Let a 0 be a constant. Evaluate the curve Απα3 /3 πα? /2 Ο πα? /4 JIR dA where R is the region enclosed by a cost, y = a sin t, 0 < t < T. None of these

Q: x'(t) = -2 4 1 -4 -6|x (t) x (0) = -2 t 0 1 -3 1 any 5-6 The only eigen value of this matrix is -3,…

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Q: A 160-lb person who runs at 8 mph for 1 hr burns about 840 calories. The same person, walking at 2…

A: 160-lb person who runs at 8 mph for 1 hr burns about 840 calories.Hence at 8 mph in 1 min he burns…

Q: Let R = Z[i]. show that FR= {r+si | r,sE Q } = Q[i] F a field, Z the integers, Q the rational…

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Q: r(t) = (2+31+3 23. Find the length of the curve r(t) = (rsint+cost)i + (sint-rcost) j+rk from 0..…

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Q: 5. Verify Gauss's theorem for D = {(x, y, z): 0 ≤ z ≤ 9-2²-y²} and F ri+yj + zk.

A: The given problem is to verify the gauss theorem for the given surface 0&lt;z&lt;9-x2-y2 for the…

Q: show two nonzero vectors a and b in the 5th dimensions. put them in vector form and in basis form.…

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Q: 1.) Graph y = 2sin(x) on the interval -2π SX ≤ 2T. Be sure to clearly identify any maximum points,…

A: We know the graph of y=sinx on -2π, 2π as below

Q: Question 1 Determine which of the following functions are a bijection from the set of real numbers…

A: f(x) = x11 - 7x7 is not one-to-one, as           0 ≠ 71/4 but f(0) = f(71/4) = 0   Consequently,…

Q: Calculate sin x So √1+x with an estimate error less than 10-6, using Romberg's integration? -dx.

A: As per the question we are given a improper definite integral which we have to solve numerically…

Q: 29-62. Definite integrals Evaluate the following integrals using the Fundamental Theorem of…

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Q: (0.4) (2) ODN (0) Jo 0<- 0 1 172

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: Integrate the expression 1017x² +840xy + 1492y² over the region bordered by the curve 1017x² +840xy…

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Q: F = xi + yj; the curve C is the counterclockwise path around the circle x² + y² = 16 O 8TT O 32TT 0…

A: We use Greens Theorem.

Q: solve the system x + x = t when x(0) = (0)

A: First we convert the second order ode into system of first order ode. And then use the Laplace…

Q: Consider a point at x = 5 on the curve Ax³y + Bx²+ Cy+D=0, where A = 3, B = 4, C = 5, and D = 1. If…

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Q: Complete the following, using exact interest. (Use Days in a year table) Note: Do not round…

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Q: Consider the differential equation 5e2t t² y" - 4y + 4y = = (a) Find r1, 72, roots of the…

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Q: end. 7) A Swimming pool is circular w/ a 10-ft diameter, the depth is consit along E/W lines and…

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Q: 39. (a) Show that a one-parameter family of solutions of the equation 102 (4xy + 3x²) dx + (2y +…

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Q: 54. Properties of integrals Suppose f(x) > 0 on [0, 2], f(x) ≤ 0 on [2, 5], ₁² f(x) dx c = 6, and ſ₂…

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Q: 1. The differential equation d³y dx³ = 1+ dy dx is (A) 2rd order, linear (B) 6th order, linear (C)…

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Q: Find all critical points of f(x,y)=x³+y³-3x²-3y²-9x and classify each as yielding local max., local…

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Q: Determine £¹{F}. 25² 2s +67s+218 F(s) = 2 (S-2) (s² £¹{F} = +8s +25) Click here to view the table of…

A: We find required Inverse Laplace Transform.

Q: 4. Graph the following transformations of the parent function graphed in number 1. Identify the…

A: Since you have posted a question with multiple subparts, we will provide the solution only to the…

Q: Let 1, Z₁, Z2, Z3, ..., Z-1 be the nth roots of unity. Then prove that (1-z₁)(1-z₂) ... (1-Zn-1) =…

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Q: ulate the angle between the two vectors i +2j+ 3k and 3i - 2j+ k er your answer in the box below,…

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Q: Parametrize this surface. Calculate the flux of the vector field F(x,y,z)=(xy,xz,zx) through the…

A: As per the question we are given the following surface : S : z = x sin(y) , 0≤x≤2 , 0≤y≤π And the…

Q: (c) (-1)"n! 2n (d) n=1 n=1 (x - 2)" n!

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Q: Use the method of Lagrange multipliers to maximize the function subject to the given constraints.…

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Q: PROBLEM 2: Solve for the optimal solution of the following OR Model: Minimize z = 80x + 60y…

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Q: Consider the following double integral: 1 1 √y cos(y) dy dx x² If you need to use any theorems…

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Q: A window has the shape of a parabola above and a circular arc below. Find the area of the window.…

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Q: 3) Solve the following boundary-value problems. a) y'(x) + 2y(x) = 0; y(0) = 0; y' (2л) = 0.

A: The given problem is to solve the given boundary value problem with given boundary conditions.

Q: Find the function represented by the following series and find the interval of convergence of the…

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Q: (8 and 9) Given the vector field F(x, y) = (e", xe") and the curve C given by 7=(2 cost, 2 sint)…

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Q: Consider the differential equation y" - 9y' +18 y = e³t (a) Find r1, 72, roots of the characteristic…

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Q: 1. Draw the complete shear and bending moment diagrams. 1 m 600 N 2 m 600 N -1 m- B

A: Now, RA + RB = 600 +600 = 1200 RA + RB = 1200 Now, Taking moment about A RB * 4 - 600 * 3 - 600 * 1…

Q: let A = ГО 1 1 1 1 0 write optimal bases of orthonormal for the four bases

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Q: Find an orthogonal basis for the column space of the matrix to the right. An orthogonal basis for…

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Q: Consider the differential equation y" - 2y +2y=e*sec(x). Then the particula Oa.e*(-cos(x)in sec(x)|…

A: The formula for the particular solution is  yp=u1y1+u2y2 (Method of variation of parameters) where…

Q: Use the accompanying radiation levels in quartile Q₁. in for 50 different cell phones. Find the W…

A: Q1 = (n+1)4th item

Q: Select the option that gives the vector product of i+k and i + j Select one: 01 Oi+j-k Oi-j-k…

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Q: Consider the initial value problem for function y given by, y" - 3y + 2 y = − 6(t – 3), (a) Find the…

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Q: Use a graphing calculator to find the first 10 terms of the sequence an its 9th term is its 10th…

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Q: (a) Show that the line through OA is orthogonal to the plane containing the face BCD. Deduce that…

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Q: 23-24. Definite integrals Evaluate the following integrals using the Fundamental Theorem of…

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Q: . The helix curve is 3 a(t) = (cost, 2 sint, 3). (a) Find the tangent vector T. (b) Find the normal…

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Q: 2. Use the (a) Euler and (b) Heun (without iteration) methods to solve d'y -t+y=0 dt2 where y(0)-2…

A: Given y''-t+y=0,y0=2,y'0=0. With 0≤t≤4 we need to solve the given DE using the step size h=0.1.…

Q: Solve the proportion: P+8 10 34 Answer: p = Enter your answer as an integer or as a reduced fraction…

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