Prove that there does not exist a Pythagorean triangle whose length of the hypotenuse and length of one leg are perfect squares.

Q: + 1/6, 9, b₁ 1/6 are ad last three tems are eries. then find the value of aam b. in egeomette Segr…

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Q: Question 2. The function () is defined as follows f(t)-3-6t+t²,0<t≤4. Define f(t), an even periodic…

A: The given problem is to find the even periodic extension for the given periodic function and find…

Q: phism, where R is a commutative ring with unity. Le he arbitrary elements of R. Then there exists a…

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Q: Let H be the set of all points (x, y) in ℝ2 such that x2 + xy + 3y2 = 3. Show that H is a closed…

A: Given Data: Let us consider the given H be the set  of all points x , y in R2 such that x2+xy+3y2=3.…

Q: Find the amount of the payment to be made into a sinking fund so that enough will be present to…

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Q: Solve a differential equation using Laplace transform and partial fraction decomposition showing…

A: The given differential equation x''-5x'+4x=e2t, x0=1, x'0=2. We have to find the solution to the…

Q: The appropriate Fourier transform to solve ²²u_du дх2 д' = u(x,0)=e-1x1, 0 0. is: -,0Q, k#0 O None…

A: Given one dimensional heat flow equation is     k2 ∂2u∂x2=∂u∂t   ,   0 &lt; x &lt; ∞ ,  k ≠ 0 The…

Q: 7. Use Stokes Theorem to calculate the circulation of the vector field F =(2²+z)i + + y² + ² = 1…

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Q: Let a and b be positive real numbers. If a arithmetic progression a, G₁, G₂, b are in g ogression…

A: Part A

Q: the sum of firsts 5terms of an arithmetic sequence is 0 and the fifth term is 8 determine the common…

A: Given that the sum of firsts 5 terms of an arithmetic sequence is 0 and the fifth term is 8. We have…

Q: For numbers 1 to 3: The city of Smallville consists of five subdivisions, Mayor Takeda wants to…

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Q: For items 1 to 3, Consider the sets A = {1,2,3,4} and B = {a, b, c, d), and the relations o = {(1,…

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Q: Verify the Kummer transformation: U(a,c;x) = x¹-U(a-c+1,2-c;x)

A: As per the question we are given the following Kummer transformation of the Tricomi confluent…

Q: Apply Newton’s Method to approximate the x-value(s) of the indicated point(s) of intersection of the…

A: We are given the graph of function f(x) = x and g(x) = tan(x) that shows the intersection point of…

Q: et a and b be positive real numbers. If a, A₁, A2,1

A: part a

Q: 15. Let X be the set of numbers from 1,...,250. There is a lottery where 25 winning numbers are…

A: X be the set of number  from 1,2,...,250 Total number of winner 25 The lottery selects a subset Y⊂X…

Q: Solve each of the following congruences. Make sure that the number you enter is in the range [0,…

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Q: Use polar coordinates to find the volume of the given solid: Insider the sphere x² + y² + z² = 16…

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Q: 1) Consider the following linear system: x + 2y + 4z = 2 -2x-3y -6 z= -1 x+2y+d²z =d For what values…

A: The given problem is to find for what values of d the system has no solution, exactly one solution…

Q: in different toys have to be distributed am the number of ways in which these toys c that exactly…

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Q: Question 8. Here is a table for income tax. Observe that the tax brackets are different from the tax…

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Q: Give an equation for a cosine function that has a maximum at (7.8), followed immediately by another…

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Q: (rosot) (x) r (x) = 3x² — x, s(x) = = x + 2 and t (x) = −x − 2|

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Q: 1C Use the noise terms phenomenon to solve the following Fredholm integral equation uit 14 물 2) 20…

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Q: Prove that for any a, b E R and a <b, ((a, b), ) is not well-ordered, where (a, b) is an open…

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Q: Utt(x, t) u (0, t) u(L, t) u(x, 0) ut(x, 0) c²uxx(x, t) + Q(x, t) A(t) B(t) f(x) 0

