The heat flow vector field for conducting objects is F= -kVT, where T(x,y,z) is the temperature in the object and k is a constant that depends on the material. Compute the outward flux of F across the surface S for the given temperature distribution. Assume k = 1. T(x,y,z) = 50e-x-Y; S consists of the faces of the cube |x|≤3, y ≤3, |z|≤3. The outward flux is (Type an exact answer.)

Q: Parametrize the path y a circle of radius 3 centered at z = 2 + 3i. Calculate the integral f,z² +…

A: a) Parametrize the path γ a circle of radius 3 centered at z=2+3i. b) Integral ∫γz2+zdz using the…

Q: Question 2 Solve the inequality. Write the solution set in interval notation. -4u(u + 2)2(3-u) > 0 O…

A:

Q: The table below lists the height h (in cm), the age a (in years), the gender g (1="Male",…

A:

Q: Does the following series diverge, converge conditionally, or converge absolutely? Explain your…

A:

Q: 2. Andrey has an obligation to pay a sum of 4000 in four years from now and a sum of 5500 in five…

A: Given that Andrey has an obligation to pay a sum of 4000 in four years from now and a sum of 5500 in…

Q: Could you do a formal proof of the following: (you may rely on Theorem 4.6.1, that is irrational).…

A:

Q: . Find the inverse Laplace transform L¹. L' s² +6s+9 (s-1)(s-2)(s+4) f

A:

Q: Write a system of linear equations for the graph below. -8 -7 -6-5 4 0 -2 144 6 00 X 08 S

A: From graph we can find linear equations below

Q: Let f(x) = sin(10x) Find approximate value of the derivative for x =11, h = 0.1 Use forward…

A:

Q: Using the distributive property of multiplication over addition, we can factor as in x² + xy = x(x +…

A:

Q: Evaluate the line integral, where C is the given space curve. [xerza xez ds, C is the line segment…

A:

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

A: Note: According to guidelines I will answer first question.

Q: 6. Let F = (4e" cos(4x), e sin(4x) + 2y) be a vector field and let C be a curve in the first…

A:

Q: Discuss and describe exponential order a. Define and draw graphs to illustrate, etc. Give an example…

A: We need to discuss and describe exponential order α.  Give example: of a function that is less than…

Q: Solve the following problem using artificial variables. Maximize z= 3x₁ + 2x₂ subject to the…

A:

Q: Joey took examinations in Algebra, Physics, Chemistry and English and scored 84, 79, 88 and 93…

A:

Q: Determine the QR-factorization A = 0 3 4 of the matrix -20 -14 27 -4 11 -2

A: A=0-20-14327-4411-2

Q: • Show that if m divides 3, then m divides 9. (We say a divides b if there exists an integer k such…

A: Let  m divides 3 .  Then there exists an integer k such that 3 = mk. Now, 9 can be written as…

Q: Find the difference of the angles. Write your answer in DᵒM'S" form. 120°45'29" and 11°39'4" 1

A: Given angles are 120045'29'' and 11039'4''. We will find the difference between these two angles.

Q: Evaluate the integral. √9-²22 √9-² 1 [** (@²+²+29)1/2 dydz dz = √9-x²

A: The given problem is to evaluate the given triple integral over the given limits of x,y,z for the…

Q: A coin is tossed five times. What is the probability that the outcome is five heads, given that…

A: Given that a coin is tossed five times and we want to find the probability of getting five heads…

Q: The gradient of f(x, y) = x sin (y²) is the vector field F (x, y) = at (2,√π/6) and ending at…

A: Here we are given that the gradient of f(x,y)=xsin(y2) is the vector field F(x,y)=sin(y2)2xycos(y2)

Q: Add as indicated in the following exp (2)/(5(k-3))+(4)/(3(k-3))

A:

Q: 0 -2 Based on the graph of f'(x), Estimate the following about f(x). (a) Where is f(x) increasing?…

A:

Q: Classify each singular point (real or complex) of the given equation as regular or irregular. (t² +…

