Find the volume of the sphere in spherical coordinates with radius a by setting f-1 and evaluating V = fff dv (0<0<2π, 0<φ<π, 0

Q: The inverse Laplace transform f(t) = £¯¹{F(s)} of the function F(s) = -25(65-8) s²+49 is of the form…

A:

Q: The system of first order differential equations: has solution: y₁ (t) Y₂(t) = Note: You must…

A:

Q: y is related to x through the differential equation: dy dx = ax + bx² + dx³ and y = c whenx = 0…

A:

Q: . Use the definition of derivative to compute the derivative of the following functions at x = 1: a.…

A:

Q: Using the midpoint basis, and expressing the answer in fraction or integer format, calculate the…

A:

Q: Suppose our recursive formula for a power series solution is a2 a3 Find the following in terms of ag…

A:

Q: Consider a surface with a metric tensor 2uv gij = u² 2uv 0²2 where x¹ = u and x² = v. What is the…

A: Given information:Metric tensor , where  and .To find:The connection coefficient .Concept…

Q: Use the linear Finite-Difference method to approximate the solution to the following boundary-value…

A:

Q: Find the derivative of the function. y'(x) = y = *sin(x) Jcos(x) In(3 + 5v) dv

A:

Q: A curve is given as y = få log(x) dx Eveluate y for a = 1.88 and b = 7.9 Give your answer to 3…

A: Here we have to find the given definite integral.

Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: above should be added, multiplied, divided or composed to create the graphs below.

A: This implies thr given graph can be obtained by adding, multiplying or composing the  functions…

Q: The limit is equal to 0 ∞ -3 O 3 lim x→0 St³+27 dt X

A:

Q: A sheet of water of uniform thickness (h= 0.03 m) flows from the device shown in the figure below.…

A:

Q: Suppose that Tesla has dealerships in Fresno and Walnut Creek and manufacturing facilities inMenlo…

A: Given Information:Tesla has dealerships in Fresno and Walnut Creek.Manufacturing facilities are in…

Q: Laplace transform to solve th-

A:

Q: The system of first order differential equations y₁ = 5y₁ + 1y2 32 y₂ = −4y₁ + 1y2 where y₁ (0)= 4,…

A:

Q: a. Find the eigenvalues and eigenvectors of the matrix y₁ (t) = y₂(t) = λ₁ [y₁ (0)] L32 (0) = 21 24]…

A:

Q: 2. i) State the equations of the horizontal asymptotes of the functions below. ii) Verify the end…

A:

Q: The Taylor series for f(x) = e at a = - 2 isen(x + 2)". n=0 Find the first few coefficients. CO www.…

A:

Q: An alphabet Σ consists of four numeric characters (1,2,3,4) and seven alphabetic Characters…

A:

Q: Show all calculations. Show that the following competition model does not admit closed orbits when…

A: We have a competition model represented by a system of differential equations.The goal is to…

Q: A table of values of an increasing function f is shown. X f(x) 10 lower estimate upper estimate 14…

A:

Q: 4. Find the solution of the vibrating string problem ᎧᎳ ᎧᎳ + əx² dy² with the boundary conditions W…

A:

Q: pply the theorem L(f* g) = L(f)L(g) to find the inverse Laplace transform; also do it in mother way…

A:

Q: can this be done on paper?

A:

Q: Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid…

A: We have to find how many valid passwords are there with the given restriction(s).

Q: from A to B. B 2 z dx + 2ydy + 2xz dz A Let M = z², N = 2y, and P = 2xz. Apply the Test for…

A: Integral

Q: Consider the equation 26 -1 = 0. (a) Find all the solutions to the above equation over C. (b) plot…

A:

Q: find each of the following on the graph: odd vertex, even vertex, bridge, loop, circuit, vertex of…

A:

Q: The object in linear regression is to obtain an equation of a curve that minimizes the sum of…

A: Given that: "The object in linear regression is to obtain an equation of a curve that minimizes the…

Q: 1. The following data represent the growth of a bacteria population over t Number of Hours 0 7 20 42…

A: The growth of the bacteria is typically modelled using the exponential growth formula.Let P(t) be…

Q: Let T be the linear transformation defined by T(x, y) = (6x - 5y, 3x+y, x4y, -x - 3y). Find its…

A:

Q: 1. 2. The degree and leading coefficient of f(x) = -x + 3x² - 2x³ + 5 is a) degree of 1 with leading…

A:

Q: 1. Let S be the portion of the graph z=4 - 2x² - 3y² that lies over the region in the xy-plane…

A: \We have to set up the double integration

Q: Let R denote, as usual, the set of all real numbers. Consider the following two functions: ƒ : R → R…

A: Given:The functions and  are given as: given by ; given by ., where  is the set of all real…

Q: How many triangles can be formed whose corners lie on the grid? A triangle has to have nonzero area.

A: A triangle have 3 vertices. So for draw a triangle it need to 3 distinct points. The given grid have…

Q: Desmond plans to sell his homemade dog biscuits. He has baked 143,265 biscuits. He is planning to…

A: The divisibility rule for 5 is that a number is divisible by 5 if its unit digit is 0 or 5. In other…

Q: 2. Compute [fs xy dS, where S is the surface of the tetrahedron with sides z = 0, y=0, x+ z = 1 and…

A: We have to Compute ∫∫S xy dS, where S is the surface of the tetrahedron with sides z = 0, y = 0, x +…

Q: 4. The behavior of the system is a sink, or a stable node. x' = x + y, y' = x + 2y

A:

Q: Let G be a graph with n ≥ 3 vertices that has a clique of size n − 2 but no cliques of size n − 1.…

A:

Q: 2. a. Use the operational properties to find 8s-16 Find L¹ -4s +15]

A: We have to find Note: According to guidelines we are allowed to solve one question at a time. Please…

Q: Let fig: DR be continuous at ce D. Prove that fg is continuous at c.

A:

Q: Consider the following differential equations. x = 4y², x(7) = 1 P(y) = dx Find the coefficient…

A:

Q: Problem: Consider a particle of mass m moving along the x axis under the action of a force, F(x),…

A: Given force function: (a) To find v(x), the velocity as a function of position, we use Newton's…

Q: = e. Convert from multiplicative to additive notation: (1) a²b³; (2) a=²(b=¹c)² =

A: Here we have to convert the multiplicative notation to additive notation of1) a2 (2) a-2(b-1c)2…

Q: You've observed the following returns on Mary Ann Data Corporation's stock over the past five years:…

A:

Q: 2.Let be a company whose total revenue and total costs, in dollars, are given respectively by: R(q)…

A:

Q: Given f(x) zero(s). = x²+x-12 (x-1)(x+4) determine the equations of all asymptotes, coordinates of…

A:

Q: 2 3. (a) Consider the function f(x) = x - x + 1 and starting point x₁ = 0. Show that the sequence…

A: