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jose wagner

jose w.

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Discuss the principles of fluid dynamics and their application in designing aerodynamic structures.

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Find the absolute maximum and minimum values of each function over the inindicated interval, and indicate the x-values at which they occur f(x) = 2x^3 - x^2 - 4x + 2, [-1, 0] The absolute maximum value is at x = (Use a comma to separate answers as needed. Type an integer or a fraction) The absolute minimum value is at x = (Use a comma to separate answers as needed. Type an integer or a fraction)

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Find the Taylor series for $f(x)$ centered at the given value of $a$. [Assume that $f$ has a power series expansion. Do not show that $R_n(x) \rightarrow 0$.] $f(x) = \frac{2}{x}$, $a = -4$ $f(x) = \sum_{n=0}^{\infty} \left( -1 - \frac{x}{8} \right)$ Find the associated radius of convergence $R$. $R = 0$

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2. Write a computer code to implement the Composite Trapezoidal Rule quadrature $T_h[f] = h\left(\frac{1}{2}f(x_0) + f(x_1) + ... + f(x_{N-1}) + \frac{1}{2}f(x_N)\right)$, (1) to approximate the definite integral $I[f] = \int_a^b f(x)dx$, (2) using the equally spaced points $x_0 = a$, $x_1 = x_0 + h$, $x_2 = x_0 + 2h$, ..., $x_N = b$, where $h = (b - a)/N$. Make sure that all your codes have a preamble which describes the purpose of the code, all the input variables, the expected output, your name, and the date of the last time you modified the code.

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A college student borrowed $34,000 to pay for tuition, room, and board. Some of the money was borrowed at 4%, some at 6%, and some at 8%. How much (in dollars) was borrowed at each simple interest rate, given that the annual interest was $1,850 and the amount borrowed at 8% was three times the amount borrowed at 4%?

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You have learned from this course (and previous coursework) that the forced response of a linear system is the sum of the responses resulting from each input (i.e., superposition). V2 (s) V?(s) + 3 4 10s + 1 Y(s) 6 Figure 1. Feedback control system having command input V? and disturbance input V2. a. (4) Use this fact to reduce the diagram in Figure 1 to find the transfer functions relating (i) Y to V? and (ii) Y to V2. That is, find these transfer functions by hand computation. b. (3) Use Matlab and determine the transfer function T? such that T? = Y/V? (i.e., the disturbance V2 = 0). c. (3) Use Matlab to simulate the reference response y(t) due to a unit step input v?(t). d. (3) Use Matlab to determine the following performance measures: percent overshoot (PO), peak-time $t_p$, rise-time $t_r$, and the settling-time $t_s$. e. (9) Repeat Steps b. through d. for T2 where T2 = Y/V2 (i.e., the command input V? = 0). f. (3) Use Matlab to plot the step response of T, where T = T? + T2.

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Use the substitution $x = 8 \tan(\theta)$ to evaluate the indefinite integral \(\int \frac{42dx}{x^2\sqrt{x^2 + 64}} \) + C

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1. The state of strain at the point on the arm has components of $\epsilon_x = 180 \times (10^{-6})$, $\epsilon_y = -275 \times (10^{-6})$, and $\gamma_{xy} = 380 \times (10^{-6})$. Use the strain transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of 30° counterclockwise from the original position. Sketch the deformed element due to these strains within the x-y plane.

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How does a lower interest rate affect investment expenditure? Explain the logic and then tell me why/how these changes can affect both the demand side and the supply side of the macroeconomy.

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29. In a right triangle, $\cos \theta = \frac{3}{5}$ and $\theta$ is an acute angle in the triangle. Find the value of $\theta$. a. $\cos^{-1}(\frac{3}{5})$ or $53.13^{\circ}$ b. $\cos^{-1}(\frac{3}{4})$ or $41.41^{\circ}$ c. $\cos^{-1}(\frac{4}{5})$ or $36.87^{\circ}$ d. Undefined

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