Consider the density function given by f(x) = 1, 0
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![Question 2
Consider the density function given by f(x) = 1, 0<x<1. Determine the moment
generating function of f(x).
(e^t -1)/t
[e^(tx)]/t
O 1/t
O [e^(tx)]/x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09fcf446-1afb-4b15-acb5-39347ac88924%2Fa3c3bcf8-79a3-406e-b1d1-f47bfedfe2ee%2Fiy3wsbd_processed.png&w=3840&q=75)
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- Concentration of a solute According to the Ficks law, the diffusion of a solute across a cell membrane is given by c(t)=kAV[Cc(t)],(1) Where A is the area of the cell membrane, V is the volume of the cell, ct is the concentration inside the cell at time t, C is the concentration outside the cell, and k is constant. If co represents the concentration of the solute inside the cell when t = 0, then it can be shown that c(t)=(c0C)ekAt/V+C.(2) a. Use the last result to find c(t). b. Substitute back into Equation 1 to show that 2 is indeed the correct antiderivative of 1.Related Rates Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. Question 2. Please explain as detail as possible, thank you.Question Find fyy for f(x, y) = e* In(y).
- Bessel's Function Tutorial sheet y = X J, (x) Find ý and ý 2.Integration explanation...Calculating Mass from Linear Density. Mass-Density Formula of a One-Dimensional Object. Given a thin rod along the r-axis over the interval (a, b), let p(x) denote a linear density function giving the density of the rod at a point z in the interval. Then the mass of the rod is given by p(z) dz m= Part 1. Setup the integral that will give the mass of a metal rod that is 1 inches long (orientated on the r-axis starting at z = = 1) if the density of the rod is given by p(x) = Iblin. m = Part 2. Calculate the mass of the wire described above. m = in. Note: enter your answer as an exact value without using decimals.
- Qi Find dy/dx of xy = x + cotyIntegration by Substitution.Speedometer readings for a vehicle (in motion) at 5-second intervals are given in the table. t (sec) v (ft/s) 29 28 10 26 15 20 20 27 25 21 (a) Estimate the distance traveled by the vehicle during this 25-second period using the velocities at the beginning of the time intervals. distance traveled 2 feet (b) Give another estimate using the velocities at the end of the time periods. distance traveled 2 feet Question Help: D Video D Post to forum
- Solve Think about a density curve that consists of two line segments. The first goes from the point (0, 1) to the point (0.7, 1). The second goes from (0.7, 1) to (0.9, 2) in the xy-plane. What percent of observations fall between 0.7 and 0.9?Using differentials, determine the appropriate increase in the volume of a sphere if the radius increases from 5 cm to 5.05 cm. O a. 539.5 cm3 O b.47.1 cm3 O . 15.7 cm3 Od.314.2 cm3EXAMPLE 3 The density at any point on a semicircular lamina is proportional to the distance from the center of the circle. Find the center of mass of the lamina. *+ y² = a* SOLUTION Let's place the lamina as the upper half of the circle x? + y? = a?. (See the figure.) Then the distance from a point (x, y) to the center of the circle (the origin) is V + y². Therefore the density function is p(x, y) = KV + y? Video Example ) where K is some constant. Both the density function and the shape of the lamina suggest that we convert to polar coordinates. Then V+ y? = r and the region D is given by Osrsa, oseS T. Thus the mass of the lamina is m = p(x, y) dA 2 dA - LLC r dr de K 2 dr de Jo Jo KT Both the lamina and the density function are symmetric with respect to the y-axis, so the center of mass must lie on the y-axis, that is x =| . The y-coordinate is given by yo(x, v) dA 3 r sin(8) (Kr)r dr de = Kina 3 sin(e) de Jo dr 3 -cos(a) The center of mass is located at the point (x, y) =
