(iv) Write down the gradient of the straight line represented by the equation y = -0.05t +47. What does this measure in the practical situation being modelled? (v) What is the y-intercept of the equation y = -0.05t + 47? Explain what it means in the practical situation being modelled.

Q: Use Laplace transform to solve the partial differential equation: d²u d²u du(x,0) = t> 0, 0<x<1,…

A: Solution

Q: 4. What are the various applications of the dot product? Explain how the dot product is used to…

A: We will use the basic knowledge from vector calculus to answer this question correctly and…

Q: Use Laplace transform to solve the partial differential equation: o'y dy +xt where y(x,0)= 0,…

A: Solution

Q: 9) Evaluate the double integral of the function f(x, y) = 12x²y + 8x³ over the rectangle 0≤x≤ 2 and…

A:

Q: If ƒ (0) = 1, ƒ (1) = 2, ƒ(2) = 33, f(3) = 244. Find a cubic spline approximation, assuming S" (0) =…

A:

Q: Given z = cos (2) + i sin (2241), where n is a po

A:

Q: u)n(p+u°О

A:

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: First find the degree of all the vertex.  The degree of vertex  V of a graph is the number of edges…

Q: If a is a translation, show that aap is the halfturn about the midpoint of points P and a(P).

A:

Q: Jse separation of variables method to solve the partial differential equation: du ²u ди du(x,0) +u…

A:

Q: 3 (a) So 4√3x dx √3x-x² 2

A:

Q: Solve for all the roots of x using Bairstow’s Method starting at r1 = 0.25 and s1 = 8.75 of the…

A: Solution:-

Q: x(n)= a"u(k − n) for k>0

A: Introduction: The Z-transform translates a discrete-time signal, which is a sequence of real or…

Q: Q2: State and prove the first isomorphism theorem.

A:

Q: In Exercises 9 to 12, determine whether the two graph are equivalent. 9. B C C A D B

A: given two graphs

Q: Calculate - 2x²y dx + 2xy² dy, where C is the circle of radius 3 centered on the origin. use this…

A: Given that, Pdx+Qdy=-2x2dx+2xy2dy, Therefore, P=-2x2y, and Q=2xy2, Thus, need to use Green's Theorem…

Q: Directions: Briefly answer the reflection questions below. 1. Why do we need not to include the…

A: Indefinite integration is denoted as ∫f(x)dx=F(x)+C Where C is constant of integration  and F(x) is…

Q: Q4) Solve the boundary value problem y - 3y + 2y = 0 with y'(1) = 1, y(3) = 2e¹-e² h = 0.5

A:

Q: Tensor Auv is type (2 0) and tensor Wv is type (0 1). prove that AuvWv is a tensor of type (1 0)…

A: It is given that, Auv be tensor of type 2,0. Wv be tensor of type 0,1. it is known to us that if A…

Q: 1. If f(x) = 5x4 - 6x² + 4x2 find f'(x) and f'(2).

A:

Q: Evaluate the following integrals: Find the area (set-up the definite integral only) of the given…

A: The solution is given below

Q: Consider the differential equation: 1+ y² xy+y³+y dz This differential equation is not linear in y,…

A:

Q: The line of best fit to the data (2, 2), (0, 1), (1, 2) is y = 1/x + 7. The least squares error is…

A:

Q: Q4) Find the largest eigen value for the matrix A- [1 2] A= with x (0)=(7/17 1) 54

A:

Q: Consider a triangle ABC, on each of whose sides equilateral triangles are dra

A:

Q: Summary of what is Mathematics in modern world about

A: Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all…

Q: Use Laplace transform to solve the partial differential equation: dy dy +xt where y(x,0)= 0,…

A: Solution

Q: Find the total area of the region satisfying the E

A:

Q: 18. ( .) Answer the questions for the following functions. The leading coefficients are only +/- 1…

A: According to our guidelines we have to answer first three subparts if question with multiple…

Q: Consider the function. + 10 f(x) = Determine the intervals on which f is increasing, decreasing,…

A:

Q: pansion of (x + 3) ¹7+ x³(x+ 17 3

A:

Q: Graph the following Equations: x+3 5. y²: 2x²+3x+2 6. r = sin + 2cos²0 7. r² = sin 20-3cos

A: We can solve this using given information

Q: Calculate 2510 S. S. S. 2² r dz dv db (volume of D)

A: Triple integration

Q: Find a natural cubic spline interpolating the data (-1, 13), (0,7), (1,9)

A: Writing data in table format x -1 0 1 y 13 7 9 Formula for natural cubic spline is:…

Q: prove that every subset of negligible. set is negligible.

A: I have used definition of negligible set.

Q: GROUP holds four properties simultaneously: i) Closure, ii) Associative, iii) Identity element; and…

A:

Q: Give an example of a non-planar graph that is not homeomorphic to K5or K3,3.

A: We can solve this using definition of planar graph.

Q: Use Laplace transform to solve the partial differential equation: d'y dy +xt where y(x,0) = 0,…

A: Solution

Q: Use Laplace transform to solve the partial differential equation: d²u du ди(x,0) , t> 0, 0<x<1,…

A: Solution:-

Q: False Position Method and Secant Method ( f(x) = 3x² - 2x - 4

A:

Q: Show that the quadrilateral having vertices at (1, −2, 3), (4, 3, −1), (2, 2, 1) and (5, 7, −3) is a…

A:

Q: 6. Let A, B, C be (3 × 3) matrices, such that det (A) = 2, det (B) = π, What is the value of det…

A: Solution:-

Q: A patient is to receive 4 ounces of qid. How many ounces will the patient receive in one day?

A: "qid" means "four times a day" Now, the patient is to receive 4 ounces of qid. So, the patient will…

Q: Use cylindrical coordinates to evaluate the following triple integrals toutube √²-² (x² + y²) dzdy…

A:

Q: Let , ² be the complex cube roots of unity. Let z₁, z₂, z, be complex numbers such that z₁+z₂+z3 = A…

A: We will use properties of cube root of unity  ω3=1  and  1 + ω + ω2 =0

Q: an= (-5)n an an = COS 4n+n3 3n+4" os(T) 8

A: The detailed solution with explanation is presented as the next step.

Q: SD a strongly connected graph? D: W

A:

Q: x[n] x₁ [n] = festas O Î X,(z) ? X(Z) x₁₂[n] = x [2n] nieven niodd x[n]→→→x(z)

A: Introduction: Signal processing is broadly speaking a department of sign evaluation wherein…

Q: Learning Task 3: Read each item carefully. St.cw all secessar, Jutions in solv. ing 1. Find the…

A:

Q: Given P(A^c-complement)=0.40, P(B) =0.40, P(AUB)=0.75, P(A)= 0.60, P(B^c)=0.75 Find P((AnB)^c)

A: Additional Law of Probability gives P( A ∪ B ) =P(A) + P(B) - P(A∩B)