Mass In Exercises 25-28, find the total mass of the wire with density
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Calculus: Early Transcendental Functions
- Find the area between the curves in Exercises 1-28. x=2, x=1, y=2x2+5, y=0arrow_forwardCalculate the fluid force on one side of the plate using the coordinate system shown below. Assume the density is 62.4 The fluid force on one side of the plate is lb/ft³. lb. (...) y (ft) Surface of pool ►x (ft) Depth -y = -2 |y| (x,y) - 12 Carrow_forwardA joint between two concrete slabs A and B is filled with a flexible epoxy that bonds securely to the concrete (see figure). B A B The height of the joint is h = 4.5 in., its length is L = 47 in., and its thickness is t = 0.9 in. Under the action of shear forces V, the slabs displace vertically through the distance d = 0.005 in. relative to each other. (a) What is the average shear strain yver in the epoxy? (Enter the magnitude in rad.) rad (b) What is the magnitude of the forces V (in kips) if the shear modulus of elasticity G for the epoxy is 140 ksi? kipsarrow_forward
- Use Green's Theorem to calculate the circulation of F = 2y i + 8xy j around the unit circle, oriented counterclockwise. circulation =arrow_forwardA sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic field is directed along the z-axis with a magnitude of 3.25 ✕ 10−5 T, find the magnitude of the magnetic force acting on the ion and the magnitude of the ion's acceleration. HINT (a) the magnitude (in N) of the magnetic force acting on the ion N (b) the magnitude (in m/s2) of the ion's acceleration m/s2arrow_forwardA block of mass m = 5.50 kg is released from rest from point and slides on the frictionless track shown in the figure below. (Let h₂ = 6.00 m.) ha 3.20 m 2.00 m (a) Determine the block's speed at points and VB= m/s m/s (b) Determine the net work done by the gravitational force on the block as it moves from point to point Ⓒ. Jarrow_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_forwardGeographers measure the geographical center of a country (which is the centroid) and the population center of the country (which is the center of mass computed with the population density). A hypothetical country is shown in the figure to the right with the location and population of five towns. Assuming no one lives outside the towns, find the geographical center of the country and the population center of the country. ▬▬ My = S S dy dx + S S dy dx + [10**- || | ▬▬ SSO dy dx 00 (Type exact answers.) (-16,16) (-8,8) Pop.= 10,000 (-11,-8) Pop. 15.000 F (-8,-8) (8-8) (16,16) (8.15) Pop. 15,000 (-16,-16) For the geographical center, determine the double integrals to be used to most efficiently find M,, the region's first moment about the y-axis. For the geographical center calculations, assume a density of 1. Use increasing limits of integration. Divide the region into three sections, going from left to right. (8,0) Pop=20,000 (16,-16) Pop.= 4,000arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,