Concept explainers
Another look at the Fundamental Theorem
70. Use Exercise 69 to prove that if two runners start and finish at the same time and place, then regardless of the velocities at which they run, their displacements are equal.
69. Suppose that f and g have continuous derivatives on an interval [a, b]. Prove that if f(a) = g(a) and f(b) = g(b), then
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CODE/CALC ET 3-HOLE
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- The following is used to model a wave that impacts a concrete wall created by the US Navy speed boat.1. Derive the complete piecewise function of F(t) and F()The concrete wall is 2.8 m long with a cross-section area of 0.05 m2. The force at time equal zero is 200 N. It is also known that the mass is modeled as lumped at the end of 1200 kg and Young’s modulus of 3.6 GPa2. Use *Matlab to simulate and plot the total response of the system at zero initial conditions and t0 = 0.5 sarrow_forwardAn insulated, electrically-heated (100 kW) tank contains400 kg of water at 65°C when its power is lost. Water iswithdrawn at a steady rate of 0.4 kg/s and cold water (at12°C) enters the tank at the same rate. Assume the tankis well-mixed, and neglect heat gains or losses throughthe tank walls. For the water, c=cp=cv=4200 J/kg C(a) Create a script (m-file) in MATLAB to calculate howlong will it take for the tank’s temperature to fall to 25°C.(b) Display the entire program code used for your scriptcreated in MATLAB. Make sure that running the scriptprovides a numeric result and include your name as acomment.arrow_forward- 4. Let = (1, 2, 1), 7 (-1,-1, 2) and w= (0,3,2). Show that ü, 7 and w are linearly dependent or independent. 5. Let = (0, 2, 1), 7 (-1,0, 2) and = (2,3,0). Find the coordinates of (2,2,2) with respect to the basis u, u and w.arrow_forward
- Reduce this term into normal from, if it exists (show your working):(λx.((λz.zwz)(((λxyx.y)(λx.y)(λy.x))((λx.xx)(λy.yyy)))))tarrow_forward2. Consider the Karnaugh map of a Boolean function k(w, x, y, z) shown at right. I (a) Use the Karnaugh map to find the DNF for k(w, x, y, z). (b) Use the Karnaugh map algorithm to find the minimal expression for k(w, x, y, z). x y z h(x, y, z) 0 0 1111OOOO: 0 0 0 0 нноонно 10 1 1 LOLOLOL 3. Use a don't care Karnaugh map to find a minimal representation for a Boolean expression h(x,y,z) agreeing with the incomplete I/O table below: 1 0 0 0 1 OLO 0 0 NE IN xy yz 1 IN WX yz 1 ÿz 1 wx wx wox xy xy fy 1 1 1 1arrow_forward2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…arrow_forward
- Verify that each function is an "eigenfunction" for the given linear operator, and determine it's eigenvalue. (a) First derivative; f(x) = e³x (b) Second derivative; g(x) = sin(2x)arrow_forwardProve, by finding constants C₁, C₂, and no that satisfy the definition of order of magnitude, that f = (g) if f(x) = 3x³ - 7x and g(x) = x³12.arrow_forwardShow that F(x, y, z) = xy + xz + yz has the value 1 if and only if at least two of the variables x, y, and z have the value 1. (arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole