Numerade

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the protein assisted movement of a polar molecule across the membrane

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Titration curves serve what purpose?

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6. Suppose that $S \subseteq \mathbb{R}$ is a set defined by $S = \{x \in \mathbb{R} : x = m\sqrt{\pi} + n\sqrt{2} \text{ for some } m, n \in \mathbb{Z}\}$ and $S'$ is a proper subset of $S$ defined by $S' = \{x \in S : x = p\sqrt{\pi} + q\sqrt{2} \text{ for some prime numbers } p, q\}$. (a) Show that $S$ is countably infinite. (b) Is there a bijection from $S'$ to $S$? Justify your answer. (If needed, you may use the fact that $\pi$, $\sqrt{2}$ are irrational numbers without proof.)

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Find an equation of the line tangent to the curve defined by $x^4 + 5xy + y^2 = 40$ at the point $(2, 2)$. y =

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Problem 5 Use the Biot-Savart law to find the B-field of a straight segment of wire carrying a current I. (a) Show that the magnitude of the B-field at a distance r from the wire is: $B(r) = \frac{\mu_0 I}{2\pi r} \frac{\sin \theta_1 + \sin \theta_2}{2}$. What is the direction of this B-field? (b) Show that this B-field violates Ampere's law unless the wire is infinitely long.

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The frequency table below summarizes student grades on a final exam. Draw a frequency polygon based on the data. able[[Grade (%),Frequency],[50 up to 60,2],[60 up to 70,6],[70 up to 80,30],[80 up to 90,6],[90 up to 100,6],[Total,50]] First find the midpoint of each class interval. able[[Grade (%),Midpoint,Frequency],[40 up to 50,,0],[50 up to 60,,2],[60 up to 70,,6],[70 up to 80,,30],[80 up to 90,,6],[90 up to 100,,6],[100 up to 110,,0]] Next, plot the midpoint and their corresponding frequency. Connect the dots with a line. Notice that a frequency polygon begins and ends with zero. The frequency table below summarizes student grades on a final exam. Draw a frequency polygon based on the data. Grade (%) Frequency 50 up to 60 2 60 up to 70 6 70 up to 80 30 80 up to 90 6 90 up to100 6 Total 50 First find the midpoint of each class interval. Grade % Midpoint Frequency 40 up to 50 0 50 up to 60 2 60 up to 70 6 70 up to 80 30 80 up to 90 6 90 up to 100 6 100 up to 110 0 Next, plot the midpoint and their corresponding frequency.Connect the dots with a line.Notice that a frequency polygon begins and ends with zero.

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4. Evaluate the double integral $ \int_{0}^{1} \int_{arcsiny}^{\frac{\pi}{2}} \cos x \sqrt{1 + \cos^{2}x} \,dx \,dy $

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1. Sketch a possible graph of a function that satisfies all of the conditions below. Where there is a [] enter a value. Explain how each condition is satisfied to get full marks. (6 marks) • x-intercept at ([ ], 0) • vertical asymptote at x= [] • As x??, y?[] • f(1) = [] • the function is never increasing • the function is Even / Odd ? (circle your choice)

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Suppose \int_{3}^{6} f(x) dx = 8 and \int_{3}^{6} g(x) dx = -4. Evaluate \int_{3}^{6} (3 f(x) - 2 g(x)) dx. Remember to include a " + C" if appropriate. Number Please explain, in your own words and in a few sentences, how you arrived at your answers. Answers with no relevant explanations may receive reduced or no credit.

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(e) Yesterday, you entered into a futures contract to buy €62,500 at $1.50/€. Your initial margin was $3,750 (-0.04 x €62,500 $1.50/€-4 percent of the contract value in dollars). Your maintenance margin is $2,000 (meaning that your broker leaves you alone until your account balance falls to $2,000). At what settle price (use 4 decimal places) do you get a margin call? B) Today's settlement price on a Chicago Mercantile Exchange (CME) yen futures contract is $0.8011//100. Your margin account currently has a balance of $2,000. The next three days' settlement prices are $0.8057//100, $0.7996//100, and $0.7985/¥100. (The contractual size of one CME yen contract is ¥12,500,000). If you have a short position in one futures contract, the changes in the margin account from daily marking-to-market will result in the balance of the margin account after the third day?

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