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ivan s.

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2. Two identical blocks of mass $m$ connected by a massless spring in an equilibrium length (the spring force constant is $k$) are moving with speed $V_o$ on a frictionless horizontal surface as shown in figure. Another block of mass $m$ initially at rest collides with and sticks to the mass $m$. The collision is completely inelastic. a) Find the speed of masses just after the collision. b) Find the maximum compression of the spring.

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What is the pH range where the following buffers are most effective? a) 0.10 M H2PO4 -/0.010 M HPO4 2- pH range = ___________________________________ b) 0.50 M H2PO4 -/0.050 M HPO4 2- pH range = ___________________________________ c) 0.010 M H3PO4 -/0.10 M H2PO4 2- pH range

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According to Yamaguchi (2001), in _____, the self acts as an agent, and individuals feel themselves to be more self-efficacious when their agency is made explicit, leading to greater feelings of autonomy and efficacy. direct control indirect control proxy control collective control

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Solve the equation. Check the solution. \frac{5x}{6} + \frac{2}{5} = 2 x =

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As a financial analyst at Deutsche Bank, NY, you are helping your client with futures hedging. Your client enters into a long position in futures contract to buy 5,000 bushels of wheat for $6.50 per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. Your client will be allowed to withdraw any balance in the margin account in excess of the initial margin and the company will get a margin call if the balance is going below the maintenance margin. a. Will the trader get a margin call if the futures price goes to $6.14? b. What will be the price that will trigger a margin call of $2,500? c. What will be the price that will allow you to withdraw just $2,500 from the margin account?

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Fatigue is one of the major factors that limit the use phase of a material. a) Please explain the general difference between \"creep\" and \"fatigue\". (2 P) b) Wöhler-curves (S/N-curves) can be used to illustrate the fatigue behaviour of materials. Please describe the stress-scenario that has been applied to create below shown Wöhler-curve with the help of given values for R and F. (4 P) 180 160 $R = -0.1$ $F = 2 \text{ Hz}$ 140 $R = \frac{\sigma_{min}}{\sigma_{max}}$ 120 $D = \sum \frac{n_i}{N_i}$ 100 80 60 $10^4$ $10^5$ $10^6$ $10^7$ $10^8$ $10^9$ $10^{10}$ c) With the help of above diagram please calculate damage D of the material after 250,000 cycles at 130 MPa and additional 4,000,000 cycles at 90 MPa. What do you conclude from your result? (6P) d) The shown Wöhler-curve does not cover stress-amplitudes above 180 MPa and below 70 MPa. Please explain. (3 P)

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Consider the function f(x) = x\textsuperscript{3} \text{\textendash} 2x + 4 on the interval [-2, 2] with h = 0.25. Use the forward, backward, and centered finite difference approximations for the first and second derivatives so as to graphically illustrate which approximation is most accurate. Graph all three first-derivative finite difference approximations along with the theoretical, and do the same for the second derivative as well.

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15. Two circular water as shown. The momentum equation in the X- direction is equal to a. $P_1A_1 + F_x - P_2A_2 = m_2V_2 + m_3V_3sin30 - m_1V_1$ b. $P_1A_1 + F_x = m_2V_2 - m_3V_3cos30 - m_1V_1$ c. $P_1A_1 + F_x + P_2A_2 = m_2V_2 + m_3V_3sin30 - m_1V_1$ d. $P_1A_1 + F_x = m_2V_2 - m_3V_3sin30 - m_1V_1$

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1. (This exercise is meant to illustrate that derivatives may not be continuous, and so Darboux's theorem is actually telling us something really cool!) Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $\qquad f(x) = \begin{cases} x^2 \sin(\frac{1}{x}) & x \neq 0\\ 0 & x = 0. \end{cases}$ (a) Prove that $f$ is differentiable at 0; (b) Prove that $f'$ is not continuous at 0 (Hint: use the sequential definition and choose $x_n = \frac{1}{2\pi n}$).

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Question 18 Not yet answered Marked out of 8.00 Flag question a) Given the amplitude and phase spectrum as below find $x(t)$ $|x(j\omega)|$ -1 1 180 $\theta(j\omega)$ 1 b) linear time invariant system with the following input output relation $\frac{d^2y(t)}{dt^2} + 5\frac{dy(t)}{dt} + 6y(t) = 4x(t)$ Find the output of the system when $x(t) = e^{-4t}$

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