Prove that n! (n-r)!r! (4) is the number of subsets (combinations) with r elements which can be chosen from the set M with n elements.

Q: given the initial value problem x^(2)y'' + xy' + y = 0, y(1) = 2, y'(1) = 3 show that the two…

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Q: || +

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Q: 5. For each linear operator T on V, find the eigenvalues of T and an ordered basis for V such that…

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Q: Find the general solution to y" - 6y +9y 5 y(x) = y(x) + C₁y₁ (x) + C₂y2(x) with y₂ = x5 Y₁ = and Y2…

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Q: Part 1: Intervals Find the open interval(s) on which f(z) is increasing/ decreasing/concave…

A: Here graph of y=f'(x) is given . So we need to find relation between f(x) , f'(x) and f''(x) to…

Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3).…

A: An inner product on real spaces V is a function that associates a number u, v with each pairs of…

Q: a) Find an equation for the plane tangent to the surface given by z = 4x² + y² at Po = (1, 1,5).…

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Q: For all sets A, B, and C, A, B, C- AU (B-C) = (AUB) - (AUC). Your answer cannot be

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Q: 1. 4.3/4.7: A rectangle is inscribed in the ellipse+y² a) Find the minimum possible area of the…

A: Given equation of the ellipse is x24+y2=1 The  general equation of an ellipse is x2a2+y2b2=1 Then…

Q: Determine whether the sequence or series converges or diverges. If it converges, find its value. n²…

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Q: Find the power series for the functions below. Write your answers with the sum starting at n=0  a)…

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Q: Consider the simple model of labour market flows with the unemployment rate following Ut+1 = (1 −…

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Q: Evaluate f (x - y)(y – z) dV for the box B with dimension: [3, 6] × [0, 5] × [0, 5]. (Use symbolic…

A: Given : B :3 ,6×0 ,5×0 ,5 To Find : I=∬∫B x-yy-zdV

Q: Question 1 Find an orthonormal basis for the solution space of the given homogeneous system of…

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Q: Use Newton's method to approximate a root of the equation cos( s(x² + 3) = x³ as follows. Let x₁ = 2…

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Q: 1. Let p be an odd prime and g be a primitive root mod p. Show that Z = {gik : k = 1,...,p-1} if and…

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Q: The odds in favor of Nolan getting promoted are 5:4. Find the probability that Nolan gets promoted.…

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Q: -4 nswer Formats Type your answers in interval notation. Use -INF and INF to denote ∞ and co. Enter…

A: Please find the answer in the next step.

Q: Exercise 2.3.5 Each ODE below depends on a parameter h. Assume the parameter h can be a real number…

A: (a) Consider the given system, u'=hu-u2=fu So, the fixed points are given by, fu=0hu-u2=0uh-u=0u=0,h…

Q: 150 135 120° 105° 90° 180° 165* 240 225 210 .592 .042 75° .582 60° .00€ 45° 315* 30° 330⁰ 15° 8=0°…

A: Given a function rθ=4cos2θ on the interval 0 , 2π in polar coordinate. To determine: How many times…

Q: Use the Cauchy-Riemann Equations to show that f (z) = z^2 is differentiable for all z and find f'(z)

A: If F(z)=u+iv then we know the cauchy -Riemann Equation is  ux=vy and uy=-vx  also F'(z)=ux+ivx

Q: Can you answer number 5?

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Q: logically

A: We solve by Truth Table.

Q: 'ind parametrizations (a) The line from (a, b) to (c,d). (b) A path from (2,0) to (0, −2) along a…

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Q: a student visits an arcade each day after school and plays one game of either laser man, millipede,…

A: Solution:

Q: Evaluating a Double Integral by Converting from Rectangular Coordinates [[ (x + y) dA where R = {(x,…

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Q: Determine the 2022nd derivative of f(x)at x = 0 1 given that f(x) = 4-x²

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Q: 3. Find an open cover of (x:x>0} with no finite subcover.

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Q: A lighthouse is located 40 meters off-shore. The beam of light from the lighthouse rotates at a rate…

A: We will use derivative to find speed of the beam

Q: What is the probability that a random integer from 92 to 734 is divisible by 15? (All integers in…

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Q: Use elementary row or column operations to find the determinant.

A: We have given a matrix, A=9-425276-541-2073410. We need to find determinant of matrix using…

Q: Solve only part  C

A: Given information Part(c):- x2k +3xk+1 -12,   k≥1. Take Px = x2k +3xk+1 -12

Q: A ball is kicked upward with an initial velocity of 20m/s from the roof of a building 30 m high.…

A: We have to model the situation by using derivatives  dvdt =acceleration dhdt= velocity

Q: 1. An object is moving along a straight line and its velocity at time t is given by: v(t) = t² − 4t…

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Q: Charlie and Daniella each began a fitness program. On day one, they both ran 500 m. On each…

A: Charlie and Daniella both ran 500 m on the first day. Charlie ran 100 m more than previous day…

Q: Evaluate the triple integral √√√₁² E xyz dv where E is the solid: 0 ≤z≤ 1, 0≤ y ≤ z, 0≤ x ≤ y.

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Q: f(x,y)=y²-4ycos(x)

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Q: 4 α 25 1 1 and A is diagonalizable, find the values of constants a, 6, 7, 8. -1 B Y Let A = Given…

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Q: Cπ/2 y cos(xy) cos y sin(xy) + 1 Determine if the conclusion of Fubini's theorem is applicable to…

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Q: An athlete runs al speed of 10 miles per hour. If one lap is 322 yards, how many laps does he run in…

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Q: order that

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Q: Πο Ω_q+1)t-q + 1 ΠΩ(q+1)t-q Πο Ω_(q+1)t-q + 1 ΠoΩq+1)t-q/Ω(6q+5) thus Ω(7q+6) > Ω—(6q+5)• Th 1 = -…

A: Given: The Information that leads to the required proof.We need to prove the equations marked in…

Q: You’d like to set up a perpetuity that pays out A thousand per year with $1 thousand per year…

A: Here, in the question its been given that the perpetuity that pays out A a thousand per year with a…

Q: 1) Solve the following ODE using the power series method

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Q: A person is depositing money into a bank account continuously at the rate of $5,000 per year, and…

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Q: Use cylindrical coordinates to calculate SSSw f(x, y, z) dV for the given function and region: f(x,…

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Q: mination with Scal. Method.

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Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral.…

A: Definite integral: It is the area under the curve of a function y=fx between the two fixed limits…

Q: Match the given characteristics of the trigonometric function given on the left with the graph or…

A: 1) Amplitude : 3 period : 4π midline : -2 phase shift : -π2 left. Answer: option (c) y=3cosx2+π2-2

Q: Let a, b E R with 0 < a < b and let n = Van+b. Prove that (n) converges and determine lim (xn).

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