4. A tank is shaped like an upside-down square pyramid, with base of 4 m by 4 m and a height of 12 m (see the following figure). How fast does the height increase when the water is 2 m deep if water is being pumped in at a rate of 2/3 m³/sec? 12

Q: Find a) the characteristic equation and (b) the eigenvalues and eigenvectors of A below, then decide…

A:

Q: Find a general solution to the differential equation. 1/4y"+4y=3tan4t-1/3e^3t..........the general…

A:

Q: A solid in the first octant is bounded by the two spheres x^2 + y^2 + z^2 = 1 and x^2 + y^2 + z^2 =…

A:

Q: b) dx dt dy dt = = 4x - 2y 2t 5 = 3x-y-2t-3

A:

Q: Determine whether each of the following sets are subspaces of R³ with the standard operations. sure…

A:

Q: Calculate the lim sup and lin inf of the following: √1+n² 2n-5 1. Xn 2. Xn where yn is bounded 3.…

A:

Q: Using the Cauchy-Riemann Equation. f=u+iv calculate the value of the function for the point z=-1

A: To find: Value of f at z=-1, where f=u+iv.

Q: Apply a theorem from the lecture to determine if there is a choice of rational numbers a, b, c, d…

A:

Q: In each of Problems 25 through 30, using integration by parts, find the Laplace transform of the…

A:

Q: As a spring is heated, its spring "constant" decreases. Suppose the spring is heated so that the…

A: Question-1 The displacement x(t) is governed by the initial value problem. 2x"(t)+x'(t)-(7-t)x(t)=0;…

Q: Consider the vector field F(x, y) = (x², −y). If (x, y) is in the first quadrant then the vector…

A: Part 1. (x, y) is in the first quadrant.  => x > 0 and y > 0 => x2 > 0 and - y < 0…

Q: Find the mass, in kilograms, of the portion of the cone x² + y² = z² between the planes z 3 if the…

A:

Q: Estimate the following integral using the trapezoidal rule with n=10. 5² = 1+x² dx

A:

Q: Let T: R³ R³ be a linear transformation such that 7(1, 1, 1) = (4, 0, -1), 7(0, -1, 2) = (-5, 3,…

A:

Q: A nine-member Olympic committee is voting using preference ballots to decide which one of A, B, or C…

A:

Q: Which of the following functions is a potential function for the conservative vector field F(x, y,…

A:

Q: Q1. The position vector of a moving point is given as: R()=(2 Inr) (-((+1¹) j (a) Express the unit…

A: Solution:

Q: DIFFERENTIAL EQUATIONS PROOF: Find a 1-parameter family of solutions for f '(x) = f (-x)

A:

Q: Use triple integrals to find the volume of the solid bounded above by  the cylinder z = 4 - 3y2 and…

A: Given equations are z=4-3y2z=4x2+y2 The two curves intersect when 4-3y2=4x2+y24x2+4y2=4x2+y2=1

Q: b) 1: Find the volume of the solid obtained by rotating the region bounded by the curve about the…

A:

Q: Q5. Sketch, evaluate, and reverse the integral: [[* dy dx/

A: 5. Given integral is ∫02∫1ex dy dx   To sketch, evaluate and reverse the integral.

Q: (a) Let F(s) = L{f(t)}, where f(t) is piecewise continuous and of exponential order on [0, ∞). Show…

A: Solution a: Given that f(t) is piecewise continuous and of exponential order on [0, ∞). We have to…

Q: QUESTION 1. In each case, find the solution to the linear homogeneous system of differen- tial…

A:

Q: QUESTION 3. Use a power series to solve the differential equation y' = -3x²y, with initial condition…

A: Please find attachment

Q: Verify that λ, is an eigenvalue of A and that x, is a corresponding eigenvector. A₁ = 5, x₁ = (1, 2,…

A:

Q: 2: Find the component of u = 2i+j - 3k that orthogonal to v = 3i – j, then verify your result.

A: Solution:

Q: аги аги + дх2 т дуг = 0 =

A: We have to solve given problem:

Q: Let C be a surface with equation x = h (y, z), and R be its projection on the yz-plane. If h has…

A: To Examine: whether the given statements are true or false.

Q: Let x = 0.9 = 0.999...; Prove x = 1. (Hint: Can you write x as a geometric series ,  arn-1?)

A: The given sequence is x=0.9=0.99=0.999=...1. To Prove: x=1.

Q: uppose the function y=h(x) is nonnegative and continuous on [x,B], which implies that the area…

A:

Q: The graph shown below measures the height, in feet, of a stone stuck in a tire after t seconds.…

A:

Q: Find the absolute maximum and absolute minimum values of the function, if they exist, over the…

A: Let us consider the given function f(x). The maxima and minima is obtained as, If f''(x)>0 then…

Q: Suppose the random variable T is the length of life of an object (possibly the lifetime of an…

A:

Q: Find the volume of the solid region in the first octant inside the cylinder x²+y2=4 and between the…

A:

Q: Part 3. Use separation of variables to obtain a product solution to the following: to be the form of…

A: Given question is as follows

Q: Question 3: Derive the expression for the following estimator which minimizes the squared sum of…

A:

Q: Solve the following DE: y' = (x/y) / (y^2+1/x^2-1) Solve the following DE: y apostrophe equals open…

A:

Q: Find the general solution of the given higher-order differential equation. y(4) - 2y" + y = 0 et +…

A:

Q: If yields ao ln x + a₁ ln x + 1| + + an ln |x +n + c where ai (i = 0, 1,,n) and c are real…

A: Partial fraction decomposition is a technique to represent a rational function into proper rational…

Q: Determine the x-coordinate of the centroid of the shaded area by integration. 3 1 25 37 Answer: Xi…

A:

Q: -X (D² — 1)y=eX (2sinx + 4cosx).

A: As per our company guideline we are supposed to answer only first qs, kindly post remaining qs in…

Q: FIND THE TOTAL MASS OF THE WIRE WITH DENSITY P t't + 2ty, ztj, ріх, у) - бду, 044 (0) :

A:

Q: Notice that if you don't use Equation 3.4, then NO CREDITS. f(x)=1-x-x², a=0 1.

A:

Q: Find the Fourier series of the periodic function coincident with the given function and plot its…

A: Introduction: The Fourier series representation is a series representation of a periodic function.…

Q: One type of strontium has a radioactive decay rate of 1.4% per day. If 30 pounds of this strontium…

A:

Q: Romberg Integration - example dx=2 compute R5,5 Sinx dr

A:

Q: a. Apply Horner's rule to evaluate the polynomial p(x) = 3x5 - 2x¹ + x³ 2x+5 at x = -2. b. Use the…

A: a Given polynomial is px=3x5−2x4+x3−2x+5..and.x=−2. We have to evaluate the polynomial px at x=−2 by…

Q: A series RL circuit with R = 50 2 and L = 10 H has a constant voltage V = 100 V applied at t = 0 by…

A:

Q: Find the Fourier series expansion of the periodic function whose definition in one period is: TL…

A:

Q: A nonhomogeneous equation and a particular solution are given. Find a general solution for the…

A: