Numerade

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An infant is brought to clinic with bright erythema in the neck and flexural folds after recent treatment with antibiotics for otitis media. What is the treatment for this condition? Topical nystatin cream under an occlusive dressing for 3-4 weeks Oral fluconazole 6 mg/kg on day 1, then 3 mg/kg/dose for 14 days Topical keratolytics and topical antibiotics for 7 to 10 days Apply nystatin with hydrocortisone cream to affected areas for 1 to 2 days

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Mark worked 60 hours last week. Calculate his earnings if his hourly rate is $22.00. (Hint: Overtime is paid when someone works more than 40 hours per week.)

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Neural connectivity begins at around the: 20$^{th}$ prenatal week 26$^{th}$ prenatal week 23$^{rd}$ prenatal week 29$^{th}$ prenatal week

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connected to a Thevenin equivalent circui~ For what value of Thevenin resistance is the. power delivered to the load maximized? Find the maximum power delivered to the load. [ Hint: Be careful; this is a trick question if you don't stop to think about it

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Consumption of prebiotics: Select one: A. blocks the absorption of cholesterol by the gastrointestinal tract. B. allows for enhanced update of amino acids by the large intestine. C. leads to the production of short-chain fatty acids. D. can increase the amount of pathogenic bacteria if ingested in excess.

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Evaluate the determinant of matrix $B$, by a cofactor expansion along a row or column of your choice. $B = \begin{bmatrix} 1 & m & m^2 \\ 1 & m & m^2 \\ 1 & m & m^2 \end{bmatrix}$

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18. Thomas has utility function $U(x, y) = x^{1/2}y^{1/2}$ and faces prices $p_x = 1$ and $p_y = 1$ and has income $I = 10$. Suppose the price of x increases to $p_x = 4$. How much does his income need to increase for him to be just as well off as before the price increase? (a) 4 (b) 10 ANSWER (c) 16 (d) 20

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Question 2: As we discussed in class, we can think about PDV (Present Discounted Value) analysis as a way to standardize, or convert, monetary values from different points in time. The motivation for PDV is that a dollar today is not worth a dollar tomorrow. However, as we also discussed, PDV analysis is highly sensitive to discount rates. Consider a household in Ohio that chooses to invest in solar panels. The solar panels cost a one-time amount of $12,000 up front, and the benefit of the panels is $1000 per year. Calculate the year that the solar panels pay for themselves (PDV positive). Use three different discount rates: 3%,5%, and 10%. You can use Excel for your calculation (it is much simpler with Excel) and then just print out the PDV of each year's annual benefit, under each discount rate. Please make sure to state any assumptions you make. Hint: "Never" is an entirely appropriate answer.

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54. A simply-supported steel beam is loaded by a distributed load as seen below. The elastic modulus of steel is 10,900 ksi and the moment of inertia about X-axis is 1500 in$^4$. The deflection at point C (2 ft from the left support) is most nearly: w = 3 lb/ft a) 0.1 in b) 0.2 in c) 0.3 in d) 0.4 in

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2. Now consider two spin-1/2 particles, like a proton and an electron. Their spins commute and the joint Hilbert space for these two particles is also four-dimensional. Here we are going to start with the basis states $|\uparrow\uparrow\rangle$ $|\downarrow\uparrow\rangle$ $|\uparrow\downarrow\rangle$ $|\downarrow\downarrow\rangle$ Note that the first quantum number refers to the z-component of the spin of the first particle and the second quantum number refers to the z-component of the spin of the second particle. The total spin is $\vec{J} = \vec{S_1} + \vec{S_2}$ (a) Construct the 4 x 4 matrix for $J_z$ in this basis. (b) Now construct the matrices for the ladder operators $J_+ = S_1^+ + S_2^+$ and $J_- = S_1^- + S_2^-$. Remember the spin operators act only on their part of the ket, so for example $J_+|\downarrow\uparrow\rangle = |\uparrow\uparrow\rangle$ and $J_-|\uparrow\downarrow\rangle = |\downarrow\downarrow\rangle$ (c) Using these expressions for the ladder operators, construct $J_x$ and $J_y$ (d) Show that the matrix for $J^2$ is $\begin{pmatrix} 2 & 0 & 0 & 0\\0 & 1 & 1 & 0\\0 & 1 & 1 & 0\\0 & 0 & 0 & 2 \end{pmatrix}$ (e) Find the eigenvectors and eigenvalues of $J^2$ (Hint: you only need to diagonalize the inner 2 x 2 matrix. The states $|\uparrow\uparrow\rangle$ and $|\downarrow\downarrow\rangle$ are already eigenvectors of $J^2$ and $J_z$, with $j = 1, m_j = +1$ and $j = 1, m_j = -1.)

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john w.