This part will explore one of the underl- by induction. Assume that TN and inductive set. Use the definition of an following: (a) Is 2 € T? Explain. (b) Is 3 = T? Explain. (c) Is 4 € T? Explain.

Q: Show that the given function is a solution of the differential equation. y" + 25y = 0, y = cos(5x) +…

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Q: - (a) In Dn, show that a*bak = b for all k € Z. Please proove using induction, the first variable is…

A: Given : Dihedral group Dn. To show : akbak=b    ∀k∈ℤ.

Q: Find f'(x) for the following function. Then find f'(10), f'(0), and f'(-18). 81 x-9 f(x) =

A: Explanation of the answer is as follows

Q: Find the area of the figure. A 12 kmF N 20 km B E 20 km D 6 km с The area of the figure is square…

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Q: (a) Consider the following phase line, where c is a positive constant. y=c y=0 i. Write down a…

A: Given: A phase line (i) We have to write a differential equation that represents this phase line.…

Q: Solve the given non homogeneous linear ODE by variation of parameters x²y + xy'-4y=1/x²

A: as per Q&A rules we have to answer only one question. for the remaining questions please post in…

Q: Joel is considering putting a $3100 laptop purchase on his credit card, which has an interest rate…

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Q: If U and V are vector spaces, define the Cartesian product of U and V to be   U X V = {(u, v) : u is…

A: Given : U×V=u, v: u∈U, v∈V To Prove: U×V is a vector space.

Q: solve the last question from the picture above, #5 eigenvalues ,2,,3,4,5 if the matrix is…

A: for ease of everything I will provide whole answer.

Q: ← Minimize w=2y₁ + y2 +4Y3 subject to: with Y₁ + y2 +Y3 2 10 3y₁ + y2 248 Y₁ 20, Y₂20, Y3 20. The…

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Q: M2x2 → P2 by g ( a b c d (a + 2b)x² - cx + 3d.

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Q: # 3 Rigid Motions for Congruence: Translations, Reflections, and Rotations y₁ -6- 5- -4 ·3· N 1 -6…

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Q: Solve the given linear programming problem without graphing NOTE: USE BASIC SOLUTIONS 3X₁ + 4X₂ ≤…

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Q: 1. Find the general solution of x" + tx' + x = 0 given that x = e-²/2 is one solution.

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Q: Classify the following sequences: (i)     6.5, 9.75, 13, 16.35,…….. (ii)    4, 8, 16, 33,………

A: A sequence is in arithmetic progression, if the difference between consecutive numbers is a…

Q: 13.) Determine whether the vectors span the vector space. (a.) Let u = 25t+6t²-t³,v=3+2t-4t2 (b.)…

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Q: Find the general solution to the homogeneous differential equation The solution has the form. d²y…

A: The characteristics equation of the differential equation of the form: ay''+by'+cy=0 is ar2+br+c=0.…

Q: The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.…

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Q: x² dx 2. √ √² + 16

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Q: Part 2: Use your Graphing Calculator. (You may also use Desmos Graphing Calculator) Month, x…

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Q: In writing your final answer, follow the format 2x^5y-3x^3ye^(x)+x^3-2y^2=0. Strictly no spaces…

A: Given differential equation is 2yx2-ydx +x2-2ydy=0. To Find : Integrating factor of the given…

Q: Solve the following DE: (1+ y² + xy2) dx + (x²y + y + 2xy) dy=0

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Q: 1 Prove property the flig Vector Spaces 6 Property 6: for all matuces A in V = M3x3 and for all real…

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Q: Prove the following. 2. Let x, y, and z be integers. If rly and ylz, then x|z.

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Q: III. Find the first derivative of the following functions. Simplify as much as possible a) w=

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Q: 4). For the sequence, determine if the divergence test applies and either state that lim n→∞ an does…

A: Concept: Divergence test: The nth term for Divergence states that if   then the series  is…

Q: The following table shows the number of new (single-unit) houses started, in thousands, in the…

A: North East (N) Middle west(M) South (S) West (W) Total 2012(A) 50 90 280 110 530 2013(B) 60…

Q: (a) Show that each of the vector fields F = 4yi + 4x j, Ğ = 24² +247 3₁ and H = √2+1+34 are gradient…

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Q: 3. Consider the curve C with parametric equations r(t) = cos(2t), y(t) = sin(t), where -≤t≤ a) Find…

A: Given the curve C with parametric equations            x(t)=cos(2t), y(t)=sin(t). where,…

Q: 10. matrix Let 01, 02, 03 be the Pauli spin matrices. Is the 4 x 4 (14-01) 1-01001-02 002-03 003) =…

A: Given: σ1,σ2,σ3 are the Pauli spin matrices.We need to check whether the 4×4 matrix…

Q: A farmer is going to divide her 30 acre farm between two crops. Seed for crop A costs $15 per acre.…

A: Given that a farmer is going to divide her 30-acre farm between two crops. The seed for crop A costs…

Q: Find a formula for the vector field V(x, y) = (vectors are shown as line segments, with a dot at the…

A: The vector field is a cluster of arrows, each with a specific magnitude and direction, that are…

Q: kindly solve the problem below on linear programming model using simplex method, and show all the…

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Q: Find the distance between two points, the midpoint, angle, slope and the equation of the line E) P,…

A: Here we have to find the mid point, angle  and solpe , equation of line so I am using formula fir…

Q: Part a: Set up an expression for the profit from producing and selling x items. We assume that the…

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Q: ■ f(x) = x² + 6x + 5

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Q: 4. Show the IVT root on the function fix)=2x²2x²-3x+1 on [1,2] 5. Find i limx-√x+2-X -4x²-3x+10 16.…

A: Disclaimer:  Since you have asked multiple question, we will solve the first question for you. If…

Q: f d a h C 6.0 g e b

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Q: Suppose you graph the function r(0) = 4cos (20) on the interval [0,2π] in polar coordinates. How…

A: Any point in the polar coordinate system is represented using the ordered pair: r, θ. At the origin,…

Q: 5. Suppose that f: R R is a continuously differentiable function (of class C¹) and that there is a…

A: The solution will depend on the following three theorems which we recall. 1. Inverse Function…

Q: The ratio of blueberries to strawberries is 1:7. If there are 84 strawberries, how many total…

A: A part of the whole thing is called a fraction. A fraction has two parts. The upper part is called…

Q: Divide the polynomial using long division. (2x³ + x² + 11x + 5) = (²+5)= (2²+5)

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Q: Find the present value of $90,000 due in 7 years at the given rate of interest. (Round your answers…

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Q: For the given function, (a) find the slope of the tangent line to the graph at the given point; (b)…

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: Relation Between Gamma and Beta Function : B (p, q) = r(p)r(q) r(p+q)

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Q: Of the 47 plays attributed to a playwright, 12 are comedies, 15 are tragedies, and 20 are histories.…

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Q: 3 Letf : R → R³ be defined by f(x) = (x, 2x², −2x). Is ƒ a linear transformation?

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Q: Convert Rectangular form into Polar form 45+20i

A: Given 45+20i We know z=x+iy=rcosθ+isinθ=reiθ x=rcosθy=rsinθ ∴45+20i=452+20245452+202+i20452+202 Now…

Q: QUESTION FOUR a Given that 21nx+1n3=In(5x+2). form px²+x+r=0 stating the values of p. q and r b.…

A: Properties of logarithmic function   ln ab=blnalna·b=lna+lnblna=ln(b)⇒a=b

Q: 1. Write the following matrix as a system of equations. Then use the matrix to solve the system. X…

A: Convert given agumented matrix into system of equations. Solve given augmented matrix by Gaussian…