Numerade

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give a solution for part 1: A circle C of radius 2𝑟 has its center at the origin. A circle of radius 𝑟 rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling circle at a distance 𝑏 from its center, 0 < 𝑏 < 𝑟. Let L be the line from the center of C to the center of the rolling circle and 𝑡 be the angle that L makes with the positive x-axis. Using 𝑡 as a parameter we will see in a video (coming soon) that parametric equations of the path traced out by P are 𝑥(𝑡) = 3𝑟 cos 𝑡 + 𝑏 cos 3𝑡 𝑎𝑛𝑑 𝑦(𝑡) = 3𝑟 sin 𝑡 + 𝑏 sin 3𝑡 Note: The path traced out by P is called an epitrochoid. 4. Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on a circle of radius 𝑏 centered at the center of the epitrochoid. Note: This is the principle of the Wankel rotary engine. When the equilateral triangle rotates with its vertices on the epitrochoid, its centroid sweeps out a circle whose center is at the center of the epitrochoid. Part 1. In most rotary engines the sides of the equilateral triangle (the rotor) are replaced by arcs of circles centered at the opposite vertices, thus the diameter of the rotor is constant. Show that the rotor will fit in the epitrochoid if 𝑏 ≤ 3 2 (2 − √3)𝑟.

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The importance of organization, effective communication, resolve conflicts, and effective delegation as a nurse within a clinical setting

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Financial strategies are option A require an integrated approach to the management. Option B involves high degree of uncertainty. Option C involve the scope of an organisations activities. Option D involve major change in the productions.

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Question 9 Our traditional "racial" categories reflect monophyletic groups, grouping people who share ancestors. True False 1 pts

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What are the benefits and cost associated with permitting the rebating practice if said insurance sales agents were allowed to offer premium rebates to customers

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2. Several models have been proposed for the formation of the Moon, including that it coformed with the Earth from the same reservoir of material. This idea is at odds, however, with the Moon’s small metallic core that is only ~300 km in radius. For it to be plausible, the Moon would either need to be significantly smaller or its core significantly bigger. a. Estimate the radius of the Moon under the idea of Earth co-formation, assuming the Moon’s core is the size it should be. Calculate the mass of this moon and its bulk density, and comment on the comparison to those values of the actual Moon. b. Estimate the radius of the Moon’s core, assuming the Moon is the size it should be. Again, calculate the mass of this moon and its bulk density, and comment on the comparison to those values of the actual Moon.

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A block oscillating on a spring has period of 2 s . What is the period if the block’s mass is doubled?

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5. In the investigation of a homicide or accidental death, it is often important to estimate the time of death. From the experimental observations, it is known that the surface temperature of an object changes at a rate proportional to the difference between the tem- perature of the object and that of the surrounding environment or ambient temperature. This is known as Newton's law of cooling. Suppose that at time t = 0 a corpse is discovered and its temperature is measured to be 85°F and that two hours later its is 74°F. It was measured the ambient temperature at 68°F and remained almost constant. We assume that at the time of death, the body temperature was at the normal value of 100°F. What is the expression that describes the surface temperature at any time?

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A. Yes, because ΔH > 0. B. Yes, because ΔS > 0. C. No, because ΔH < 0. D. No, because ΔS < 0. E. It's impossible to tell without knowing the temperature of the system.

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What is the area of \triangle ABC such that b = 28 cm, c = 14 cm, and m\angle A = 30^{\circ}? Round the answer to three decimal places. 98 cm$^2$ 169.741 cm$^2$ 193.654 cm$^2$ 196 cm$^2$

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jose angel h.