Use Pascal's Triangle to expand (1+x2)5. Express your answer in simplest form.

Q: Joanna was driving from Fresno to Bakersfield. Because it was a business meeting, she would be…

A: Let the distance from Fresno to Bakersfield = x miles When she left Fresno, she noted that her…

Q: Task 5 (D1) Prove the following using de Moivre’s Theorem. Cos(3x) = cos3(x)-3cos(x) sin2 (x)

A: Sol:- We start with de Moivre's Theorem, which states that: (cos(x) + i sin(x))n = cos(nx) + i…

Q: (b) i) Find the centroid of the plane region defined by the polar coordinate a ≤0 ≤ α (0 < a ≤ π).…

A: Given: Let consider the polar coordinate inequalities 0≤r≤a,-α≤θ≤α and 0&lt;α&lt;π. i) The centroid…

Q: we have the equation θ=b, convert this to rectangular coordinates and then convert to spherical…

A: We know that for any point (x,y) in xy-plane, the polar coordinate of (x,y) is (r,θ) where,…

Q: 4) Find whether the given systems are invertible or non-invertible? a. y(t) = 5x(t) b. y(t) = 3 +…

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Q: Consider the expression below. Assume the variable m represents an integer. 6m(3m +21) Enter an…

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Q: Maximize 60x+90y+300z subject to the constraints below. X 2x x20, yz0, zzo X + + 5y y + + N N VI VI…

A: Maximize w=60x+90y+300z Subject to x+y+z≤400x+5y≤4002x+z≤500x, y,z≥0 We have to solve the given…

Q: U₁ = Consider the two dimensional subspace U of R³ spanned by the set {₁, ₂} where -0-0 U₁ = -1 22 =…

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Q: Use the Direct Comparison Test to determine whether the following series converges or diverges. 1…

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Q: Use variation of parameters to find a general solution to the differential equation given that the…

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Q: Use the limit comparison test to determine whether Σ an = n=11 n=11 lim a. Choose a seriesbn, with…

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Q: Consider the second-order initial value problem, y" - 3y + 2y = 0, y(0) = 0, y'(0) = 1, 0≤x≤1 4.1…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Use Simpson's rule with n = 6 to estimate the curved surface area when the parabol y = 2x² on the…

A: Given: The equation of parabola is: y=2x2. To Do: Using Simpson's rule with n=6 on the interval 0, 3…

Q: Use the Error Bound to find a value of N for which error (TN) ≤ 10. Let K₂ be the maximum of If"(x)]…

A: Given ∫257xdx, We have to calculate N by using error bound.

Q: Solve thid Differencial Equation

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Q: Find the minimum and maximum values of z=6x + 2y, if possible, for the following set of constraints.…

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Q: Question 1. Sketch the region bounded by the parabola y=x²-4x and the z-axis. Set up the following…

A: Given:- Region is bounded by parabola,y=x2-4x And the x-axis.

Q: Use Table 12-2 to solve. Analysts at Sky West Airlines did a 3 year projection of expenses. They…

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Q: Month Temperature 1 W|N 2 3 4 5 6 7 8 9 10 11 12 14 13.1 18 20 26 27.9 30 26.9 24 21 16 13.1 20 35…

A: The given data, Month  Temperature 1 2 3 4 5 6 7 8 9 10 11 12 14 13.1 18 20 26 27.9 30 26.9…

Q: 8 Soe e 32 dz 2 22 e (1 + €²²) ²

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Q: An incidence geometry with no parallel lines is called a projective geometry. Give an example of a…

A: Given that: An incidence geometry with no parallel lines is called projective geometry. To find:…

Q: Find the partial derivatives 5xex² + y2 2 W = Əw Әх Əw ду = = 5x26 +12 2 е+2 5xye+2+1,2 Əw aw Әх ду…

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Q: Consider the parametric curve a = - a Cartesian equation of the curve. Equation: (sin(t)) and y=-…

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Q: he linear approximation to approximate a suitable function f(x, y) and thereby estimate…

A: To approximate a funtion f(x,y) from R^2 to R at some point(xo,yo)

Q: (a) The matrix M is given by M = 2 (1) (11) (111) (iv) (v) 00 1 -1 0/ Evaluate M-¹ (using elementary…

A: We can show that the given expression of (iv).

