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Stokes’ Theorem for evaluating line
12. F = 〈y, xz, –y〉; C is the ellipse x2 + y2/4 = 1 in the plane z = 1.
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- (Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a cylinder, this moment of inertia is given by this formula: J=mr2/2+m( l 2 +3r 2 )/12misthecylindersmass( kg).listhecylinderslength(m).risthecylindersradius(m). Using this formula, determine the units for the cylinder’s polar moment of inertia.arrow_forward5. The derivative is the gradient of the tangent to the function. In the case of a semi-circle, this means that the gradient vector (1, dy/d.r) should be orthogonal to the vector(arn, Y0). Verify this using the dot product and also by plotting both vectors (normalise the gradient vector).arrow_forward7. Given the following truth table, write an algebraic expression for the given function and simplify the expression using a Karnaugh map. A F 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1arrow_forward
- Suppose that a parachutist with linear drag (m=50 kg, c=12.5kg/s) jumps from an airplane flying at an altitude of a kilometer with a horizontal velocity of 220 m/s relative to the ground. a) Write a system of four differential equations for x,y,vx=dx/dt and vy=dy/dt. b) If theinitial horizontal position is defined as x=0, use Euler’s methods with t=0.4 s to compute the jumper’s position over the first 40 s. c) Develop plots of y versus t and y versus x. Use the plot to graphically estimate when and where the jumper would hit the ground if the chute failed to open.arrow_forward4. Find the reflection of the triangle (2, 1), (6,1), (4,6) based on а. Хахis b. Y axis c. Origin d. Line x = yarrow_forward3. (1 pt) Simplify the Boolean function using K-map. AB 00 01 11 10 1 1 1 1arrow_forward
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- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology PtrOperations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole