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A diligent student has a slow leak in her bike tire, but has been too busy studying for exams to fix it. We’ll assume that the pressure in the tire decreases at a rate proportional to the difference between the atmospheric pressure (15 lbs.) and the tire pressure. Monday at 6:00 pm she pumped up the pressure to 85 lbs. By 6:00 pm Tuesday it was down to 75 lbs. When does she need to pump up the tire if she wants to keep the pressure at a minimum of 40 lbs.? Give the day and time.

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For an op-amp, the open-loop gain A is the same as the op-amp circuit's closed-loop gain G True False

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Which economist is credited with developing the theory of diminishing marginal utility? Group of answer choices Thomas Malthus David Ricardo Adam Smith Jeremy Bentham

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Calculate the successive rates of change for the function H(x), in the table below to decide whether the graph of H(x) is concave up or concave down. Round the answers to 3 decimal places. X 12 H(x) 20.96 Rate of change H(x) is concave i 15 21.12 i 18 21.34 i 21 21.62

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Q-1) In the complex plane a set is given by $z$ such that $Im \{z^2\} > 4$. Here $Im$ means, the imaginary part of the complex number $z$. (a) Sketch this set (b) Is this set open or closed or neither open nor closed? Explain. (c) Is this set bounded? Why? (d) Is this set connected? Why? Hint: $z = x + iy$, and $Im\{z\} = y$, think $z^2$. Q-2) Calculate a) $i^i$ (all values) b) $i^{Log(-1)}$ (principal value) Q-3) Consider the following branch of the logarithmic function $log z$ as $r > 0, \frac{\pi}{2} < \theta < \frac{5\pi}{2}$ a. Draw the Branch cut b. Calculate $log 1$ and $log(-1)$. Q-4) Solve $z^2 + i(2z - 1) + 5 - 3z = 0$ Q-5) $(4\sqrt{3} - i4)^{1/3} = ?$ a) Obtain the roots b) Show the roots in complex plane Q-6) Determine the set of points at which the given function $f$ is NOT analytic (EXPLAIN THE REASON) a) $f(z) = (z^6 - 1)(z - 2)^2$ b) $f(z) = \frac{z^2}{z^4 - 1}$ c) $f(z) = \frac{z^2}{z - i}$

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Members of the Whig Party believed that a strong federal government was: Oa violation of individual liberty. Onecessary in order to promote liberty and prosperity. Oa threat to the principle of states' rights.

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Why would an economist use real GDP per capita to measure economic progress? Real GDP per capita is adjusting for fluctuations in the price level. Real GDP per capita allows for easy comparisons among countries that otherwise may be different. Real GDP per capita is adjusting for fluctuations in population size. All of these are reasons an economist would use GDP per capita.

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8. Estimate the following portfolio's expected return and beta Security $ Invested % (Weight) Beta Wgt*Beta Stock W $4,000.00 0.85 Stock X $10,000.00 0.95 Stock Y $14,000.00 1.2 Stock Z $4,000.00 1.1 Total: Beta Portfolio= a. Is the portfolio more/less risky than the individual securities? Why?

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Q.10) 110 V, 800 rpm shunt generator. Ra=0.12 ohm, Rf=55 ohms. The load is 220 lamps (60 W each). Prot=410 W. Find 1. total Pcu, FL 2. Tin 3. Mechanical efficiency, electrical efficiency and overall efficiency.

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A circular hydrostatic bearing operates at a speed of 200 [rps], with a minimum film thickness of 50 [Î¼m] and supports a load of 50 [kN]. The bearing's outside radius is three times larger than the recess radius. A lubricant is delivered through a capillary length of I = 80 [mm] and diameter d = 0.7 [mm]. The pump supply pressure is 3 [MPa] and the lubricant's viscosity is 8.5 [cP]. Calculate the bearing dimensions, friction coefficient, and power loss. Answer: R = 0.051 [m], R = 0.154 [m], Î¼ = 0.0005, and H = 27.32 [W].

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jonathan m.