A natural cubic spline S for a function f is defined by +3 x² x 3 + 3 2 1≤x≤2 2≤x≤: 3≤x≤ 5(x) = - 12 +3 12 x 12 + 4 3x² 4 4 a + ax + 17 6

Q: Anxn be an invertible square matrix. Show that cofactor(A)=A The formula of matrix inverse you might…

A:

Q: The drawing below shows a right-angled triangle. A straight line crosses the triangle parallel to…

A: We have named the points on the triangle as shown below. From the diagram, BE∥CD Given that…

Q: A factory manufactures two types of gadgets, regular and premium. Each gadget requires the use of…

A:

Q: Solve the following ODES by Undetermined Coeff. X 2 2X • "Y + 5y + 4y = x 2² 4X -4X 2X 2 Ans: y=c₁e…

A:

Q: 1. Compute the Frenet apparatus k, 7, T, N and B of the following curve a(s) = (1 - √/cos cos s, 3+…

A: Given- Consider the level surface S defined by fx, y, z = 0, where f is smooth and its partial…

Q: Question 3 A certain non-homogeneous system of linear equations has a parametric solution x = a +…

A:

Q: Evaluate the given integral SS₂ e-x² - y² JA where Coordinates Semicircle polar bounded by the by…

A:

Q: Show that A = P-¹BP. [2-13] -4 and B = 1 -2 -2 2 are similar matrices by finding an invertible…

A: To show that          A=7-132-4, and   B=1-2-22 are similiar matrices.

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: 5. Prove that the series converges using the corresponding test: n=1 (-1)+¹(X+Y+ 1) n²

A:

Q: Mang Ruben has only an 11-liter can and a 5-liter can. How can he measure out exactly 7 liters of…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: H.w: Use the bisection method to determine the drag coefficient c needed for a parachutist of mass m…

A: It is provided that: f(c)=gmc1-e-cmt-40, m=68.1, t=10, g=9.81.

Q: Use the method of variation of parameters to determine the general solution of the given…

A: Sol:- y''' +y' =tantGeneral Solution :-y = yc(t)+Y(t)Fot yc(t):-A linear homogeneous ODE with…

Q: Evaluate the iterated integral. ITT*³. /0 10 6ze-x6 dy dx dz

A: Integrate usually but first with respect to y then x then z.

Q: 2.1 Use the Taylor series approach to find the local truncation error, E, when the approximation: ap…

A: Recall mean value error of taylor series and then compare .

Q: Find the general solution to the equation y(4) — 4y" + 4y″ = 0. NOTE: Use C₁, C2, C3, and c4 as…

A:

Q: If I have an exam which lasts 3 hours and there are 42 questions, 34 which are worth 2% and 8 that…

A:

Q: The graph below is the function f(x) 16 O N -5-4-3-2-1 -2 -4 -54 Determine which one of the…

A:

Q: How the following groups act on the plane R" ? | How the "Quotient Space " look like? ● Z nZ ZX Z…

A:

Q: e² - in a Laurent series that converges for 0 < |z| < R Z²-z³ Expand the function f(z) and determine…

A: In this question, the concept of the Laurent Series is applied. Laurent Series Laurent’s series,…

Q: ind and classify the equilibrium points of the following equations: 2 (9 + r − 3y)r y = (1+r-y)y…

A: Given the system of equations. x.=9+x-3yxy.=1+x-yy To find the equilibrium points and discuss the…

Q: Let W₁ be the solid half-cone bounded by z = √√√x² + y², z = 1 5 and the yz-plane with √x² + y², z =…

A: Given W1 and W2we have to find whether following integral is positive or negative or zero.

