Numerade

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Eastern Aviation Equipment pays Jim Davis a $1710 monthly salary plus a 10% commission on merchandise he sells each month. Assume Jim's sales were \$92,000 for last month.\nCalculate the following amounts:\n1. Amount of Commission:\n2. Gross Pay:

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A steam turbine receives steam at 7 MPa and 540°C and exhausts at 25 kPa. The efficiency is 87%. Find the steam enthalpy, the work done, and the dryness at exhaust.

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what is the result on the AD curve if the government starts an export subsidy.

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Which of the following statements about the relationship of gender and identity achievement is most accurate? a. For both men and women, identity achievement is associated with positive ego qualities. b. Identity achievement is associated with positive ego strengths for women but not for men c. Identity achievement is associated with positive ego strengths for men but not for women. d. Identity achievement is associated with a process of crisis and commitment for men but not for women.

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Finding potential Consider the conservative vector field 2 F(x, y, z) = (8 y³ x, 12 y² x² + 5 ze^{5zy}, 5ye^{5zy}) and the path C given by t r(t) = \left[ \frac{t}{\pi}, 3 \cos(t) + 4, 3 \sin(t) + 5 \right] \text{ for } 0 \le t \le \frac{3\pi}{2} Determine a potential \Psi for F. Then determine the circulation of F along C. A potential such that \Psi(0,0,0) = 1 is \Psi = The circulation along C is

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b) Evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{5+4\cos\theta} d\theta$ using the complex integral

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5. In class, we the wrote down the normal-mode frequencies and the corresponding eigenvectors for a system of three coupled oscillators. However, we skipped a lot of intermediate steps in the derivation. In this problem, you're going to fill in those intermediate steps. No computers or calculators are allowed on any part of this problem. (a) Find the normal-mode frequencies $\omega_n$ for the three normal modes of the system. Use the labeling convention in which the index $n$ labels the modes in order of increasing frequency. (b) Use your result from part (a) to derive the corresponding eigenvectors $|e_n\rangle$ for these normal modes. Normalize the $|e_n\rangle$ such that $\langle e_n|e_n\rangle = 1$. (c) Verify that the $|e_n\rangle$ that you've derived are all mutually orthogonal.

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12. [10 points] The Helmholtz energy A is introduced via A = U - TS and related to the canonical partition function via A = -kT ln Q. You will use this to derive the entropy S of N particles of a perfect monoatomic gas as a function of temperature and volume. a. [2] Combine the equations and reorder them to obtain an expression for entropy S. Replace U by its expression for the average internal energy U of a perfect gas in three dimensions. Replace Q by the canonical partition function which is given by Q = V! Note the division by N! (factorial!), since the gas particles are not distinguishable. The translational molecular partition function qrans is given by qrans = (T^2), with V and T being the volume and temperature of the gas, and a factor, which includes the mass m of the gas particles as well as Planck and Boltzmann constants: = 3 ; ( is not important, (2.tmk)^2 but keep it). Write down your complete expression for S up to this point. b. [2] Use the Sterling approximation ln N! ~ Nln N - N and collect all terms. You can replace the number of particles N by the number of moles n and Avogadro's number Na. This allows you to replace kN by R as well. Then write your result as a sum of 3 terms: one that contains only volume dependence, a second that depends on T only; and a remaining term that contains only constants. [You ended up with a version of the Sackur-Tetrode equation]

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Solve the inequality and graph the solution on the line provided. 5x - 7 \leq -32 Inequality Notation: Number Line: -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Touch and drag to plot line.

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Touch-screen devices usually feature ______ keyboards. a. laser-projection b. optical c. virtual d. physical

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