 10 0.04 90 50 0.08 45

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5. The graph of y = f"(x) is shown on the right. At what value(s) of x does the graph of f have an inflection point? Justify your answer in a sentence. Graph of y = f" (x) 6. Show whether or not the conditions of Rolle's Theorem are met. If the conditions are met, find the value of c that the theorem guarantees. f(x)=(x-3)(x+1)$^2$, [-1, 3]

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1. Use the Bisection method, to find a bound for the number of iterations needed to approximate a solution to the equation $x^3 + x - 4 = 0$ on the interval $[1, 4]$ to an accuracy of $10^{-3}$? (1.5 Marks) 2. Use the Use the Bisection method to find an approximation to $\sqrt{3}$ that is accurate to within $10^{-4}$. (1.5 Marks) 3. Let $f(x) = x^2 - 6$ with $x_0 = 3$ and $x_1 = 2$, find $x_3$ for (a) the Secant method and (b) the method of False Position (c) compare results? (1.5 Marks) 4. Apply Newton's method to find a solution, accurate to within $10^{-4}$, to the value of x that produces the closest point on the graph of $y = x^2$ to the point $(1, 0)$?Hint: first derive the distance from the point to the graph (1.5 Marks)

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