Integrals over boxes Evaluate the following integrals. A sketch of the region of
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- 5. Simplify the following functions using a K-map: f)F(X,Y,Z)=(22÷7)(0,2,5,7)arrow_forwardComparison with analytic solution The analytic solution for free-fall with ²-dependent air drag is: Yanalyt (t) = yo + Vanalyt (t) 2m DpA In [] # Analytic solution In cosh 2mg DpA (√² ;)] Dp Ag 2m t Dp Ag 2m tanh Exercise 2: Write code for the analytic velocity solution In the code cell below, we already implemented the equation for y_analyt. Add the equation for the velocity, storing the result in v_analyt. The hyperbolic tangent function is available as np. tanh. For the time t, use the vector time that we populated in the loop above. Note: If your code generates any error message (in red), you need to fix this error before continuing. Get help from your instructor or classmates if needed. You will need to use some parentheses () for the trigonometric and square root functions, and to enforce the order of operations. However, use them only where necessary; an excessive number of parentheses makes it harder to debug your code. y_analyt = y0 + 2*m/(D*rho*A) * np.log(np.cosh…arrow_forward3: The function f(x)= max x, searches for the maximum value between a number. Prove formally that the function f(x) is convex.arrow_forward
- Q3: Two Variables es are define by the following equations: f1=E m(2,4,5,10, 12,13,14). f2=Em (2,9,10,11,13,14,15). Show how these functions can be implemented on a PLAarrow_forwardIf A = {1, 2, 6} and B = {2, 3, 5}, then the union of A and B isarrow_forwardCreate K-maps and then simplify for the following functions. 3) F(x, y, z) = xyz + xy’z’ + x’yz + x’y’zarrow_forward
- Q1/Simplify the following Boolean functions in products of sums using K-map: a) F(w, x, y, z) = Sigma(0, 2, 5, 6, 7, 8, 10) b) F (A, B, C, D) = Pi(1, 3, 5, 7, 13, 15)arrow_forward7. The roots of the quadratic equation ax² + bx + c = 0, a 0 are given by the following formula: -b = √b² - 4ac 2a In this formula, the term b² - 4ac is called the discriminant. If b²-4ac0, then the equation has a single (repeated) root. If 200arrow_forward1. F(a,,b,c,d)=sum m (1,3,4,6,7,9,12)arrow_forward
- Write a program that does the following: 1- Ask the user to enter the number of variables on a Linear- System 2- Ask the user to enter matrix elements 3- Ask the user enter vector elements 4- Ask the user to enter initial approximation for the solution 5- Solve the linear-system using Jacobi iteration and show the results and number of iterations needed 6- Solve the linear-system using Gauss-Seidel iteration and show the results and number of iterations needed 7- Show which of the two methods is betterarrow_forwardGiven f1(x) = −3x + 4 and f2(x) = x2 are functions from R to R. Find: a. f1.f2(x) b. f1.f2(-1)arrow_forward3. Let A = {1, 2, 3} and B = {4,5}. a) Find A x B b) Find B x Aarrow_forward
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