Pedro, who deposited P500,000.00 today with a financial Institution M, agreed with the latter that Pedro’s money shall earn monthly compounded interest. If the prevailing interest rate of the Institution M is 8 % compounded yearly, how much will the value of his deposit be after 14 months?

Q: Find the Fourier Series of the function: f(x)=X+n if - < X < n and f(x+2) = f(x)

A: Sol: Fourier series of function fx on interval -L≤ x≤ L is defined as: fx=A0+∑n=1∞ An·cosnπxL+∑n=1∞…

Q: (8) Show that for a field F, the set S of all all matrices of the form a b (88) 00 for a, b F is a…

A: An ideal is a special kind of subring of a ring R. If a∈I and r∈R implies that ra∈I then, the…

Q: Equation: 150x-66y+10z=1500 1x+120y-55z=1200 1x-75y+110z=-900 Using Gauss-Seidel Method, determine…

A: Solution: Total Equations are 3 150x-66y+10z=1500 x+120y-55z=1200 x-75y+110z=-900 From the above…

Q: Mu=Φ x 0.85 x fc' x a x b x (d - a/2) 266000000 = 0.9 x 0.85 x 21 x a x 366 x (486 - a/2) a= uknown…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: Q3- Find the Maclaurin series generated by the following function: f(x) = sinh(x)

A: Given function fx=sinhx We have to find the Maclaurin series for f(x).

Q: In a Hilbert space. Prove that x →x provided ||x₁||→||x|| and (x₁, x) → (x, x). n

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Q: Let h(x, y) = x5 + y sin²x x² + y² 0, if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that his…

A:

Q: Count the number of arrangements of the word EULERIAN that have no isolated vowels; that is, any…

A: The main objective is to find the number of arrangements of the word EULERIAN such that have no…

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: The representation of an even integer is 2k for some integer k. The representation of a odd integer…

Q: State the principle of uniform boundedness. Use it to show that a set E in a normed space X is…

A: Introduction:      A family of bounded linear operators from a Banach space X to a normed space Y is…

Q: Part I: Directions: Complete the table below. EQUATION CENTER 1. C(0,0) 6. 4. x² + y² = 64 x² + y² -…

A: To complete the given table  for the given conditions :-

Q: Prove that the ring of integers ≺ Zp,⊕,⊙ ≻ can be embedded in every integral domain          D = ≺…

A: Given that ℤp,⊕,⊙ is a ring of integers. Also D=D,+,· is an integral domain of prime characteristics…

Q: A: Solve the following - 4y = 16 t differential equation by Laplace: dy dx -6, y(0) = 3

A:

Q: -> 2. For the given vectors u and v, find the value of u and normalize u + v. V, = (3,−3,1,–3,3), v…

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Q: . Solve the following equation by Finite Differences Method, choose h = 0.25 -y=x+y . y(0) = 0 &…

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Q: Solve the initial value problem. (cos x) + y sin x = 5x cos ²x, dx The solution is y(x) = y 3x 19x²…

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Q: 4. Let f(x) = x 22/5 - - 19 sin(x). Determine the largest n for which fis n-times continuously…

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Q: s 19 An = 6n +41 give the first & terms. 27) An = 4886 i insent 5 terms. 3.) an = {-13₁-6,…

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Q: Determine and sketch the domain of the function f(x, y) = (x2+y2)/(4x-3). Sketch the contour map by…

A: Let us consider the given function z=f(x,y). The level curve is obtained by taking f(x,y)=k where k…

Q: 2. Determine the real root of f (x) = 5x³-5x² +6x-2 (c) Perform the same computation as in (b) but…

A:

Q: Find the equilibria of the autonomous system of equations, classify them and x=2-2√1+x+y sketch the…

A: The given system of equations is: x˙=2-21+x+yy˙=exp54x+2y+y2-1 Therefore the equilibrium points can…

Q: Consider vectors C = 5a, 3a + 2a and D = 3a, - 2a0 – 4a in spherical coordinates. (a) Transform C…

A: We are given the following vectors C=5ar-3aθ+2aϕ and D=3ar-2aθ-4aϕ in spherical coordinates.  For…

Q: The function f(x,y) = y²tan(y/x) function of degree is a homogeneous

A:

Q: (a) True or false: The ring (b) True or false: The ring Z., Ⓒ is a field. Justify your answer. ZxZ,…

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-parts…

Q: quation: 150x-66y+10z=1500 1x+120y-55z=1200 1x-75y+110z=-900 Using Jacobi Method, determine X3,…

A: Sol:- Total Equations are 3150x-66y+10z=1500x+120y-55z=1200x-75y+110z=-900From the above…

Q: Construct the truth table for (p→→q) → [(pv-q) → (pv q)].

