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Learning Goal: To find the resultant of multiple forces using Cartesian components and to determine the direction of this resultant from its components. As shown, three forces act on the tip of a pole. $\vec{F_1} = (-60\hat{i} + 95\hat{j} + 35\hat{k})$ N. $F_2 = 150$ N and forms the following angles with the x, y, and z axes, respectively: $\alpha = 54.2^\circ$, $\beta = 66.6^\circ$, and $\gamma = 135.0^\circ$. $F_3 = 90$ N, forms the angle $\phi = 26^\circ$ with the z axis, and forms the angle $\theta = 15^\circ$ between the x axis and the projection of $\vec{F_3}$ in the xy plane. Part C - Direction of a resultant For the given forces $\vec{F_1}$, $\vec{F_2}$, and $\vec{F_3}$, find the three direction angles $\alpha_R$, $\beta_R$, and $\gamma_R$ between the resultant force $\vec{R}_{xyz}$ found in Part B and the x, y, and z axes, respectively. Express your answers, separated by commas, in degrees to three significant figures. Part D - Find the direction angle $\alpha$ when given direction angles $\beta$ and $\gamma$ As shown, a force of 255 N acts at the tip of a tower. Two of the force's direction angles are known, $\beta_1 = 35^\circ$ and $\gamma_1 = 69^\circ$, that define the angles between the force and the y and z axes, respectively. Find $\alpha_1$, the angle between the x axis and the force. Express your answer in degrees to three significant figures.

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F. Neutralization Reactions 1. nitric acid + sodium hydroxide $\rightarrow$ water + sodium nitrate $HNO_3$ + $NaOH$ $\rightarrow$ $H_2O$ + $NaNO_3$ 2. sulfuric acid + sodium hydroxide $\rightarrow$ water + sodium sulfate 3. phosphoric acid + sodium hydroxide $\rightarrow$ water + sodium phosphate

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Question 3 What is the molar mass of $Al_2(Cr_2O_7)_3$? A 270. g/mol B 404. g/mol C 547. g/mol D 702. g/mol E 476. g/mol

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Predict whether the solubility of propionic acid, CH3CH2COOH, is greater in water or 1,2-dimethylbenzene, C8H10.

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The decay of cesium-135 is first order with a half life is 3.0 million years. How much of 1.4942 g sample would remain after 5.49 million years?

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The melody of The Ride of the Valkyries is conjunct. ? True ? False

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Match the following chordates to their most accurate clade. Whale shark, caecilian, coelacanth, hagfish, tunicate, tuna, crocodile, lamprey, eagle, platypus, bat, kangaroo, tiktaalik, ratfish, cobra, frog, axolotl, lemur, dimetrodon Group of answer choices: Bony fish, tetrapods, chordates, amniotes, mammals, reptiles, vertebrates

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All of the following are structures located in the middle ear EXCEPT the: O incus O malleus O saccule O stapes

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What is the difference between real and nominal GDP? Group of answer choices Nominal GDP measures in current-day prices, and real GDP measures in past prices Nominal GDP measures in current-day prices, and real GDP adjusts for inflation over time Nominal GDP measures in past prices, and real GDP measures in current-day prices Nominal GDP adjusts for inflation over time, and real GDP measures in current-day prices

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Please read the article in the Council on Foreign Relations regarding the US inequality debate and quotations. The article discusses income and wealth inequality in the United States and factors that have contributed to income inequality. 1. Do you think the repeated cuts in the top US income tax rate have contributed to income inequality? Do you think the income tax rate should be raised? If so, at what income level do you think the tax rate should be raised? Please explain your reasoning. If not, please explain your position. 2. Discuss the relationship between income inequality and lower union membership over the years. Do you think higher union membership in the US would contribute to higher wages for US workers and less income disparity?

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christopher v.