Q: Using the Simpson’s 1/3 Rule Method, manually solve for the approximate value of the integral of the…

A:

Q: 1      -1       0 Find the inverse of the following matrix A =  1        0      -1…

A:

Q: Marie has bought a plant which she needs to transfer from its cylindrical pot to the ground. The pot…

A: Part (i) The diameter of the cylindrical pot is 10 cm and the height is 21 cm The hole has to be 4…

Q: ry=3 e Sy_²₁ fx=1+√4-(y-1)² z=2(x+y+1) y=-1³√x=1-√4-(y-1)² √z=x²+y² 4. Evaluate dz dx dy

A:

Q: Ⓒ Solve the following ODES by Undetermined Coeff. ✓ 2 (D² +8D³² +16) y = - sinx Ans: Y=G₁s2x+ C₂…

A: The given problem is to find the solution for the given ordinary differential equation by using the…

Q: 7. An oil tank in the shape of a sphere has a diameter of 60 ft. How much oil does the tank contain…

A: The volume of a spherical cap is given by the equation; V=13πh2(3R-h) where h is the height of the…

Q: The dimensions (355-milliliter) centimeters) centimeters) of a classic 12-fluid-ounce can of Coke is…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: What is the equation for the horizontal asymptote of the graph of the function shown? -8 -4 D -4 -8…

A: I have given the answer in the next step. Hope you understand that

Q: An implicit general solution to the following equation (y/x^2)y'+ e^(2x^3+y^2) = 0, where y=y(x) can…

A:

Q: Find the exact value of the definite integral below, using the substitution u = x x (√6+√2) 1+x² -…

A:

Q: 4.1 In aerodynamics and fluid mechanics, the functions u(x,y) and v(x,y) in f(z) = u(x,y) + iv(x,y),…

A: As per the policy, we are solving the first question. Please repost the question and specify which…

Q: Determine the interval(s) on which x² + 2x-3 > 0. O a) x>1 b) -3 1

A: We want to find the interval which satisfy given inequality.

Q: Find the work done in a moving particle along the closed path (0,0) → (2,2) → (2,4) → (0,6) under…

A:

Q: -8 -6 -4 for 0 ≤ y ≤ 6 -2 8 -2 6 2 2 X The x y coordinate plane is given. A smooth directed curve is…

A:

Q: If possible, write 25 – 21x – 14x² as a linear combination of 2 − x − x², 2 – 2x − x² and 3x − 3 +…

A:

Q: Perform the indicated operation and simplify as much as possible. List any restrictions on the…

A:

Q: Suppose Sanx",Σ bnan converges for all x in (-1,1). Σana" = Σbnan in a subset E of (-1,1) implies…

A: It is given that,  ∑anxn and ∑bnxn are convergent for all x in (-1, 1). Then,  ∑anxn = ∑bnxn in a…

Q: Consider the initial-value problem (x² − 1)y"+y' + y = ex y(1) = 1 y' (1) = -1 Does the Existence…

A:

Q: Alden works in the city and lives in the suburbs with Nikka. Every afternoon, Alden gets on a train…

A: This is a summary of the question. Every day Nikka leaves home before 5 PM to pick Alden up from…

Q: Solve the following ODES by Inverse Operator method 1-2 X ý -2ý ty ở sinx X X Anss y=cie + c₂xě - e…

A:

Q: Determine a root of the polynomial function given below using Muller's Method. Show the step by step…

A: Use the following formulae, to find the root of the function fx by the Muller method.…

Q: 1. Here is a list of months and a code for each: January: 7110; February:826; March: 5313; April:…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Given y(4) - 2y" - 4y" + 8y' = t² + 7 + tsint, determine a suitable form for Y(t) if the method of…

A: The given problem is to find the suitable form of the solution for the given differential equation…

Q: prove by vector method that diagonals of rectangle are equal in length and bisect each oth

A:

Q: Exercise 10. Apply BFGS method for minimizing f(x) = x¹(532)x+ (0,1)x with x(¹) = (0) and H(¹) = I₂.…

A: Given that: fx=12xT5-3-32x+0,1x with x1=00, H1=I2. The objective is to show that H3=G-1. Now…

Q: Find the measure of angle x in the figure. 1250 1300 130 125° x 144° Note: Angles not drawn to…

A: The given polygon is a Septagon. We know that the sum of total angles of a septagon is 900°

Q: Set up Calculate planes Following triple integral, but do not. Solid bounded by X=y² and the it: a X…

A: We have to set up triple integral for the region bounded by x=y2 and planes z=0 and x+z=3

Q: Find the solution of the given initial value problem: y(t) = = y (4) + 2y""+y" + 8y' - 12y = 12…

A: Sol:- The general solution to anxyn+...+a1xy'+a0xy=gx can be written asy=yh+ypyh is the solution to…