Solve the boundary-value problem y" – 12y' + 36y = 0, y(0) = 2, y(1) = 0. y(x) = help (formulas) Note: If there is no solution, type "None".

Q: Determine whether the following series converge. You do not need to calculate their values. IM8 (-1)…

A: Determine whether the following series converge.

Q: Let g be continuous on [a, b] where g(x) > 0 for all x € [a, b] and define F(t) = f g(x)dx for te…

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Q: Calculate the integral of f(x, y) = 7x over the region D bounded above by y = x(2 - x) and below by…

A: We will find out the required value.

Q: 1 -1 Let C = 0 0 1 0. The characteristic polynomials of both these 0 2 02 matrices is p(x) = (x −…

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Q: Let V = (x)i + (5y)j + (2z)k be a vector field. Let St the upward-oriented surface given by z = 4x²…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

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Q: Suppose R is the shaded region in the figure. As an iterated integral in polar coordinates, B D f…

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Q: For the function F(x) = -6+ (a) graph the rational function using transformations. (b) use the final…

A: Vertical shifting: To graph of y=f(x) -c, shift the graph of y=f(x) down by c units.

Q: Calculate P(FIE), if P(E|F) = 0.59 P(E) = 0.88 P(F) = 0.62 Round your answer to five decimals.

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Q: Create a truth table according to these specifications: There are 3 input bits, x2, x1, x0, and 2…

A: Given Information: are the input bits. are the output bits.Condition:  bit output is the largest…

Q: 15 If square OABC is rotated 18 about its center, what will th dinates of O be?

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Q: Use geometric series formula to calculate: 10+50+250+...+10*5^m, where m(greater than or equal to)0

A: geometric series

Q: X-2=2 2x+y=-7 5x+1-2x = ²5 rewrite in matrix form AX = b

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Q: Find PA, MA for A = What about over Q? Justify your answers. Select one: 0 1 2 1 20 201 O over R. Is…

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Q: Find the minimal polynomial m₁(x) of A = Is A diagonalisable over this field? Select one: 1 2 3 3 1…

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Q: T T T T F 18. Let A and B be sets then A + B if, and only if A ¢ B and B ¢ A. For sets A, B, and C,…

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Q: RYGDON 20 X-2=2 2x+y=-7 5x+y -22=-5 Fuse A- to solve System the given linear

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Q: X y 0 1 You need to find the value of the integral f(x) dx where the following data is available: 1…

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Q: Use arithmetic series formula to calculate: 15+10+5+0+(-5)+(-10)+(-15)+...+(-5m)

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Q: Prove that 2 is not a primitive root modulo 31.

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Q: Use Stokes' theorem to evaluate dr where = (yz, 2xz, exy) and C is the circle x² + y² = 16, z = 4,…

A: We have to evaluate  where  and  is the circle  viewed from above

Q: Set up but do not evaluate the integral (s) that would give the area between the graphs of f(x) =…

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Q: equation Consider the elliptic curve group based on the where a = y² = x³ + ax + b X3 7, b = 2, and…

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Q: Let F(x) = f(x) = x" for x = [a, b] and some positive odd integer n. Show [₁ 62_a²n 2 fdF =

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Q: Evaluate the integral 3 √√9-x² √√9-x² ! 0 0 3 √√9-x² √√9-x² 177. 0 0 0 0 dz dy dx = dz dy dx. (Type…

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Q: Calcula la distancia entre los puntos A y B. A 7,2 m nà als of bles E 50° 73° D B 71° 5,25 m 48° C

A: Consider the triangle Using the first formula we getor, or, Therefore, the length of AD is

Q: Let T P₁ P₁ is a linear operator represented by [3 -31 for some ordered basis B, and 2-2 MB(T) =…

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Q: Find the vectors T and N given the following vector function. r(t) = (sin³ t, cos³ t, sin² t)

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Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

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Q: Let ƒ be a function defined by the rule -¹ (3.3 ln(x)) Compute the derivative and evaluate it at ï…

A: Given that the function is                               To find the derivative of the given…

Q: ) Find all primitive roots modulo 7.

A: We have to find all primitive root modulo 7.

Q: equation Consider the elliptic curve group based on the y² = x³ + ax + b mod p where a = 852, b =…

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Q: Let V = R²×2 be the vector space of 2 × 2 matrices and let L : V → V be defined by L(X) = = image of…

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Q: Each character in a password is either a digit [0-9] or lowercase letter [a - z]. How many valid…

A: We have to find how many valid passwords are there with the given restriction(s).

Q: 15. In the following figure, two poles are 25 m and 15 m high. A cable 14 m long joins the tops of…

A: Pythagoras theorem is used

Q: Let a : V → V be a diagonalisable linear map where V is a vector space of dimension 4 over the field…

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Q: . Let S denote the sphere centered at (5, 0, 4) with radius 3, oriented so that the top of 5 points…

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Q: Identify the equation of the quadratic function with a vertex of (0, -1), that passes through the…

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Q: I understood that just fine, but what is stumping me is how to show that there is a limit using…

A: We shall show that the limit exists using the above theorem.

Q: 6. If the complex number -2+3i is an eigenvalue of a matrix A = a, b, c, d are real numbers, then…

A: Given system of differential equation  and the eigen value is Claim:  is true

Q: Sketch the gradient vector field for the funtion f(x, y) = xy.

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Q: The image displays that K1 = -2 is wrong. I got the same answer in my own work and still confused on…

A: Please check question carefully, It says that answer must contain at least three decimal places.

Q: Sketch the region of integration for O A. -9 Choose the correct sketch of the region below. 81- O B.…

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Q: 35 40 i The small ants first destroy the large ant colony in year The large ants harvest the fruit…

A: (a) We have to Construct a table showing each colony's population in years t = 5, 10, 15, 20, 25,…

Q: Use the Divergence Theorem to evaluate [/F F. N dS and find the outward flux of F through the…

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Q: Let R be the region between the graphs of y = 1 + cos(x) and y=x² x = 1. Set up, but do not…

A: For a given region R we have to find an integral expression  for volume generated when R is rotated…

Q: 5. Consider the series below ∞ 1 n² + n n=1 1 (a) Use partial fraction decomposition to rewrite as…

A: First we partial decompose the given sum. And then find the limit of the partial sums.

Q: 6. Let f be continuous on [a, b]. Show ffdF = f(x) [F(b) – F(a)] for some x € [a, b].

A: This is a consequence of the intermediate value theorem

Q: 10. Let f be a continuous function with period 27. If f is an even function (that is, ƒ(x) = f(−x)…

A: The function  is continuous  with period and  is even that is Given  Claim:  for every .

Q: Problem10 a. Euler circuit b. Euler path In the following graph check whether the given graph has an…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…