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Q: Determine the period of the sinusoidal function y=-3 sin| 2| x- -~-3 m 2 ( x − 3 ) | + -- +1. a) 1…

A: If y = A*Sin(B(x+C))+D is the sinusoidal function, then Amplitude = A Period = 2π/B Phase Shift = C…

Q: where co T= -2 C₂ Find the solution of x²y" +5xy' + (4 + 3x)y 1. Enter n = 1, 2, 3,... 0,0 of the…

A: The given problem is to find the series solution for the given differential equation. Given…

Q: A car dealer sells a new car for $18,000. He also offers to sell the same car for payments of $375…

A: Given: The selling price of a car (A) = $18000 Monthly payment size (R) = $375 n = 12×5=60 Our aim…

Q: (i) find the curvature of the function f(x) = 4x^2 at the point (0,0).  (ii) find the equation for…

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Q: If the planes x - cy - bz = 0, cx - y) + az = 0 bx + ay − 3 = 0 passes through the a straight line,…

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Q: Let M=(23) and T be the linear operator on V defined by T(A) = MA. Find the matrix representation of…

A: As per the question we are given a 2×2 transformation matrix M and the linear transformation T on…

Q: the common difference of the AP.

A: A

Q: Xi -1 0 1 Yi 7 35 19t9h

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Q: iven that sin (0), state the value(s) of in degrees, correct to one decimal, such that 90° ≤ 0 ≤…

A: The correct option is 186.4 and 353.6

Q: find the sum of 1X ¹x (2-6) X (2-60²) + 2X (3 - w) x ( 2² w²) + -+ (-1x (m-w) x (m-1²);

A: A

Q: Suppose that a fire truck is parked in front of a building as shown in the figure. The beacon light…

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Q: Find the two critical points on the function f(x, y) = e(x² - y²), what is the value of the function…

A: The given problem is to find the critical points of the given function and also to determine the…

Q: 5. Define f: R→→ R and g: R → R defined by f(x) = max{-x, x} and g(x) = |x|, respectively. Prove…

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Q: QUESTION 6. The 75 teachers on the faculty of Democracy College have filled out ballots in the form…

A: The candidates are Mike the mathematician, Beverly the Biologist, Helen the Historian, Sophia the…

Q: 5. Let P2(C) be the vector space of polynomials of degree less than or equal to 2 over C. Let C3 be…

A: 5) Let P2ℂ be the vector space of all polynomials of degree less than or equal to 2 over ℂ. and ℂ3…

Q: Which row exchanges will produce another Sudoku matrix?

A: To Explain : Which row exchanges will produce another Sudoku matrix?

Q: £.(+).. 2 for TS t co for os t.<I 2 t

A: The given function is: ft=0-π&lt;t&lt;0t20&lt;t&lt;π We have to find the Fourier series for the…

Q: Prove that the interval (0, 1) has cardinality N₁.

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Q: 1 2 Ĵ(x) with Ĵ(1) = (1, 2, −1) and Ĵ'′ (x) = {- , ,-2) " 'x' √√x' Show the arc length of the graph…

A: The given vector function is J→'(x)=1x,2x,-2 with J→(1)=1,2,-1. The objectives are to calculate the…

Q: 9. Let P3(C) be a vector space over C and let D: P3(C)→ P3(C) be the differential operator defined…

A: Since you have posted a multiple question according to guildlines I will solve first (Q9)question…

Q: Use the shifted inverse power method to approximate, for the matrix A , the eigenvalue closest to α.…

A: Given:  A=141253, x0=11, k=5 To find: Dominant Eigenvector and eigenvalue.

Q: = 3 Consider the equation ï + ax + bx = 0 when b a², so that the characteristic equation has a…

A: Given Data: Let us consider the given equation is x..+ax.+bx=0 when b=14a2. Prove that:  This is a…

Q: Question 1 Using sine Fourier Intergral representation of the function f(x)=ex, x>0, we have 5.°…

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Q: uestion 3. efine an odd periodic extension of =2+3t, 0<t≤4 d hence find its half-range sine series…

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