Numerade

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$ \frac{\sqrt{2(x+h)+3} - \sqrt{2x+3}}{h} $

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Perform the indicated operation. If possible, reduce the answer to its lowest terms.\\ $\frac{2}{3} \cdot \frac{7}{11}$

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Calcular la integral $\oint_C \frac{e^{3z}}{(z-1)^2(z-2i)} dz$ donde C es la curva $\frac{x^2}{2} + y^2 = 1$

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If an object is projected upward from ground level with an initial velocity of 144 ft per sec, then its height in feet after t seconds is given by s(t) = -16t^2 + 144t. Find the number of seconds it will take to reach its maximum height. What is this maximum height?

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4. The following collection of 10 triangles (each denoted by their three vertices) represents a triangulation of a compact surface X: T? = {v?, v?, v?}, T? = {v?, v?, v?}, T? = {v?, v?, v?}, T? = {v?, v?, v?}, T? = {v?, v?, v?}, T? = {v?, v?, v?}, T? = {v?, v?, v?}, T? = {v?, v?, v?}, T? = {v?, v?, v?}, T?? = {v?, v?, v?}. Assemble these triangles into a plane model for X. Can you tell what surface it is? [Hint: To clarify the notation, note that triangle T? has vertices v?, v? and v? and meets triangle T? only in the vertex v?, whereas triangle T? and triangle T? share a common edge between their vertices v? and v?. Begin by \"laying down\" any one of these triangles in the Euclidean plane. Then, one by one, always take a triangle that can be matched up along a free edge with what you have already assembled in the plane so far. If two edges of triangles that have already been laid out are to be identified, label and direct them accordingly.] 5. Suppose that Y is a compact surface with the property that X#Y is topologi- cally equivalent to X for every compact surface X.

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Texts: 1. A single-phase load is supplied with a sinusoidal voltage: v(t) = 340Sin(377t) The resultant instantaneous power is: p(t) = 1500 + 1875cos(754t-36.870) (a) Determine the complex power supplied to the load. (3) (b) Determine the instantaneous current i(t) and the RMS values of the current supplied to the load. (4) (c) Determine the load impedance. (3)

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The most common purchases on account include O supplies. O inventory. O inventory and supplies. O inventory, supplies, and staff wages.

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7. A 4 in. long 3/8 in. diameter bar of metal is set up in tension impact with a 60 lb. 31.5 in. arm set at 76°. The rise angle after the impact is 15°. (a) What is the energy absorbed in foot pounds by the test sample? 6 (b) What is the energy in foot pounds per cubic inch absorbed by the sample? 4 8. Using the material tested in Problem 6, what diameter rod 4 in. long would be needed to absorb 7500 in.-lb. of energy? 6 9. A 30 kg. 80 cm. long impact test hammer is set initially at 76°. After impact in a Charpy test the rise angle is 18°. What is the energy absorbed in newton- meters? 6

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For problems 19-21, you need to SHOW YOUR WORK, and may get partial credit if your work demonstrates your understanding of the concepts. Clearly indicate your final answer!!! (7 pts each) Answer all problems on this page A current of 55.4A passes clockwise around an ideal solenoid which is 0.415 m long with 350,000 turns. 19) Calculate the Magnetic field inside the solenoid. 20) A single, small, square loop with an area of 0.0300 m$^2$ is located inside the solenoid such that the magnetic field created by the solenoid goes straight through the loop. What is the magnetic flux through the square loop? 21) If the square loop is rotated such that the magnetic field is now going through the loop at a 45 degree angle, what is the new magnetic flux?

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You have invested $25,000 in the stock of Bombardier, and $75,000 in the stock of Lululemon. The expected rate of return of Bombardier is 12%, and that of Lululemon is 7%. Bombardier stock has a standard deviation of 30%, while Lululemon stock has a standard deviation of 18%. The correlation between Bombardier and Lululemon is 0.2. What is the expected rate of return of your portfolio and what is the standard deviation of your portfolio? Points: 8

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