Q: 512x 1-x -3 - =—1 find volue of Σ(x²)"=? n=1

A: Given that the equation 512x1-x-3=-1   .

Q: The graph of the total profit P(x) (in dollars) from the sale of x cordless electric screwdrivers is…

A: A) Brief verbal description of the graph of maximum profit function y=P'(x):

Q: The position of a baseball (in ft) is represented by r(t) = 50√2ti +(3+50√2t - 16t2). Find the arc…

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Q: 21 3x A- Find the domain and the range for the function y = x-2

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Q: 3. Given integral *² √²-* ƒ(x, y, z)dzdydx, do the following. (a). Sketch the region of integration.…

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Q: The boundary of a lamina consists of y = x² and x = y². Find the center of mass of the lamina if the…

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Q: Factorise 108q - 36 + 7q^3 - 59q^2

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Q: Where does the plane tangent to z = At z = 5exy at (7, 7, 5) meet the z-axis?

A: We find equation of tangent plane to z=5e^(x-y) at (7,7,5)

Q: Establish the following identities through algebraic techniques and identities. AE 5a) tan a-cot a…

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Q: For any A E M 2x2 (K), define a function TA M2x2 (K) → M 2x2 (K) by : TA(X) = AX-XA, where X EM 2x2…

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Q: Find the determinant for the given matrix 3 4 5 6 7 8 9 8 5 4 3 2 1 0 773, 765

A: The given matrix is A=3456789876543210 We have to find the determinant of the given matrix.

Q: Which of the following statements MUST be true? (i) The curve defined by an equation of the form y =…

A: To Examine: Which of the following are true: (i) The curve defined by an equation of the form y=f(x)…

Q: 5. Let A be a nonsingular 2 × 2 matrix. (a) Find P, the projection matrix onto C(A). (b) Find C(A)…

A: The answer provided below has been developed in a clear step by step manner.

Q: 11. Solve the systems of congruences: a. x = 7(mod 11), x = 4(mod 24) b. 3x = 11(mod 17), 2x = 3(mod…

A: The given problem is to solve the given system of congruence equations. Given system of congruence…

Q: Let S be the parallelogram determined by the vectors b₁ = image of S under the mapping x+Ax. - 3 and…

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Q: Few companies take the time to estimate the value of a good customer (and often spend little effort…

A: (a) We have to develop a mathematical model to compute the gross profit during a customer's lifetime…

Q: 6. (8 points) Solve the problem below using the simplex method. Minimize C = 9x₁ + 2x2 subject to…

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Q: Show that the equation cosx + x²³²-3 has a real root

A: Given: Equation: cos x+x3-3=e-xTo show: Given equation has a real root.

Q: The figure low shows the stope net equation cos(y). On a print out of this slope field, sketch the…

A: Given That : A differential equation is y'=sinxcosy To Find : a) Sketch the solution that passes…

Q: Find lul, lvl, 12ul, u = −3i + 4j, |u| = 1 |vl = |2u| = HỈN = |u + v = |uv| = |u| - |v| = v, lu +…

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Q: Given that = 4 and = 5 and the angle between u and is 120°, determine the unit vector in the same…

A: Given that  u→ = 4  and  v→ = 5  . The angle between  u→ and  v→ is  120o          Now     u→+v→2…

Q: Use a double integral to determine the volume of the region formed by the intersection of the two…

A: Volume between cylinders using double Integrals

Q: Use the kappa formula in subsection a) to determine the Curvature of y = In(cos x), -pi/2 < x <…

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Q: If you invest $5000 in an account that pays 3.55% annual interest compounded continuously, how will…

A: Here the invested amount is $500. Rate of interest is 3.55% and the interest is compounded…

Q: Let x (t) = = x"(t) x' (t) If x (0) 21(t) = = = x₂(t) = sin( 9 [] -11 -21 Put the eigenvalues in…

A: Rewrite the system of first order differential equations.