The center of mass of a composite body:Is the same as the center of gravity of the composite object.Requires integration for its calculation in all cases.O is calculated as the sum of the mass of each figure involved in the composite body multiplied by the distance of the centroid ofthat figure from a coordinate axis established on the object.O is calculated as the sum of the product of the mass of each figure involved in the composite body divided by the total mass ofthe object.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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find the centroid of area, If the area is equal to 1/6
2+1 = 0 dv Vt- dt V+1
To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-filled pool and in a pool where the water was thickened with food grade guar gum to create a syrup-like consistency. Velocity, in meters per second, was recorded and the results are given in the table below. Swimmer Velocity (m/s) Water Guar Syrup 1 0.90 0.94 2 0.92 0.99 3 1.00 0.95 4 1.10 1.15 S 1.20 1.24 6 1.25 1.24 7 1.25 1.29 8 1.30 1.30 9 1.35 1.31 10 1.40 1.42 11 1.40 1.41 1.50 1.54 13 1.65 1.57 14 1.70 1.70 1.75 16 1.80 1.79 17 1.80 1.81 18 1.85 1.86 19 1.90 1.87 20 1.95 1.95 The researchers concluded that swimming in guar syrup does not change mean swimming speed. Are the given data consistent with this conclusion? Carry out a hypothesis test using a 0.01 significance level. (Use "water" "guar syrup) State the appropriate null and alternative hypotheses. HH-0 Ho-0 Ho: H0 Find the test statistic. (Round your answer to two decimal places.) Use technology to find the P-value.…
A cylindrical can is to be designed with a capacity of 1000 mL. Find the dimensions of the can, rounded to one decimal, that will minimize the cost of the metal used to make the can, given that the radius must be between 3 cm and 10 cm.
The force on a sailboat mast can be represented by the following function: f(2)=200 (5)22/ where = the elevation above the deck and H= the height of the mast. The total force F exerted on the mast can be determined by integrating this function over the height of the mast: F="f3 dz The line of action can also be determined by integration: főzf(z) dz Sof(z) dz (a) Use the composite trapezoidal rule to compute F and d for the case where H= 30 (n = 6). (b) Repeat (a), but use the composite Simpson's 1/3 rule.
A 500 gallon tank is filled with fresh water in which 80 pounds of salt are dissolved. Fresh water is flowing into the tank at a rate of 2 gallons per minute and a saline solution with a concentration of 0.8 pounds of salt per gallon is flowing into the tank at a rate of 3 gallons per minute.. The well mixed solution in the tank drains at a rate of 5 gallons per minute. Let Q be the amount of salt, in pounds (Ibs), in the solution after t minutes (min) have elapsed. a. Draw a diagram that represents this situation, then setup a differential equation with an initial condition that describes the rate of change in the amount of salt in the tank. b. Draw a phase line for this differential equation and describe the behavior of the equilibrium solutions. What does the amount of salt in this tank approach after a long time (write answer using limit notation)? c. Solve this differential equation and determine the amount of time it takes get within 3% of the equilibrium amount.
Determine the centroid of the following Fig from X and Y axes. Y 30 centT1 CentQ1 X -2 -1 1. 7. -1 Select one: O*X = 3.13 Y = 1.5 Ob. X = 2.5 Y = 1.5 X = 2.63 Y = 1.7 %3D Od. X = 3.13 Y = 1.75
The "Yaw Damper System" provides airplane stabilization about the yaw axis. The Yaw Damper minimizes dutch roll during flight by providing rudder displacement proportional to, and opposing, the yaw rate of the airplane. Transfer function of the yaw damper is taken as: 4.833 yaw rate rudder angle (s+0.551)(s+0.1 ±0.541*i) (s+0.616)(s +0.058+ i)(s+0.007) a) Give a brief knowledge about yaw dampers. b) Draw and interpret "root-locus" graphic of this transfer function. c) Draw and interpret the yaw rate distribution according to time.
5. Okay, time for some mathematics. We're going to focus on the interactions between the hares and their main predators, the lynx. The tool we need is differential equations (last seen when we talked about the S-I-R disease model). We will let H(t) be the density of hares at time t, and L(t) the density of lynx at time t. Our first assumption is that, if there are no lynx around, the hares grow exponentially. Hares lead to more hares and faster growth. This gives us the differential equation (trust me): HP = aH dt where a is a positive constant. Second we assume that, if there are no hares around, the lynx starve and thus their numbers decay exponentially. This gives us: TP = -bL dt
The centroid of the plane region bounded by the graphs of y = f(x), y = 0, x = 0, and x = 3 is (1.2, 1.4). Without integrating, find the centroid of each of the regions bounded by the graphs of the following sets of equations. Explain your reasoning. (a) y = f(x) + 2, y = 2, x = 0, and x = 3 (b) y = f(x − 2), y = 0, x = 2, and x = 5 (c) y = −f(x), y = 0, x = 0, and x = 3

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