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Think About It The center of mass of a solid of constant density is shown in the figure. In Exercises 43-46, make a conjecture about how the center of mass
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Calculus: Early Transcendental Functions
- Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a orthocenter? b centroid?arrow_forwardAstronomers use a technique called stellar stereography todetermine the density of stars in a star cluster from theobserved (two-dimensional) density that can be analyzedfrom a photograph. Suppose that in a spherical cluster ofradius R the density of stars depends only on the distancefrom the center of the cluster. If the perceived star density isgiven by y(s) , where is the observed planar distance fromthe center of the cluster, and x (r ) is the actual density, it canbe shown that y(s) = integral s to r 2 r /sqrt ( r2 - s2 ) x(r) dr If the actual density of stars in a cluster is x (r ) = 1/2 (R-r)2 ,find the perceived density y(s)arrow_forwardy = ex, y = 0, x = 0, x = 3 Find the exact coordinates of the centroid. (x, y) =arrow_forward
- A point charge, Q=2 µC is located at A (4, 3, 5) in free space. Calculate E,, Es and E, at the point P (8, 12, 2). (a)arrow_forwardCalculate the fluid force on one side of the plate The fluid force on one side of the plate is using the coordinate system shown below. Assume Ib. the density is 62.4 lb/ ft3. ... у (f) Surface of pool x (ft) -у3 — 2 Depth \y| (x,y) 7arrow_forwardCalculate the fluid force on a side of the plate in Figure 11(B), submerged in a fluid of mass density p = 800 kg/m³. 2 m 3 m 4 m 4 m 2 m 2 m (B) (A) FIGURE 11arrow_forward
- divĒ = 0 divĤ = 0 1 ƏĦ curlĒ c ðt 1 DỂ curlĦ - c ət Using Maxwell's equations, show 1 ²Ē c2 Ət² (V · V)Ẽ =arrow_forward人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT 12. Find the moments of inertia, as well as the radii of gyration in x and y for the triangle 0 ≤ x < b, 0≦y shassuming that the density is constant, o = 0_0. 13. Find the centroid and the moments of inertia Ix, ly and Iz of the tetrahedron whose vertices are the points (0, 0, 0), (1, 0, 0), (0, 1, 0) and (0, 0, 1).arrow_forwardConsider the lamina in the shape of the triangle whose vertices are (0, 0), (L, 0), and (0,L) for some L ∈ R+. Calculate the moments of inertia, Ix and Iy, for this lamina whose density is proportional to the square of the distance from the vertex opposite the hypotenuse.arrow_forward
- Please provide Handwritten answer. Advanced Math We consider a thin plate occupying the region D located in the upper half-plane (where y ≥ 0) and between the parabolas of equations : y = 2 - x2 and y = 1 - 2x2 The density of the plate is proportional to the distance from the x axis. a) Calculate the moments of inertia (second moments) of the plate with respect to the coordinate axes.b) Is it easier to rotate the plate around the x-axis or the y-axis? Justify your answer.arrow_forwardQ1,- A- Locate the centroid (X only) of the shaded area y=12 -3x 3 m Fig. L.A 2 marrow_forwardHow do you find the center of mass of the lune?arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage