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Q5 Mechaincs - Logarithms 2 10 Points Consider the function $f(x) = -5\log_5(x+5)$ Answer the following questions based on this function: A) Determine the domain of the function. B) Determine the range of the function. C) Find the x- and the y-intercept of the function. D) Identify the vertical asymptote of the function E) Find the inverse function, $f^{-1}(x)$.

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Transform theorems Superposition Theorem $$a_1x_1(t) + a_2x_2(t) \longleftrightarrow a_1X_1(f) + a_2X_2(f)$$ Time-Delay Theorem $$x(t-t_0) \longleftrightarrow X(f)e^{-j2\pi ft_0}$$ Scale-Change Theorem $$x(at) \longleftrightarrow \frac{1}{|a|}X(\frac{f}{a})$$ Duality Theorem $$X(t) \longleftrightarrow x(-f)$$ Frequency Translation Theorem $$x(t)e^{j2\pi f_0t} \longleftrightarrow X(f-f_0)$$

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Solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. $3x + y = 15$ $x = -\frac{1}{3}y + 5$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The system is consistent. The solution is (Type an ordered pair.) B. The system is dependent. C. The system is inconsistent.

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A 70-year-old widow with osteoporosis lives alone and attends a nearby church. While walking to her mailbox, she fell and fractured her left hip. After undergoing an open reduction internal fixation (ORIF), she is being discharged. What considerations would be appropriate to assess before she is sent home?

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a) What is the complex conjugate of z = 6 + j8? b) What is $\bar{z}z$ for z = 6 + j8? c) What is the phase of z = -2? d) What is the magnitude of z = j2? e) What is the phase of z = j2? f) What is the phase of z = -1 - j? g) What does the set \{z ? C | |z| = 1\} look like? h) What does the set \{z ? C | $\frac{\pi}{2}$ ? ?z ? $\frac{3\pi}{2}$ \} look like?

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Consider the following equity or economic justice issue: It is unfair to impose draconian sentences for non-violent crimes such as burglary committed by the lower classes. And now consider the following efficiency argument: It is efficient to impose tough sentences for non-violent crimes to reduce these socially undesirable activities.

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QUESTION 4 Identify -+- Pressure Compensated Flow Control Valve • Quick Release Coupling with 1 Check Valve Quick Exhaust Valve Quick Release Coupling with 2 Check Valves

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4. Given a triangle with vertices at the coordinates A(2, 4), B(1, -2), C(3, 7): (a) Find the lengths of the sides. (b) Use the Law of Cosines formula to find $\cos(\angle BAC)$. NOTE the formula can be rewritten as $\cos(\angle BAC) = \frac{b^2 + c^2 - a^2}{2bc}$ where $a$, $b$, $c$ are BC, AC, AB respectively. (c) Confirm your answer by finding $\cos(\angle BAC)$ by using the dot product for- mula to find the angle between $a = \overrightarrow{AB} = (-1, -6)$ and $b = \overrightarrow{AC} = (1, 3)$. NOTE that you found the magnitudes in part (a), and you can compute the dot product by just using arithmetic operations.

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1. Dear all, you have 30 minutes to complete the test. You won't be able to submit your answers after 15:00 so please use your time efficiently. You must type your answers on the space you are provided under each question. You don't have to type the entire solution, typing your final answer is sufficient (if you want you can type the entire solution, its up to you). I will post the solutions of this quiz after the exam. Each question is 25 points. Good luck. 2. Btech corp. has announced that it will distribute 2$ dividend two years from now. The company also plans to distribute a 5$ dividend after three years of it's first dividend payment. If the required rate of return is 13% and if the predicted selling price in year 5 is 30$, how much the stock should worth right now? 3. There is an available project that requires you to invest 53,000$ today. This project is expected to generate -15,000 in it's first year. However, in the following years the project will yield positive cash flows. In the fourth year, the project is expected to generate 32,000. After that, the project will generate 30,000 in both sixth and seventh years. If the avarage return on similar projects is 8%, what is the NPV of this project?

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Problem 3 (20 points) A spring of spring constant 8 lb/ft is attached to a cable PQ at Q. The other end of the spring is attached to a roller R so that the spring remains horizontal as it stretches. A weight of 15 lb is suspended from Q and a spring stretch of 2 inches is measured. Determine: a) The angle $\theta$ that the cable PQ makes with the horizontal for equilibrium, in degrees b) The tension, in the cable PQ, in lb.

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