Questions asked
Question 3 (10 pts): A concrete post with a 50.8 cm diameter supports a compressive load of 8910 N. Determine the stress the post is bearing.
Let $f(t)$ be a function on $[0, \infty)$. The Laplace transform of $f$ is the function $F$ defined by the integral $F(s) = \int_0^\infty e^{-st}f(t)dt$. Use this definition to determine the Laplace transform of the following function. $f(t) = te^{-4t}$ The Laplace transform of $f(t)$ is $F(s) = \text{_____}$. (Type an expression using $s$ as the variable.) It is defined for $s > \text{_____}$. (Type an integer or a fraction.)
2) For the anatomy illustrated below, what will be the intensity amplitude of the ultrasound signal that has been reflected by the first fat-muscle interface when it returns to the transducer? How long will it take for signal to reach the interface and come back to the transducer? The amplitude should be on a decibel scale and the time should be in microseconds. Ignore any reflected signal from the transducer/fat interface. At a transducer frequency of 5 MHz, the intensity attenuation coefficient for muscle is 5 dB cm$^{-1}$ and for fat is 7 dB cm$^{-1}$. Relevant values of the characteristic acoustic impedance and speed of sound are given below. transducer Characteristic Acoustic Impedance Speed of Sound $\times 10^5 (g \, cm^{-2} \, s^{-1})$ $(m \, s^{-1})$ 2 cm fat Air Blood Bone 0.0004 330 1.61 1550 7.8 3500 Fat 1.38 1450 Brain 1.58 1540 3 cm muscle Muscle 1.7 1580 Vitreous humor (eye) 1.52 1520 Liver 1.65 1570 Kidney 1.62 1560 fat
b. For the function $f(x, y) = \begin{cases} \frac{\cos x - \cos y}{x - y} & \text{if } x \neq y \\ 0 & \text{if } x = y \end{cases}$ i. Find $f_x(0, 0)$. ii. Find $f_y(x, y)$. c. Let $f(x, y) = x^2 + y^3$, find the slope of the line tangent to the surface at $(-1, 1, 2)$, lying in i. $x = -1$ ii. $y = 1$
A pharmacist wants to establish an optimal inventory policy for a new antibiotic that requires refrigeration in storage. The pharmacist expects to sell 3600 packages of this antibiotic at a steady rate during the next year. She plans to place several orders of the same size spaced equally throughout the year. The ordering cost for each delivery is $12, and carrying costs, based on the average number of packages in inventory, amount to $6 per year for one package. Use this information to answer the following questions. (a) Let x be the order quantity and r the number of orders placed during the year. Find the inventory cost (ordering cost plus carrying cost) in terms of x and r. C = (b) Find the constraint function. (Type an equation.) (c) Determine the economic order quantity that minimizes the inventory cost and then find the minimum inventory cost. x = C = $
4. Consider a GaAs p-n junction with $N_A = 10^{17} cm^{-3}$ and $N_D = 10^{17} cm^{-3}$. The minority carrier lifetime on the p-side is 1 µs, and the minority carrier lifetime on the n-side is 0.1 µs. (same as problem #1) a. What is the excess electron concentration for $V_{app} = 1 V$? b. What is the excess electron concentration for $V_{app} = 1.2 V$? c. Find the following ratio: $\frac{\Delta n(1.2 V)}{\Delta n(1 V)}$ d. How much brighter is the LED when operated at 1.2 V versus 1 V?
Write the correct answer. 1. A={1, 2, 3, 4, 5} 2. A={2, 4, 6, 8} 3. A={a, b, c, d, e, f, g} 4. A={a, b, c, d} 5. A={1, 4, 7, 9, 10} B={3, 4, 5, 6} B={1, 4, 8, 12} B={b, d, f, h, i} B={e, f, g, h, i} B={1, 3, 5, 7, 9} A?B= A?B= A?B= A?B= A?B=
4. Write the equation of the line in point-slope form with slope = 4 passing through (-1, -7)
How might one best accomplish the following synthesis? NHTO ? ???? ???? ???????? A. (1) C3H7COCI + AICI3(I) HNO3& heat (W) excess H2& Pt catalyst B. (1) HNO3& heat (U) C4H9Cl + AlCl3(W) excess H2& Pt catalyst C. (1) C4H9Cl + AlCl3 (IU) HNO3& heat (W) excess H2& Pt catalyst D. (1) HNO3& heat (II) C3H7COCI + AlCl3(W) excess H2& Pt catalyst E. (1) HNO3& heat (U) excess H2& Pt catalyst (M) C3H7COCI + AICI (Iv) excess H?& Pt catalyst
11. Indicate the following: a. The number of valence electrons that a phosphide ion, P³, have b. The number of core electrons that a chlorine atom has d. Two chemical species among the following that make an isoelectronic pair: CI?, O²?, F?, Ca²?, Fe³? e. The number of 3d electrons that the manganese(II) ion, Mn²?, has 12. a. Which of the elements listed below has the greatest atomic radius? B, Al, S, P, Si b. Which of the following elements has the smallest ionization energy? Li, Na, Be, K, Rb c. Which of the following elements has the greatest metallic character? Br Se Ni As Si
