Numerade

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In Sundiata an Epic of Old Mali, Sundiata's father's name was Soumaoro Kante Maghan Kon Fatta Moussa Tounkara Dankaran Toumani Keita

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During the solution of a linear differential equation for x(t), with the initial condition x(2) = 15, the following step has been reached: $$\frac{d}{dt}(x(t)e^t) = \cos(t^4)$$ Finish the solution of the problem. (Hint: you may need to leave an unevaluated definite integral in your solution.)

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This problem explores how a current-carrying wire can be accelerated by a magnetic field. You will use the ideas of magnetic flux and the EMF due to change of flux through a loop. Note that there is an involved follow-up part that will be shown once you have found the answer to Part B.What is the acceleration ar(t) of the rod? Take m to be the mass of the rod.

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Decision Point: How Will You Respond to Economic Changes? You call a meeting with your marketing analysts to discuss the situation. You give them your prediction that the economic environment will produce positive results for Gerlach's business, and ask for their recommendations as to how Gerlach should respond. Which recommendation will you follow?

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c. Calculate the probability that the next twenty five calls will occur within 10 minutes of each other

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Show the inverse Mellin Transformation of the following function h: $\mathcal{M}^{-1}[h(p, \theta)] = \frac{1}{2\pi i} \int_{c - i\infty}^{c + i\infty} r^{-p} \frac{\sin p\theta}{\sin 2p\alpha} dp = \\ \frac{(\frac{1}{2\alpha}) r^n \sin n\theta}{(1 + 2r^n \cos n\theta + r^{2n})} \text{where } n = \frac{\pi}{2\alpha} \text{ or } 2\alpha = \frac{\pi}{n}$

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Let $\vec{v} = (1 - 2xyz - xe^z \cos y, y^2z, e^z \cos y)$ be the velocity field of a fluid. Compute the flux of $\vec{v}$ across the surface $x^2 + y^2 + z^2 = 16$ where $x > 0$ and the surface is oriented away from the origin. Hint: This is a very tricky question. If the total divergence is zero, that does not necessarily mean there is no flow through the closed surface formed by the hemisphere and its disk-shaped base. It means the flow into the closed surface is equal to the flow out of the closed surface. Assuming the divergence is zero (you should check!), the flow (or flux) in through the disk at the base will equal the flow (or flux) out of the hemisphere. Thus, find a way to calculate the flow through the disk at the base of the closed surface. :)

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What are three elements of a homeostatic mechanism? BE sure to give an example of each and what it regulates.

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Given vectors $u = 2xi + 8j$ and $v = xi - 5j$, find x so that u and v are orthogonal. $x = $ (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

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QUESTION 2 A. The figure below shows the relationship between crater-wear and average tool-chip interface temperature. a, b and c are plots representing 3 types of tool materials. Which is the hardest tool material? Why?

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bryan g.