A: We have to construct the truth table.

Q: Mu= x 0.85 x fc' x axbx (d-a/2) 266000000 (486-a/2) = 0.9 x 0.85 x 21 x ax 366 x a= uknown "x" Using…

A: The main objective is to estimate the x value by using Newton Raphson method.

Q: 5. Let A 15 Find a diagonal matrix D and an orthogonal matrix P such that A = P'DP.

A: Given : A=5115 To Find : D Diagonal matrix  and P Orthogonal matrix

Q: Q5. Find the directional derivative of the function [f(x, y, z) = xy + y.z + z.x] at the point 1-z…

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Q: In the following figure, the vectors A and B have magnitudes of 55 and 105 units respectively and…

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Q: Using the substitution y=vxanddy=vdx + xdv, the homogeneous differential equation [xsin ()-y]dx A B…

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Q: - = A solid is bounded by the spheres x² + y² + (z − 1)² : 1 and x² + y² + z² = 9. Write a set of…

A: Given that a solid is bounded by spheres                     x2+y2+(z-1)2=1 and x2+y2+z2=9.

Q: 2 p ↑ (pv~ (PV q) 7)]

A: The given problem is ~[p→(p∨~q)] So we have to draw a truth table  for the mentioned problem

Q: Cavity Candies mass produces an assortment of hard candies, consisting of three flavors: cinnamon,…

A: Solution:

Q: C. Use Polya's four-step problem-solving strategy to solve the given problem 1. If the length of the…

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Q: Using the substitution y=vxanddy=vdx+xdv, solve the homogeneous differential equation y (2) - Jax- X…

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Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: (1). Definition of Even integer- The number which are divisible by 2 , is called Even integer. For…

Q: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the…

A: Solution:-

Q: Question 3. > Given the triple is a ring. Is it a commutative ring? Justify your answer. (b) Does…

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Q: x Add: + 6 7 15 ● Enter your answer as a single fraction.

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Q: Given the data X 1 0 5 2.5 6.5 3 7 (a) Calculate / (3.4) using Newton's interpolating polynomials of…

A: According to guidelines we can solved only first question thank you   ByNewtown interpolating…

Q: - Construct the truth table for [(pq) v (p →r)] → (-q ^p).

A: Here we have to find truth table of given expression.

Q: Here is a contour plot of the function f(x, y) = 4+x³+y³ − 3xy: (Click the image to enlarge it.) By…

A: (1,1) is a point of local minima. Second Critical point is (0,0) and it is local minima.

Q: 8. We have seen that the matrix R(0) = ( cos sin 0 around the y-axis rotates vectors in R2…

A: Given: In this problem, the given matrix is R(θ)=cosθ-sinθsinθcosθ , rotates vectors in…

Q: How do you solve this question?

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Q: B: use Lagrange interpolation formula to determine the relationship between the force and velocity…

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Q: h(x, y) = xy²/³ + xy 3√x⁹ + 2y³ if (x, y) = (0,0) 1 √√3' if (x, y) = (0,0) is continuous at the…

A: Removable Singularity: A discontinuity is removable at a point x=a if the limx→a f(x) exists and…

Q: Question 2 Write a logic formula for each of the following statements: (a.) "There exists a natural…

A: To find- Write a logic formula for each of the following statements: There exists a natural number…

Q: (b) Describe and sketch the region given by 3|x| + 2|y| + |z| ≤ 6. Hint: look at the equation in…

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Q: Find an integrating factor of the form xy and solve the equation. (3xy²-8y)dx + (3x²y-8x)dy = 0 An…

A: