(a) Use mathematical Induction to prove that 4n + 7" + 10 is divisible by 3 for every non-negative integer n. (b) Prove by induction (ordinary or strong) that any amount (integer) of postage greater than 27 takas can be formed with a combination of five and eight taka coins.

Q: rove: There are integers a, b, and c such that a|bc, but a∤b and a∤c.

A: We want to prove there are integers a, b, and c such that a|bc, but a∤b and a∤c.

Q: 9. Use Euler's Theorem to show that 3 (26) = 1 (mod 26). Show your work or explain your reasoning…

A: Since you have asked multiple questions, we will solve only question number 9 for you. If you want…

Q: 5. Identify and sketch the graph of the following equations in R³. (a) x2 + 4y² + 2² – 8x + 16y – 2z…

A:

Q: Let F be a field of 4 elements and let f(X) e F[X] be an irreducible polynomial of degree 4. How…

A:

Q: a) Show that the matrix H constructed from a matrix A, as H = i(A – A†), is Hermitian, whether A is…

A:

Q: Given this: C 1 2 3 4 5 P 15 JK 6 7 8 9 10 11| 12 A B F M 13 R V 14 16 17 18 19 20 21 22 23 24 25 0…

A:

Q: Question 4 Suppose that at t = 4 the position of a particle is s(4) = 8 m and its velocity is v(4) =…

A: Given at t=4 the position of a particle is s4=8 m and its velocity is v4=3 m/s

Q: Let 7,V be a projection af the Vect or space. Accordling to this: Show that every Xe Im (T) for…

A: The given problem is related with projection. Given that T is a projection of the vector space V .…

Q: Consider the following. W = {(5t, t): t is a real number} (a) Give a geometric description of the…

A:

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 9/3 and whose components have…

A:

Q: Gram-Schmidt process on the following two vectors to find an orthonormal basis set:…

A:

Q: 10. Given à = 5î – 2ĵ – 2k and B = 4î + ĵ – k, compute Proj A. %3D

A:

Q: Which of the following is/are homogeneous equation/s? 1. 3y" - 2y +1 = 0 dy II. 3 dy? dy + 2y = 0…

A:

Q: 3. ト Find the quotient of A if A = and B- 2.

A:

Q: Q5) If the vector field T = (axy + Bz³)a, + (3x² – yz)a, + (3xz² – y)a, is irrotational, determine…

A:

Q: It's a Linear Algebra Problem: Execute the Gram-Schmidt process on the following two vectors to…

A:

Q: Consider the points A(1, –1,4), B(2, –3, 2), C(-1, –2, 2), and D(4,3, –6). (a) Find the volume of…

A: Given the vertices A(1, -1, 4), B(2, -3, 2), C(-1, -2, 2) and D(4, 3, -6) of the parallelepiped…

Q: Suppose z = (0, 4), then arg(z) = {+ 2nn,n E R %3D

A:

Q: Evaluate the determinant A by any method, |1 3 6 2 1 0 2 |0 A = |3 2 3 0 2 9 5 1 0 10 0 8 6 0 1 2

A: Consider , A = 1310206223302951010086012 We need to find determinant of A. For that we will use ,…

Q: Consider the functionf(x, y) = 7x? – 7y² subject to the condition x + y = 36. %3D Use Lagrange…

A:

Q: a3 – 4x2 x(x + 8)(x – 2) (x+2)3 8(7x - 4) (x+ 2)ª f(x) = with f'(x) = and f"(x)= %3D (x +2)² ' d.…

A: d(i). Determining the intervals on which the function is increasing or decreasing. If the first…

Q: Lin early exPand the in lefendent Set x+1, 2x3 to asface base PUR ficla R Hint PoLIR The natural…

A:

Q: Given four points (0,0), (2, 2), (3,6), and (4, 12), find the least square approximate solution to…

A:

Q: Construct a table of values for sinx, x = 0, 0.1,0.2, ..., 0.6. Using the difference quotient,…

A:

Q: Solve: y/" – 4y" + 53y = 0 O y = C1 + C2e cos2x + C3e-7* sin2x 7x O y = C1 + C2e cos2x + C3 e7"…

A:

Q: 43. r = 2 + sin 0

A: We have to identify the type of the given polar equations. Then, we have to sketch the graph of each…

Q: A Moving to the next question prevents changes to this answer. Question 2 Given the system of…

A:

Q: Use the operator method described in this section to find the general solution of each of the…

A:

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. k + 5 k(k + 6)…

A: Series and sequences

Q: Is the statement true? Or is it false? Why?

A: We have to state whether the given statement is true or false. Also, we have to explain the reason.

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 3 /3 and whose components have…

A: In the equation ∇g=λ∇f, delta represents partial derivative. A partial derivative is a derivative in…

Q: Use a compound angle formula to rewrite cos(30) in terms of sinO and / or cose.

A: compound angle formula

Q: Use the substitution x = e' to transform the given Cauchy-Euler equation to a differential equation…

A:

Q: /4 g- x sin x dx

A: Given integral is ∫0π4x sin(x)dx So here f(x) = x sin(x) As π4 ≈ 0.785 Let n = 5  => h = 0.157…

Q: Express .fCG). as a poower series ; from nere, find Ane sum of ueing ithi resiilt from tres power…

A: We have to find power series and sum of given series.

Q: Use the Egyptian's formula to calculate the area of a circle with diameter of 4 units. (roundoff…

A:

Q: For a data set {xi, yi ; i=1,n}, which of the following conditions must be satisfied by an…

A:

Q: Refer to the figure below. Make use of Euclid's axioms and postulates. Line AB crosses lines CD and…

A:

Q: Explain why S is not a basis for P2. S = {1, 4x, -9 + x², 7x} S is linearly dependent. O s does not…

A: Given S={1,4x,-9+x2,7x}. We explain why S is not a basis for P2.

Q: Problem Set 3.1. Verify the following differential equation if exact or not, if exact find the…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

A: Given, V=13b2hb1=b2=6cmh=9 cm

Q: Given 급 (1+ 블" -를 -용), dy * = k). What is the value of k such that y is perpendicular to the curve…

A:

Q: Write v as a linear combination of u and w, if possible, where u = (1, 1) and w = (1, -3). (Enter…

A:

Q: What is im ) 1+2i 3-4i 1 А. D. 2/5 B.

A:

Q: f (x) = e2* if x> 0 The Fourier transform of the function: 0if x<0

A:

Q: Consider a rectangular plate with width w and hight h. If the temperature at all edges are kept to…

A: Hi! As per norms, we will be answering only the first question. If you need an answer to others,…

Q: (-1)"x²n (2n)! 1. For all x € R, cos ax = n=0 (a) Find a power series that is equal to x cos(x²) for…

A:

Q: Given: In(1 + x) = -1)“, xu+1 if |x| < 1. n+1 1. Find the Maclaurin series for f(x) = xln(1+¨). 2.…

A: We will use given Maclaurin series of ln(1+x) and use substitution to find series for given function…

Q: 4. Any non-empty set A and its power set P(A) do not have the same cardinality (i.e. there exists no…

A:

Q: Find the volume of the paraboloid, z = 9 – x2 - y², that lies inside the cylinder x2 + y? = 4.

A: we know the volume of any surface is given by ∬∫EdV ,where E is surface inside the cylinder x2+y2=4…