Numerade

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Problem 4: (17% of Assignment Value) Three protons are on three corners of a square of side d = 5.4 × 10-6 m. What will be the magnitude of the net force on an electron put on the fourth corner of the square? Give your answer in newtons. Useful Information: Charge of electron = -1.6 × 10-19 C Charge of proton = 1.6 × 10-19 C 1/(4πε₀) = 9 × 109 Nm² C-2 F = 1.7*10^(-14)

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2.14 Prove that if $n > 4$ is composite then \newline $(n-1)! \equiv 0 \pmod{n}$.

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The graph of the second derivative $f''$ of a function $f$ is shown. State the x-coordinates of the inflection points of $f$. (Enter your answers as a comma-separated list.) $x =$

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Problem (6-2) Construct the influence line for a) the reaction at A, C and E b) the shear at point D c) the moment at point D d) shear before and after support C e) moment at point C of the beam in the figure below.

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Task and the brief Task 4: Matrices problem Four parachutists are connected by a strong cord as shown in the diagram below. Assuming that the four parachutists are falling freely at a velocity of 10m/s compute the tension in each section of the cord and the acceleration of the parachutists. The following table gives the required information about each parachutist. Parachutists Mass (kg) Drag coefficient (kg/s) 1 87 10 2 76 14 3 65 17 4 58 20 1. Draw a free body diagram for each parachutist within the system. (2) 2. State four modelling assumptions you will use for this system. (2) 3. Using Newtons Laws of motion, derive an equation of motion for each particle. (4) 4. Using matrix algebra, setup the solution matrix in the form Ax = B. (2) 5. Solve this matrix to find the variables of the pulley system, using an analytical method, showing each step. Write each step in the equation builder in Microsoft Word. (4) 6. Then solve the same matrix using the available formulae in Microsoft Excel. (2) 7. Compare the two solutions; they should be identical. (2) 20

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on the basis of a survey conducted by the bureau of labor statistics it is estimated that 5.1 percent of the entire workforce was unemployed during the last month

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Casper has a swimming pool in his backyard. Using water from one hose requires 3hr to fill the pool. If a second hose is turned on, the pool can be filled in 1.2hr. How long would it take the second hose to fill the pool alone?

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Quarterly sales of three years are below: Exhibit 1 Quarter Year 1 Year 2 Year 3 1 923 1,112 1,243 2 1,056 1,156 1,301 3 1,124 1,124 1,254 4 992 1,078 1,198 Using the "quarterly seasonality with trend" model, the quarter1 forecast for year 5 is a. 560 b. 980 c. 1431 d. 1092

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9. You need $10'000 for 2 years and you go to your bank asking for a loan. The loan officer gives you the following options: a) 12% APR, yearly compounding b) 11.5% APR, semi-annually compounding c) 11% APR, monthly compounding Which one would you choose and why? Page 2 of 3 10. Which statement is true and which one is false. Explain in 2 lines max. a. Interest rate on a 20-year mortgage is higher than the interest rate on a 30-year mortgage. b. Interest rate on credit card debt is higher than the interest rate on a mortgage. c. Interest rate on a AAA corporate bond is lower than interest rate on a BB corporate bond with the same maturity. d. Interest rate on a AAA corporate bond with 1 year until maturity is necessarily higher than interest rate on a 10-year treasury bond.

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Problem 2 (Interrupting the current through an inductor): Plot the voltage across the $v_L(t)$ in the circuit below for $0 < t < 6$ sec (the switch was closed at $t = 0$ and opened at $t = 3$ sec). Make a comment on the result. 0.5 k? 4 mA 4 µF 0.25 H t = 3s

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jacqueline z.