Evaluate 1 x² + y² + z² E between the spheres x² + y² + x² + y² + z² ///₂ = dV, where E lies ² = 4 and = 16 in the first octant.

Q: Find the critical points of the functions f (x, y) = x² + 2y² − 4y + 2x, g (x, y) = x² — 12xy + y…

A:

Q: Calculate f (3xy + 4e²) dS, where S is the triangle with vertices (0, 0, 3), (1, 0, 2), and (0, 4,…

A:

Q: 5. Let A be a 3 × 3 real matrix which is not diagonal. If (A + I)² = 0, find the real canonical form…

A: If A+I=O  then A=−I, which diagonal matrix.So A+I≠OTherefore (x+1)2 is minimal polynomial and(x+1)3…

Q: s. t. Max 14x1 + 7x2 2x₁ + 5x₂ ≤ 14 x₁ + 2x₂ ≤ 6 x1 x₁ ≥ 0, X₂ ≥ 0

A: "Since you have posted a question with multi subparts, we will solve the first three subparts…

Q: Question 1 For each function f(x) given below, define F(x) = f(1) dt. Is F(x) an antiderivative of…

A:

Q: A mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a…

A:

Q: IS F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F…

A:

Q: Suppose you have a set of 15 elements, and you want to form subsets from this set. How many…

A:

Q: 13 A 10 Q Apply the sorted edges algorithm to the graph above. Give your answer as a list of…

A:

Q: Select all equations that are not linear differential equation □+u'(t)- t = 0. □x²b²=b""+b'. 0x³…

A: Consider the differential equations:a) b) c) d) e) To Find:Which of the above equations is not the…

Q: 29. Two wheels are fixed to an axle as shown. Due to their different sizes, the two wheels trace two…

A:

Q: Sketch the following parametric curves on your work sheet. Attach the photos to this question. 4…

A:

Q: Prove that the set of numbers Q(√2) = { a+b√2: a, b = Q} is a field.

A:

Q: Problem 5 Let p be a prime number and a, b are any nonzero integers such that a = b (mod p² − p).…

A: Given that: p is a prime number and a, b are any nonzero integers such that a ≡ b (mod p^2 - p).we…

Q: K For the piecewise function, find the values h( – 6), h(2), h(5), and h(6). -2x-16, for x < -4 h(x)…

A: You have posted multiple questions. According to our guidelines we solve the first question. That is…

Q: Find gcd (3084, 1424)

A:

Q: 8. Show that Q[√3] = {a+b√√3 | a,b ≤ Q} is a field. You may first show that it is a ring by showing…

A: To show that  is a field, will follow these steps:1. Show that  is a subring of a well-known field…

Q: The set B={1+t, 2t-t, 1+t+t} is a basis for P₂. Find the coordinate vector of p(t)= -3+7t-7t…

A:

Q: 7. Recall that if m ≤ f(a) ≤ M on [a,b], then m(b − a) ≤ f(x) da ≤ M(b − a). Use this fact to…

A: (a) f,′,(,x,) f,(,0,) f,′,(,x,) ​ comma space integral subscript negative 1 end subscript…

Q: equal

A: Euler's phi (or totient) function of a positive integer n is the number of integers in {1,2,3,...,n}…

Q: Use the results from a survey of a simple random sample of 1081 adults. Among the 1081 respondents,…

A:

Q: HW4.3. Suppose that LA=In. Show that the equation Ax=0 has only the trivial solution.

A:

Q: Suppose " + x = f (t), where f(t) is a periodic extension (with period=1) of the external forcing…

A: We have to find particular solution using Fourier series.

Q: Given a collection of data points {(x, yi)}₁ find the best least squares approxima- ax² + bx³. tion…

A: From the given data points are   , we need to fit the curve  by the method of least squares. Let…

Q: < Six people were asked to determine the amount of money they were carrying, to the nearest dollar.…

A:

Q: Find the slope-intercept form for the line passing through (7.4) and parallel to the line passing…

A:

Q: Compute the normal vector to the surface (u, v) = (2² – ²,u + v, u-v) at the point (2,4) and use it…

A:

Q: Find the degree and leading coefficient for the given polynomial. Degree: Number Leading Number…

A:

Q: Find the cosine of the angle between A and B with respect to the standard inner product on M22. 4 52…

A:

Q: Max 14x1 + 7x2 s.t. 2x₂ + 5x₂ ≤ 14 x₂ + 2x₂ ≤6 x₁ ≥ 0, x₂ ≥ 0

A: c) The corresponding dual model as follows

Q: Justify wether the following is an inner product or not =5x1y1-x1y2-x2y1+2x2y2 where x=(x1,x1) and…

A: By using axioms of inner product we have to show whether &lt;x, y&gt; is an inner product or not.

Q: Utilize spherical coordinates to calculate SSSµ z³ √√x² + y² + z²dV when His the solid hemisphere…

A:

Q: Use a technique of integration or a substitution to find an explicit solution of the given…

A: We have to solve the given differential equation.

Q: Evaluate sin sin(x) dx + z cos(y) dy + sin(y) dz where C is the elipse 25x² + 16y2 = 49, oriented…

A:

Q: Suppose that λ =A₁, A₂ are constants such that u(z,y) = F (z+ Ay) statisfied the PDE 82 -4 ( 5²2 U…

A:

Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A:

Q: a) i. Let M and 4 be any two numbers of the form 42+1 ii. Let Mand N be any off the form 4r +3 Prove…

A: Since you have posted multiple questions, we will answer the first question for you. If you want any…

Q: dy dx || xy + y3 x3

A:

Q: #6. Assuming for the cy!! we know the modern formelos key properties of conds and ·linders translate…

A: The given Archimedean statement can be translated into a familiar modern formula as follows:Let's…

Q: Determine whether the line integrals of the vector fields along the oriented curves are positive or…

A: Since the line integral is a dot product.When the angle between the direction field of flow and…

Q: Translate each argument into symbolic form. Then determine whether the argument is valid or invalid.…

A:

Q: ʼn each part, apply the Gram-Schmidt process to the given subset S of the inner product space o…

A:

Q: Problem 10 Let Find c, d, a. b. f(6.0), g(6.0), h(p.6.0) and V. y = √3 -L hp.6.0dpadde denote the…

A: The region is bounded by x=0.Which represents the yz plane.

Q: 62-30cos(XT) where t represents The maximum afternoon temperature in Granderson is modeled by t =…

A:

Q: Compute the normal vector to the surface (u, v) = (u² - v², u + v, u-v) at the point (2,4) and use…

A: Given  The normal vector to the given parametrized surface at a point is the cross product of the of…

Q: Find the general solution to the linear first-order differential equation: -+ dx 3x x²+1= 1 6x x²+1

A: The given differential equation,.The objective is to find the general solution to the differential…

Q: sement Practice Proble a. Use the Leading Coefficient the y-intercept by computing f…

A:

Q: 11. Identify R+¹ with the set Pn of polynomials of degree ≤n, via the corre- spondence (An, . . . ,…

A:

Q: 1. DEFINITE INTEGRAL AS RIGHT RIEMANN SUMS Show that the right Riemann sum R4 approximation of L'de…

A:

Q: Q1] (A) If F(x+y-2₁x² + y²)=0 where z=2(x, y) and дz дz -у-=х-у ду ах - 0 then prov

A: (.)  Leibniz rule :      Given ,(A).        where   and   .