Numerade

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write a balanced scheme for the reaction between NaBH4 and BF3. BH3 and NaF are formed

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2. 17.42 A disc drive is driven by a friction driver, as shown in Fig. P17.42. Initially, the angular velocity of the disc is $ \omega_2 $ [rad/s], clockwise, and that of the driver is $ \omega_1 $ [rad/s], counterclockwise. Derive a formula for the constant an- gular acceleration $ \alpha_1 $ [rad/s$^2$] that the driver must have to increase the disc's angular speed from $ \omega_2 $ to $ \omega_3 $ in time t [s]. Express the result in terms of $ r_1 $, $ r_2 $, $ \omega_1 $, $ \omega_3 $, and t.

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As more satisfaction is achieved from consuming a good with diminishing marginal utility, then total utility

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If an ounce of gold is priced at $1,000 in the U.S. but can be purchased in Mexico for MX $25,000 with an exchange rate of $1 = 20 MX$, then according to the principle of arbitrage, ? Mexicans would buy gold in the US, which would raise the price of gold in Mexico and increase the price difference between the two countries. ? Americans would buy gold in Mexico, which would raise the price of gold in Mexico and reduce the price difference between the two countries. ? Mexicans would buy gold in the U.S., which would raise the price of gold in the US and reduce the price difference between the two countries.

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Choose the inequality that represents the following graph. Choose 1 answer: (A) $ x<-4 $ (B) $ x \leq-4 $ (C) $ x>-4 $ (D) $ x \geq-4 $

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When mixing artificial salt water, why can you not simply mix table salt and water together?

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4. Which of the following reactions releases the least amount of heat upon hydrogenation?

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2. Please answer all parts (a) - (d) of this question. Consider the following function of $x_1$ and $x_2$: $f(x_1, x_2) = bx_1^a x_2^{(1-a)} - cx_1^2 - x_2$ where $a, b > 0$ and $a < 1$. [Note that no sign is being imposed to $c$.] (a) [5 marks] Write out the first-order conditions associated with any stationary points. Do not solve. (b) [10 marks] Write out the Hessian matrix of the function. Leave it in terms of arbitrary $x_1$ and $x_2$. (c) [15 marks] Assume there is a unique stationary point associated with the first-order con- ditions. Using the Hessian matrix, provide sufficient conditions on $c$ such that you can establish whether the stationary point is a local maximum. If not possible, explain why. (d) [5 marks] Discuss a possible economic interpretation of this optimization problem using no more than 2 sentences.

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5. Let $Q \subset \mathbb{R}^2$ denote the rhombus given by $|x| + |y| = 1$. Then show that $Q \times Q \subset \mathbb{R}^4$ is a regular space.

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Consider the function $f(x) = \frac{4}{x^2} - \frac{3}{x^7}$. Let $F(x)$ be the antiderivative of $f(x)$ with $F(1) = 0$. Then $F(x) = $

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mercedes g.