Use mathematical induction to prove the following: 2 1+8+27+·..+ n³ n(n+1) %3D 2

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A: Mean: Mean is the average of the given sample data. x=sum of all valuesTotal number of values Answer...

Q: The solution of the following separable differential equation y' = x²y-y with y(3) = -1 is y+1 y = C...

A:   Given differential equation is :   dydx = y(x2 - 1)y+1⇒y+1y dy = (x2 - 1) dxIntegrating both sides...

Q: Selecting classroom officers for president, vice president, treasurer. Combination Permutation

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A: Q5. (c) Simple graph : A simple graph G is a graph that does not have more than one edge between any...

Q: Q4: Find the chromatic polynomials of (i) the complete bipartite graph ; (ii) the cycle graph C5.

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Q: Determine the amplitude, period and displacement for the given function, and sketch the graph of the...

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Q: Another model for a limited population is the so-called Gompertz function, which is a solution of th...

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Q: 5. Evaluate z z = tanh(4-j5)

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Q: a b c If det A =| d e f =k find the value of the given determinant. ghi a – 3g b-3h c-3i 39 -d 3h 3i...

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Q: Q1) Evaluate the following integral: y = | tanx dx

A: We have to evaluate the integral:y=∫tan3xdxy=∫tan2xtanxdxy=∫sec2x-1tanxdx                Using tan2x...

Q: q22 When monitoring the spread of disease, the population can be divided into three groups; the port...

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Q: 1. A coin is flipped seven times where each flip comes up either heads or tails. How many possible o...

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Q: There are 10 doors to a coliseum. In how many ways can a person go in and out if one can enter any d...

A: There are 10 doors to a coliseum . A person can go in in 10 ways.

Q: E.C. Based on the figure below, state and prove the Spherical "Pythagorean" relationship for right s...

A: We will use the basic knowledge of spherical geometry to answer this question.

Q: What is 2x=6

A: To find : 2x = 6 

Q: d) Let X = {1,2,3, 4}. Define a binary relation R on subsets of X by ARB if and only if A and B have...

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Q: blem 2 Let A > 0 and A + na. y" (t) +X'y (t) =Dan cos (nat) n=1

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Q: May you help me please :)

A: What can be said about the addition of third choice for school presidential election .

Q: Find two roots for the following equation using Newton-Raphson method: tan x +x-1=0

A: The equation in form f(x)=0 is called a transcendental equation. The solution of the equation is def...

Q: Find the number of permutations of the letters of the word MOMMY. 20 12 O 24

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Q: Show that following Matrix is an idempotent Matrix A=5 ーマ

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Q: 41: find Second livearly ndependent salution vming reduction of order.

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Q: Rewrite 37–39 by separating off the final term. k+1 m+1 n+1 37. Σί() 38. Σ 39. т(т + 1) k-1

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Q: 2 7 -3 -구 Find lAB)"

A: We want to find (AB)-1

Q: 1. ( Prove that for any x, y E R, we have || - |y|| 1, then X¢ PQ, 5. where PQ is the line segment ...

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Q: Q1: Find the solution for these equations: X+2Y+Z=4 .. (1) 3X-4Y-2Z=2. . (2) 5X+3Y-5Z=-1... (3)

A: We have to find the solution X, Y, Z of the given system of linear equations. For this, we have to w...

Q: -0.5x - 4 if x 2 -7- 6- -2- -8-7 -6 -5 43 -2- 2 3 6 7 -2 -3- -6- -8- Clear All Draw:

A: The given function defines a piecewise defined function.

Q: d) The number of vertices of degree 4 is. e) The sum of the degrees of G is.

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Q: Solve the given nonhomogeneous ODE (Show the details of your work.) Sketch or graph the solution. (x...

A: Given differential equation is x2D2−xD−4I=1x2.....1. We have to find the solution of the given nonho...

Q: 2 4 -8 Let A = and B = |. If AB = [ab 1, then which of the following is the value of ab? 10 A. 8 +10...

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A: According to the definition of indefinite integral ∫f(x)dx=F(x), where dFdx=f(x). In this problem, w...

Q: A hollow spherical iron ball has a diameter of 15.3 cm and has a mass of 12.3 kilograms. Assuming th...

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Q: The auxiliary roots of the following differential equation y" – 2y' + 5y = 0 are 3- 3+V29 d = 12 = -...

A: We have given the differential equation, y'' - 2y' + 5y = 0 Here , f(D)y = 0 , where f(D) = D2 - 2D ...

Q: a) 1 3 2 0 1 3 0 0 1

A: Let us find the inverse of the given matrices in the next steps using row reduction.

Q: Find a non-linear trend equation from the following three normal equations obtained from the origin ...

A: To fit a quadratic curve y=a+bx+cx2, apply the method of least squares. Use the following normal equ...

Q: A committee of 4 members chosen from 6 women and 5 men. Combination Not Combination

A: We have to find the type of given statement.

Q: O Let (eto-) is aring of complex-numberrs and M be aringof2x2 matrices aud desined as sollows. g e M...

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Q: 1. Suppose that f is an infinitely differentiable function (that is, all its derivatives exist and a...

A: For part (d) we perform Integration by Parts on the integration in part (c) and then generalize the ...

Q: Can you show me step by step long division.33.714 divided by 9

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Q: Evaluate: P(6,2)

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Q: maximum

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Q: Find the equation of the quadratic function in factored form that has roots 3 and -1 and passes thro...

A: The standard form of the quadratic function is fx=ax2+bx+c, where x is a variable and a, b and c are...

Q: Q1:Euler's formula O m-n-f=2 m-n+f=2 n-m+f=2 Q2: Tree is a * graph with two faces graph with one cyc...

A: To find the correct solution .

Q: Death Rate se in a certain country. Complete parts (a) through (c) below. 256.9 2000 2002 2004 240 8...

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Q: Find the Maclaurin series for e^x^4. What is the radius of convergence?

A: Here we can use power series of ex ex=1+x1!+x22!+x33!+........∞=∑n=0∞xnn! A series ∑an will be conve...

Q: 3s+ 8 Solve the inver se Laplace Transforms of : s*+ 2s+5

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Q: Your friend, Lajos, wanted you to settle his hunch that the daily average of the number of customers...

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Q: Solve the following linear-quadratic system. Include full solution. y=x^2-6x+3 and 2x-y=13

A: We have to solve the given linear-quadratic system. This implies that we have to find the point of i...

Q: d) Let X = {1,2, 3, 4}. Define a binary relation R on subsets of X by ARB if and only if A and B hav...

A: I just use the definition to solve the problem d and e.