Numerade

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Do the two cars ever have the same position at one instant of time? In which frame number (or numbers)?

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I react Mg and HCl via the following reaction. $Mg(s) + 2HCl(aq) \to 2H_2(g) + MgCl_2(aq)$ MgCl$_2$ is white as a solid and colorless if it dissolves in water. HCl is also colorless when it is dissolved in water. If Mg is the limiting reagent, at the end of the reaction magnesium metal will be at the bottom of the flask. the solution will be completely transparent but there will be solid MgCl$_2$ at the bottom of the flask. the solution will be completely transparent because the MgCl$_2$ is soluble and dissolved in the water. hydrogen gas will continue to bubble through the solution. Adding more HCl will make the reaction start again and produce more product.

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2.0000 moles of an ideal gas at 24.70 oC and 10000.0 Pa occupy 495.0 L. Additional gas is added to this container such that the temperature and pressure change to 85.00 oC and 18900.0 Pa with the volume remaining the same. How many moles of this gas were added?

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The given equation involves a power of the variable. Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) x2 + 25 = 0

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Find all solutions of the equation in the interval [0, 2\pi). 2\sin 3x \cos x + 2\cos 3x \sin x = -1 Write your answer in radians in terms of \pi. If there is more than one solution, separate them with commas.

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6. Consider an infinite square well with an initial state $|\psi(0)\rangle = \frac{1}{\sqrt{2}}|E_1\rangle + \frac{1}{\sqrt{2}}|E_2\rangle$. Calculate $\langle \hat{x}(t)\rangle$ and $\langle \hat{p}(t)\rangle$, and show that Ehrenfest's theorem is obeyed $m\frac{d}{dt}\langle \hat{x}(t)\rangle = \langle \hat{p}(t)\rangle$.

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Q2: For $G(s) = \frac{10(s^2 + 10s + 49)}{s^2 + 2s + 1}$. Find $|G(jw)|$ for $w$ between 0.1 and 1000 rad/s (You may add any value in between).

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Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(6, -7, 8, 6), (4, 6, -4, 1)} (a) u = (6, 25, -20, -3) u = S1+ S2 (b) v = ($rac{43}{2}$, $rac{113}{4}$, -18, $rac{13}{2}$) v = S1+ S2 (c) w = (-4, -14, $rac{21}{8}$, $rac{59}{8}$) w = S1+ S2 (d) z = (10, -9, 11, $rac{37}{4}$) z = S1+ S2

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4. The annualized yield is 3% for 91-day commercial paper and 3.5% for 182-day commercial paper. What is the expected 91-day commercial paper rate 91 days from now?

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7. Frovatriptan, shown below, is an anti-migraine drug. What class of organic functional group does frovatriptan belong to? (3 pts) H H${\rm 3}$C-N IN -NH${\rm 2}$ A. ester B. acyl chloride C. acid anhydride D. amide E. amine 8. What is the best way to carry out the following transformation? (3 pts) OH CN OH OH 1. NaOH 2. NaCN A 1. HBr 2. NaCN B OH OH 1. TsCl/pyridine 2. NaCN 1. PBr${\rm 3}$ 2. NaCN C D

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ana e.