Ld by using Evaluate 1+x2 (i) Trapezoidal rule, vie (üi) Simpson's 318 rule, (iv) Weddle's rule and compare the result with its actual value. (ii) Simpson's 1/3 rule
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- You are designing an RPG (role-playing game) for a gaming console and have decided to use an open world design, where players can explore the terrain freely, encountering enemies by chance. Your design team has coded this in-game world to exist on the circle x^2 + y^2 ≤ 900 on the xy-plane. At any point (x,y) in this world you've also associated a danger function d(x,y) that measures how likely it is to encounter an enemy at that point. Thus high values of d(x,y) correspond to dangerous points, while low values of d(x,y) correspond to safe points. If d(x,y) = e^(-x^2)(y), find the safest point(s) and most dangerous point(s) in-game.X^2+2*x on the interval 0 to 3 with a step size of .5 using trapezoid ruleThe number of defects on the front side (X) of a wooden panel and the number of defectsa on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy(x,y)=c(x+y), x= 1,2,3 and y=1,2,3. Determine the value of c.
- The vertical distance covered by a rocket from -8 to t-30 seconds is given by 140000 x-ו ) 2000In -9.8tdt 140000 2100t a) Find the distance covered from t= 10 to 25 seconds Use the two-segment trapezoidal rule b) Use four segment Simpson's 1/3rd Rule to estimate x. For part b, design an EXCEL spreadsheet that the estimates x for n-2, 4, and 6.( a) The differences between the Z- interval and T- interval. (b) What determines when to use Z interval and T intervalThe functionf(x, y, z) = x2+y+z an absolute maximum and absolute minimum subject to theconstraint 2x2+2y2+z2=2. Use Lagrange multipliers to find these values. I have tried a few ways to solve for the critical points, but they have all been incorrect.
- Trapezoid and Simpson rule when n=6 to estimate this problemrectangle ABCD has side AB on the negative x axis, and side AD on the negative y-axis. POint C is on curve y = (2/3) sin3x, (-2pi/3) <= x<= (2pi/3). Find co-ordinates of "c" that maximize the perimeter of ABCD. Exact answer requiredYou are manufacturing a can which is a perfect cylinder. The ideal volume of the can is 375 cm3 . Since the bases of the cylinders are exactly 50 cm2 , the volume of the can is V = 50h where h is the height of the can in centimeters. You need to cut the sides of the can so the volume has at most an error of 10 cm3 . Give the range of heights the can could have and still meet the required specifications for its volume.
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