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Finding Moments of Inertia and Radii of GyrationIn Exercises 41 and 42, find
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Multivariable Calculus (looseleaf)
- Using the Midpoint Formula Use the result of Exercise 53 to find the endpoint (x2,y2) of each line segment with the given endpoint (x1,y1) and midpoint (xm,ym). ax1,y1=1,2xm,ym=4,1bx1,y1=5,11xm,ym=2,4arrow_forwardDetermine the moments of inertia of the Z-section about its centroidal xo- and yo-axes. 15 mm Answers: Ixo = Iyo 170 mm = IM i IM i 130 mm- yo -xo 15 mm 130 mm- 15 mm (106) mm 4 (10%) mm 4arrow_forwardIdentify the center and radius for each. r? + y? = 49 x² + y? = 324 x² + (y + 2) = 64 (r + 2)² + y² = 64 (1 – 5)² + (y – 3)² = 144 (z+1) + (y – 10)? = 100 :: Center: (0, 2), r = 8 : Center (-1, 10), r = 10 : Center: (-2, 0), r = 8 :: Center: (1, – 10), r = 10 :: Center: (0, 0), r = 18 : Center: (5, 3), r = 12 : Center: (2, 0),r = 8 : Center. (0, 0), r = 7 : Center (-5,-3), r = 12 : Center (0, -2), r = 8arrow_forward
- Q1 mathematical Mechanicsarrow_forwardDetermine the moments of inertia of the Z-section about its centroidal xo- and yo-axes. -130 mm 21 mm yo 155 mm 21 mm 21 mm -130 mm Answers: (106) mm4 i (106) mm4 i lyo IIarrow_forwardNonuniform straight-line motion Consider the motion of an object given by the position function r(t) = ƒ(t)⟨a, b, c⟩ + ⟨x0, y0, z0⟩, for t ≥ 0,where a, b, c, x0, y0, and z0 are constants, and ƒ is a differentiable scalar function, for t ≥ 0.a. Explain why r describes motion along a line.b. Find the velocity function. In general, is the velocity constant in magnitude or direction along the path?arrow_forward
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