A:

Q: Let f1(x) = − 1 6 (x − 1)(x − 2)(x − 3), f2(x) = 1 2 x(x − 2)(x − 3), f3(x) = − 1 2 x(x − 1)(x − 3)…

A:

Q: Let S be the surface parametrized by r (u, v) 0 ≤ ≤ 27. What shape is S? a sphere part of a sphere…

A:

Q: Find all eigenvalues with their algebraic multiplicities. 1000 1500 1510 1515 Let X₁ and ₂ be the…

A:

Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system. X(t) = X' = +…

A:

Q: Which number needs to be the last term of the sequence 1, -2, 3, -4,5,... so that the sum would be…

A: If we expand the given sequence, then it will be        1, -2, 3, -4, 5, -6, 7, -8, . . . . . . . .…

Q: What ????????? Really????     Is clearly mentioned to use forward difference method.   Please…

A:

Q: Determine all the singular points of the given differential equation. (t²-t-2) x² + (t+1)x' - (t−…

A:

Q: Let S be the unit sphere centered at the origin. What is ſſ (3+z) dS? (Use syntax like 2*pi/3 .)

A:

Q: Oprah says I can solve this Primal Min LP min w = 3y₁ + 2y + Y3 8.t. Y1 + y2 + Y3 Y2 - Y3 91 + y2 +…

A:

Q: ii) 1₁ = √9n²+n- 3n. In = 2.

A:

Q: Find all eigenvalues with their algebraic multiplicities. [555 555 55 Let λ₁ and λ₂ be the…

A:

Q: Determine £¹{F}. F(s) = 3 6s³ - 3s² - 9s+27 3 s (s-3)

A: Introduction: To find the inverse Laplace transform , first find the partial fraction of the given…

Q: Given the Jacobian matrix below and a critical point (1, 2) of the Lagrangian is (2,4), which of the…

A: Here the Jacobian matrix is given by Dhx1,x2=2x144x2 Here the critical point of x1,x2 of the…

Q: Find the area of the region which is inside the polar curve T= 5 cos(0) and outside the curve T=4-3…

A: Since you have posted multiple questions  so as per guidelines we will solve the first question for…

Q: True or false: If x > 0, then True False x ≥ 1+ln(x).

A:

Q: juices will be packaged in 2-qt (64-oz) cartons. One carton of pineapple-orange juice requires 7 oz…

A:

Q: For the tableau, Assume columns labeled as has optimal tableau [1 0 0 Z 21 22 81 [1 82 rhs -4 -11 00…

A: For the Table:                        1-4-1100004510340520130 has optimal Tableau:…

Q: Evaluate the definite integral below. -2 1² (12x+18) (-2x² - 6x - 3) ³. dx Enter your answer in…

A: Given that the definite integral  ∫-3-212x+18-2x2-6x-33 dx

Q: A population of viruses is increasing at a constant relative growth rate in the bloodstream of its…

A: (a) Given that t=0 then A(0)=290 at t=3 then A(3)=1720. Since it is known that population virus is,…

Q: 2. Consider the power series √n(x-1)". n=0 (a) What is the centre of convergence of the power…

A:

Q: Let B be the standard basis of the space P₂ of polynomials.Use coordinate vectors to test whether…

A:

Q: Sketch a contour map of f(x, y) = y - x², labeling the value of f on each contour. Then fill in the…

A: Given the function fx,y=y-x2. The contours are given by y-x2=c, for c∈ℝ. Let us take integer sample…

Q: ath 2110Q need it. convert the following triple integral from Cartesian coordinates to cylindrical…

A:

Q: Find the directional derivative of f(x, y, z)=1/√4x² +9y²+z² at P(1, 1, 0) in the direction of [2,…

A: A function is fx , y , z=14x2+9y2+z2 . To Find: Direction derivative at 1 , 1, 0in the direction of…

Q: Find the flux of F= ²7 + x³z³7 + 3xzk out of the closed region bounded by the planes z = 0, y = 0, x…

A: