Evaluate the integrals: -2 sin²x 2 1₁ = "*2sin² xdx and 12 = √" dx using simpson's 3/8 method. Divide the whole interval into six subintervals.

Q: Determine the rectangular representations of the vector F. F=750 N 45 60

A: Given data in question  Vector F Angles Co ordinate system To find out  Rectangular component…

Q: Determine location of centroidal x and y and the moment of inertia Ix of the figure shown. Use the…

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Q: nd the 4th iterative root (n=4) of the equation cos x = 3x - 1 up to 4 ecimal places using…

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Q: Force F = 1,600 N acts from A towards B. (a) Determine the moment of the force about point C in N…

A: Solution- F = 1600 NM = F→ x r→    = F.r sin θr→ = CA→Sin θ ⇒ angle between CA & AB = θMinimum…

Q: Use midpoint method. Divide the whole interval into 8 subintervals. Use trapezoidal method. Divide…

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Q: 15 20 25 20 | 33 t (ms) 5 10 30 35 40 45 50 55 60 a (m/s?) 0 3 8 42 40 48 60 12 8. 4 3 60 I(f) =…

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Q: Determine whether given differential equation is exact. If it is, find the solution. 3y (x² – 1) dx…

A: First we have to check whether it is exact or not by doing partial differentiation which is done as…

Q: C_ Using the method of adding vectors, find the result of the following figure: 60 If you know the…

A: Draw the figure. Assume n = 0

Q: A. Solve the following system of equations using the Gauss-Jacobi iteration method. 2. 27x + 6y –z =…

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Q: a.) Solve the by Gauss elimination. Show all steps of the computation b.) Substitute your results…

A: Rewrite the eqn and apply transformation

Q: Solve the value of x using completing the square and quadratic Formula: 2x2 + 6x + 2 = 0

A: To solve the given quadratic equation using: method of completing the square the quadratic formula…

Q: When azimuth of AB direction (AB) = 43.287 and B = 137,5593 are given find the azimuth of (BC).…

A: Given Azimuth of AB = 43.287o Internal angle = 137.5593o   To find Azimuth of BC

Q: using trapezoidal rule

A: Given: f(X)=x3+2  a=0 b=5 To find: Integrate f(x) with respect to x=0 to x=5 using Simpson's 1/3rd…

Q: A quadratic equation x²-4x+4=O is defined with an initial guess of 2 and 2.5. Find the approximated…

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Q: For the given vectors, determine the magnitude of the vector difference V₂-V₁ and the angle which it…

A: Given Data: The data is given as: V1=10 unitsV2=12 units The angle subtended by the vector V2 with…

Q: c. Consider the function y=x" 1 D Sketch It. 2. For the function determined in part (1), consider a…

A: | 8 | * 4 | * 0 | *…

Q: dy Find using logarithmic differentiation if y = %3D dx Va²+4

A: To determine the value of dydx for given function using logarithmic differentiation.   Given:…

Q: Find the root of the function f(x) = e 2x – x – 6. Correct to four decimal places. Use initial guess…

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Q: The circle below has radius 1, and the longer circular arc joining A and B is twice as long as the…

A: Solution: Let 'M' be the point on AB where the perpendicular from O meets, Therefore; ∠AOM=θ From…

Q: Determine the location of centroidal x and y and the moment of inertia Ix of the figure shown. Use…

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Q: Use Simpson's 1/3 Rule to approximate the given integral with the specified value of 4 dx n = 10…

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Q: Prove Δv/v = Δe/1+e

A: General formula for settlement due to compaction:

Q: C. Consider the function y = x³ 1. Draw the function and write an expression to represent an upward…

A: Step 1: Step 2: Step 3: Step 4:

Q: Use Bisection method to find a real root of x² - 2 in the interval [1,2]. What is the approximated…

A: Given,  Data for analysis by bisection method

Q: y2 = 4x and x2 = 4y

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Q: Given the function, S(x) = 25x - 9x² + 9x + 52 Estimate the value of the integral bounded from a-0…

A: Let the step size, h = 0.1 Hence the steps are at, 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, and 0.8 The…

Q: Determine the area of the region bounded by the curve y2 = 4x, the lines x=0, and y=2.

A: ASKED: To determine the area bounded by the curve y2=4x, x=0 and y=2.

Q: Calculate the second moment of area of the arbitrary area shown in Figure 4.2g with respect to…

A: Given Data: The distance of x-axis from the centroidal axis x’ is d=60 mm. The distance of x1-axis…

Q: the next iterative value of the of x? - 4 = O using secant method, if the initial guess is 3 and 4 O…

A: Given:-  the next iterative value of the of x² - 4: O using secant method, if the initial guess is 3…

Q: Use fixed point method to solve f(x) = 2x2 + 7x - 10

A: To solve the given equation using fixed point method.   Given: fx=2x2+7x-10   The given equation,…

Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.