Set up and evaluate the following optimization problem: to carry a suitcase on a plane the length+width+height of the box must be less than or equal to 62in. Assuming the height is fixed show that the maximum volume is V=h(31-(1/2)h)^2 what height allows you to have the largest volume?

Q: 4 A. 1 B. 2 C. 3 D. 4 If the correct answer in (2) is equal to -λ, how many case/s is/are possible?

A: If the equation obtained after the separation of variable is equated with -λ. then the number of…

Q: we the initial value problem below using the method of Laplace transforms. 2ty'' - 6ty' +6y= 18,…

A:

Q: Application of Optimization Problems. Use bordered determinants to check the following functions for…

A:

Q: Find three linearly independent solutions of the given third-order differential equation and write a…

A:

Q: Using Gauss-Jacobi, compute a solution to the problem Ax=b where 2-4 7 2 -2 A = 8 3 49 7 b= 16 23

A: We need to determine the solution of the the system: Ax=b using the Gauss-Jacobi method. Here,…

Q: A = 1 0 0. Find th 01

A: A generalisation of diagonalization, singular value decomposition of a matrix is a kind of change of…

Q: Find (by hand and calculator) the least squares fit and RMSE error for the periodic models y = F3(t)…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: By inspection, find the eigenvalues of the following matrix: Enter the eigenvalues in increasing…

A: Eigenvalues of the matrix

Q: 1. Determine the interval of convergence for the series: 27 81 - x³ +²=²x² + · ... 7 3 9 3x + 5x²+3…

A:

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 5t³ L{f(t)} = =

A: Given function is f(t) = 5t3

Q: Consider the function f(x, y) = 2x²y² - y² - 8x² Compute the stationary points of the function f(x,…

A:

Q: 5. Use the difference quotient (Newton's quotient) to find when the function f(x) = 2x² - 4x + 5 has…

A: Introduction: The definition of the derivative of a function includes the difference quotient…

Q: For the next three exercises, calculate the area of the region. 3 Bounded by the circle r = 2 sin…

A: The area of the region bounded by the function r=fθ for α≤θ≤β is: A=12∫αβr2 dθ

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 area inside the inner loop of r = +5 12cosθ .

A: Given equation as r=5+12cosθ

Q: Q4. Find the inverse Laplace transform of 2s+19 s²-6s+58

A:

Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: 2 Given definite integral is ∫−11x2+1dx. We have to estimate the given definite integrals by using…

Q: Let Σ be part of the paraboloid z = 3 - x² – y² that lies above the xy-plane, oriented downward,…

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: = { [ * ] | ² ≥ 6 } Consider W = (a) Determine whether W is closed under addition, is closed under…

A: Let V be a vector space and W be the subspace if it follows, If w1,w2∈W  then w1+w2∈W that is…

Q: Calculate the Fourier series of the periodic function depicted in the figure below. T(X) 1 0.8 0.6…

A: Introduction: The Fourier series representation is a very important infinite series representation…

Q: 4. Solve for x log (35-x³) log (5-x) = 3

A: Given log35-x3log5-x = 3

Q: Evaluate the double integrals025 025 f(x,y) dx dy, and f(x,y) as given in the following ta X 0.25…

A: We need use the given table to approximate the integral: ∫0.251∫0.250.75f(x, y) dx dy.

Q: In Problems 6-8, let R be the region bounded by the lines y = 4-x, y = 1, and x = 1. Each problem…

A:

Q: Determine the values of x and y for which the 2x2 matrices A and B are equal. 1 x A y -4 X = y = 1 B…

A:

Q: Express the function below using window and step functions and compute its Laplace transform. Ag(t)…

A:

Q: -- 0 Let W₁ = and W₂ = (88) (a) Find a basis for W₁ W₂. What is dim(W₁ W₂)? (b) Show that R³ = W₁+…

A: Let the two vectors spanning W1 be u1,u2 and the two vectors spanning W2 be v1,v2 respectively.  If…

Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: 3 Given integral is ∫121s2ds. We have to estimate the given integral by using the Trapezoidal rule…

Q: B/ Evaluate the double integrals 0.25 0.25 f(x,y) dx dy, and f(x, y) as given in the following ta…

A:

Q: dP/dt + 2tP= P + 6t - 6 a) Find the general solution of the given differential equation. b) Give the…

A: To solve this problem ,we use the following concepts  1)interval of defination: let  dp/dt +f(t)p…

Q: (d) If F(x, y) = (4x² - y², -2xy), then f(x, y) =

A:

Q: Prove that R" is connected; Prove that [0, 1] × [0, 1] (with the relative topology from R²) is not…

A:

Q: Example 0.8.1. Evaluate SSS √² + y² + z²dV, where V is the solid that is inside the cone z = x² + y²…

A:

Q: On the same set of axes, use technology to graph the pair of functions for the given range of x.…

A:

Q: Use the procedures illustrated in this example or in this video to balance the given chemical…

A:

Q: Use either Gaussian elimination or Gauss-Jordan elimination to solve the given system of linear…

A: x1-x2-x3=32x1+3x2+5x3=-19x1-2x2+3x3=-19 Matrix representation 1-1-12351-23x1x2x3=3-19-19

Q: Consider the three-dimensional Euclidean space with coordinates x, y and z. The intersection of the…

A:

Q: Nine students are participating in a race. In how many ways can the first three prizes be won? 504…

A: Given that 9 students are participating in a race. Evaluate the number of chances of any student…

Q: 3. Prove that, Σk() = n2n-¹. k=1

A:

Q: At a party, 10 people speak English and 8 people speak French. 5 people are bilingual, and every…

A:

Q: Solve the initial value problem 25y" — 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t) =

A:

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

A:

Q: Consider the matrix mapping A:R6→R³ where 1 0 A = r2 0 LO 2 0 2 0 4 0 0 1 3 1 2 4 0. and the…

A: We are given the matrix A=210400022131000240 To find basis for kernel, find rrefA.…

Q: Find the general solution to y"" + 23y" + 136y' + 114y = 0

A:

Q: Could you please solve d) too

A: given matrix  A=510510-116 find the transpose AT=55-1111006 (d) determine if the matrix A+AT is…

Q: Determine whether the function is a linear transformation. 0 0 1 = 0 1 0 A 1 0 0 T: M3,3 M3,3, T(A)…

A:

Q: b) Find the Fourier Transform for the following function: - {ezu 0 F(t) = -1<t <1 otherwise

A:

Q: A client's medication bottle contains 36 Motrin tablets. If the client took out 4 tablets from the…

A: The client's medication bottle contains 36 Motrin tablets. The client took out 4 tablets from the…

Q: Determine h if V = 1.1535 m³ and r= 1m using Fixed point iteration on the given convergent equation.…

A: Given function is h=h3+3Vπ3r We have V=1.1535 m3, r=1 m. So we have h=h3+1.1023 For more convenient…

Q: Consider the matrix A = 5 1 0 5 1 0 l-1 1 6 a) Diagonalize the matrix in the form A = SAS-¹, with S…

A: Solution a) Given matrix is A=510510-116 Let the eigenvalue be λ, then…