Use mathematical induction to prove that cos(x+n) = (-1)" cosx where n≥le J*.

Q: 3. A man invests R2500.00 at a compound interest rate of 8% per annum. If at the end of the year, he…

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Q: Let z = − √ 3−i. (a) Please find |z|. (b) Please find the argument of z. (c) Please express z in…

A: Given: z=-3-i. To Do: (a) Find z. (b) Find the argument of z. (c) Express z in polar form.

Q: Evaluate the given expression. Take 0 -1 -0.5 2 1 --[] •[] ªnd ²-[-] A = -2 0 B = 0 0.5 C= -1 -1 1…

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Q: Every canonical function is one to one

A: As per the question we have to show that every canonical function (in context with Boolean algebra)…

Q: A thermometer is taken from a room where the temperature is 24°C to the outdoors, where the…

A: A thermometer is taken from a room where the temperature is 24°C to the outdoors, where the…

Q: Find f o go h. S-XX = (x) 9(x) = x2 {+ x = (x)4

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Q: Problem4 A small river stream flows into a large reservoir and fills it with water. We will assume…

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Q: The fuel economy of a car (miles per gallon) varies with its speed. In an experiment, the following…

A: Let s represent the speed in mph. Each cubic spline passes through two consecutive data…

Q: 31 Approximate the following integrals by using Maclaurin series (with three non- zero terms) ( -01…

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Q: for all nEN there are infinitely many prime numbers p=^ (modu) Prove that for each finite abelian…

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Q: A "S number" is a positive even number that is not the product of two even numbers. A "B number" is…

A: Given: S number= positive even number that is not the product of two even numbers,  B number=an…

Q: Give an example of a commutative ring without zero-divisors thatis not an integral domain.

A: To Do: Give an example of a commutative ring without zero-divisors that is not an integral domain.

Q: Find the amplitude, the period in radians, the phase shift of radians, the vertical shift, and the…

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Q: Use matrix inversion to solve the given system of linear equations. (You previously solved this…

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Q: Let A = 10-4 02-3 - 4 4 2 and b = 0 1 6 Denote the columns of A by a₁, a2, a3, and let W = Span {a₁,…

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Q: Solve the following ordinary differential equations: 2) (3y³-x) dx = 3xy-dy

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Q: Using the Laplace transform to solve the partial differential equation utt=a²uxx , x>0, t>0…

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Q: 23. Find the formal solution to the heat flow problem (1)-(3) with ß = 2 and L = 1 if f(x) = [=1 /…

A: Answer :

Q: 3. R a Figure 1: Problem 3 Consider any AABC, where the bisector of ZBAC intersects the bi- sector…

A: We draw the perpendiculars from Q to the sides of the triangle, intersecting at R, S and P.  Now,…

Q: (e) Find the point of intersection of the tangent lines to the curve r(t) = (5 sin(xt), 3 sin(xt), 6…

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Q: dy 9. dr dt Find the solution satisfying y(0)=1. dy(0)/dt=0 +2y=0

A: 9. Given that the differential equation is                       d2ydt2+3dydt+2y=0,    and  y(0)=1,…

Q: f. If Europe has approximately 3.7 million mi of land, what is the total area of land on Earth?…

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Q: rmulate but do not solve the problem. Michael Perez deposited a total of $2000 with two savings…

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Q: 3) Let V be a vector space of dimension 7. Which of the following statements is true?

A: V is a vector space of dimension 7. We have to choose the correct option.

Q: Solve the equation. (4x + 2x¹y + 2x¹y²)dx + (1+2y)dy = 0 An implicit solution in the form F(x,y) = C…

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Q: Determine whether the function is a linear transformatio T: R² → R³, T(x, y) = (√x, 4xy, √y) linear…

A: Given: T : R2→R3, Tx,y=x, 4xy, y. We have to determine whether T is a linear transformation or not.

Q: Find the eigenvalues and eigenvectors of 5 dx dt Number of eigenvectors: two r1 r2 = 12 (2). 2 9 NIC…

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Q: . Determine lim 818 ax ( 2² + a² + b) ª 3 r² where a, b and c are nonzero constants. I mazá $…

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Q: 6.(a) Show that (f.g) = f f(x)g(x)dx satisfies the axioms of an inner product on C[a, b], the space…

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Q: f(t) = L-¹{F(s)} e nt sin(at) sin(6t) + 6t cos(6t) F(s)=L{f(t)} $-2500 s¹Y (s) - s³yo - s²yo - syo -…

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Q: g(x, y) = = sin(xy) xy Prove that g is continuous on R². if (x, y) = (0,0) if x = 0 or y = 0.

A: Given  g(x,y) = sin(xy)/xy  if (x,y) does not equal to (0,0)                1  if x=0 and y=0

Q: 5. In X-linked inheritance, suppose that none of the females of genotype Aa survive to maturity.…

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Q: Express the following system of linear equations as a vector equation. 1x1 +4x2 - 6x3 = -5 -2x1 +…

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Q: use the Laplace transform to solve the given initial-value problem. Q. y′′+4y =4sint+3δ(t−2),…

A: use the Laplace transform to solve the given initial-value problem. Q. y′′+4y =4sint+3δ(t−2),…

Q: A fair coin was rolled 6 times with each outcome either head or tail. How many possible outcomes for…

A: The step by step solution of the given problem is as follows:

Q: Write the system of equations corresponding to the augmented matrix. (Use x, y, and z as your…

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Q: Inventory A certain bookstore chain has two stores, one in San Francisco and one in Los Angeles. It…

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Q: Find the area of the parallelogram determined by v = (7, 0, 0) and w = (0,7, -3).

A: The step by step solution of the given problem is as follows:

Q: 3. (5 pts) Show that f(x) = √ is not differentiable at = 0.( Show the limit of the difference…

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Q: Solve the equation. (3x²)dx + (2y - 4x³y1¹)dy = 0 What is an integrating factor for the equation?…

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Q: determine L−1[F].

A: Inverse Laplace transformation of the function

Q: 2. Use LU decomposition with partial pivoting to solve the following problem. 2x₁ +5x₂ + x3 = -7 2x₂…

A: The given equations are: 2x1+5x2+x3=-72x2+4x3=66x1+x2=12 We have to solve the given equation using…

Q: Consider the Euler-Mascheroni constant. Compute the limit. y = lim k→∞ Σ()-inki In|k|

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Q: The mean score on a set of 25 tests is 76. What is the sum of all the test​ scores?

A: The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all…

Q: (X+xy)dx-(ў+x)dy=

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Q: A quantity P is an exponential function of time t, such that Po a³ (a) Find values for the…

A: Given that a quantity P is an exponential function of time 't' such that P0a3=75, and P0a2=50. And…

Q: 14. Let v(1,2), va- (2,3) and let 5= matrix from (w), wy) to (v₁, v₂) (a) w₁(1,5) and wa-(9,4) (b)w,…

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Q: all is correct except step one... a11= 1 is correct, a12 = 1/2 is inccorect (a12=0 is correct)…

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Q: a) Graph the function f(x)= b) Draw tangent lines to the graph at the points whose x-coordinates are…

A: Given f(x)=2/x

Q: Evaluate the given expression. Take -3 2 0-2 1 1 ^-[1 ²] A = -2 0 and C= -1 -1 2 1 1 AT + 3CT -5 -3…

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