If a fraction is equal to m 100 3 8 3 100 8 and the sum of the numerator and denominator is 66, what is the fraction?

Q: State and prove the following theorems. (i) Extreme value theorem. (ii) Rolle's theorem.

A: Statement of Extreme Value Theorem:- If a function f:ℝ→ℝ is continuous on a closed interval [a,b],…

Q: In each of Problems 9 and 10, use Euler's method to find approximate values of the solution of the…

A: The Eulers's method is: yn+1=yn+h·ftn,yn, where, tn+1=tn+h. We have given that, fx,y=5-3y t0=0,…

Q: State and prove the following theorems. (i) Extreme value theorem. (ii) Rolle's theorem.

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Q: Theorem 2 For all n € N, let fn : [0,1] → R be a continuous non-decreasing function. We assume that…

A: If we remove the assumption that the limit function f is continuous, the theorem is no longer true.…

Q: 12 Exact differential equations 1. Verify that the following is an exact differential equation and…

A: Since You didn't mention the question number to be solved so I solved First question only.

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

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Q: Need help with part (a). Please explain each step and neatly type up. Thank you :)

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Q: 2. For the following systems with complex eigenvalues, find the general solutions: -5 ›× - ( 13³ ) ×…

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Q: 13. Use trapezoidal rule with n =4 to estimate, 1 = 1² correct to five decimal places. Repeat the…

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Q: A grandparent puts $5,000 into a college education fund for a grandchild. If the fund earns 3.75%…

A: Given that: Principal(P) is $5000. The rate of interest(r) is 3.75%. Time(t) is 16 years and n is…

Q: Find the enclosed area of the following lines and curves. Graph the given functions and properly…

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Q: (c) Prove that if (nsn) converges to L = 1, then (sn) converges also converges.

A: nsn converges to :L=1

Q: ABCD is a parallelogram. Find the point of intersection of the diagonals of this parallelogram and…

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Q: The characters in the passwords are all either letters or digits. It is case sensitive. State how…

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Q: Find the volume of the solid under the surface f(x, y) = x²y over the upper half of the circle x² +…

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Q: 4) Three planes form a triangular prism with the equations: y = 0 -√3x + y = 0 x + √3y = 4 a. Find…

A: The angle between the planes is the same of the angle between the normals. If n1 and n2 are two…

Q: Find the matrix A of the quadratic form associated with the equation. 6x2 - 4xy + 6y2 + 16z² 33 = 0…

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Q: If f_X,Y (x,y) = 6e^-(2x + 3y) for x, y >=0 then what is P[X>Y] ?

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Q: For the matrix A, find (if possible) a nonsingular matrix P such that PAP is diagonal. (If not…

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Q: S01.5 Formulate methods and solutions using appropriate knowledge of the fundamental principles of…

A: Using the fact that the inverse of an invertible lower triangular matrix is also lower triangular.

Q: Suppose that the exchange rate is $0.92/€. Let rs = 4%, and re = 3%, u = 1.2, d = 0.9, T = 0.75,…

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Q: Three forces act on an object as shown in the diagram. Determine the equilibrant of these three…

A: The force is in equilibirum if all vectors must add to 0

Q: 6. Use the Divergence Theorem to calculate the surface integral J1₂ FdS, where F(x, y, z) = x³ + y³…

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Q: B. Find the missing value by using shifting operator E. X y 2 2 5 ==== 7 3

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Q: Problem A Given y'=x + y, y(0)-2, compute y(0.2) and y(0.4) using 4th order Runge-Kutta method (…

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Q: 4.F.4 Let A be the matrix below, and consider the discrete dynamical system Ark 23 - [22]. 12 a)…

A: xk+1=AxkA=2312

Q: solve the initial value problem y' = 0.4xy + y, y(1) = 1

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Q: y' + ycosx - 2xe-sin(x), y(0) = 0

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Q: Find a value for the constants p and q so that x₁ optimal solution of the resulting program. = 0, x2…

A: Note: We will be solving part (c) as asked. The given linear programing problem is: Maximize px1+qx2…

Q: 25. Use Euler's method to solve the differential equation y'= - y' with the initial condition y(0) =…

A: Since Given differential equation is  y' = - y'⇒2y'= 0⇒y'=0 ...(1)compare (1) with y' = f(t,y)we…

Q: Let C₁ (t) esti + 7 sin(t)j + tªk and c₂ (t) = e¯5ti + 3 cos(t)j - 4t¹k. (Enter your solution as a…

A: Given that c1(t) = e5ti + 7sin(t)j + t4kc2(t) = e-5ti + 3cos(t)j -4 t4k

Q: (a) Find A-1. (b) Find (AT)-¹. (c) Find (3A)-¹. (d) Compute det(A). (e) Compute det(A-¹). (f)…

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Q: Choose the number that best approximates each of the following 6 8 10 21 (a) + + + 25 33 41 (i) 3…

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Q: 9. Given that C is the counterclockwise oriented boundary of the region between r = 1 and r = 2 in…

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Q: 4. Show that x² P.V. Lx (2² + 1) (²2²2 + 4) d² = 75 dx 1)(x² 3 -∞ using the Residue Theorem. You may…

A: Let  fz = z2z2+1z2+4       For obtain poles of fz , equate the denominator part to zero…

Q: Use the method for solving homogeneous equations to solve the following differential equation. 2…

A: The differential equation is given by: 14y2-xy dx+x2 dy=0                 ........(1) Rewrite the…

Q: -2 1 3 7 LU and hence solve the system AX = B, where B = [4 8 10]T [5 20. Decompose the matrix A = 7…

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Q: 5 Step functions Calculate the Laplace transform. f(t)=tH(t-5)+ tcos (2t-6) H(t-3)

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Q: Given the following function f: N× N→N, f(m,n)=2"-¹(2n-1), determine if it is onto or one-to-one.

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Q: Find the volume of solid generated by revolving the region bounded by the curves y = √x +2.y=x-2x =…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. [x C is…

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Q: In the figure below, m2 = 46° and mZQPR = 133º. Find m Z1. P 1 2 A R S Q m2 1 = 0.

A: The given measures are m∠2=46° and ∠QPR=133°. Using the given figure, we have to find the measure of…

Q: Evaluate the line integral by applying Green's theorem. Jo 9xy dx + (x + y) dy, where C is the…

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Q: 1 First order ODES 1. Use the method of the integrating factor to find the general solution of 2.

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Assume that all the given functions have continuous second-order partial derivatives. ²+ s² and y If…

A: We use chain rule,

Q: e second-order Taylor polinomial for the function f(x)=√1+x about x = 0 ls P₂ - 1+Using the given…

A: Given f(x)=√(1+x) and we have to apply the Taylor's series method.

Q: The general term of the Fibonacci sequence is: A) F₁ = √5 ((¹+√5)" + (¹³)") F₁ = √5 ((¹-√³)" -…

A: The given problem is to find the general term of the Fibonacci sequence.

Q: (7) Let F be a field, and 3 algebraic over F. Show that 3 and 1 + 3-¹ have the same degree over F.

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Q: Use generating functions to determine the number of different ways 32 identical stuffed animals can…

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Q: Write an integral that represents the area of the shaded region of the figure. Do not evaluate the…

A: Here we have to set up an integral that shows area of the shaded region.