First, compute the gradient of the function p(x,y)=√√9-x² - y². Then evaluate it at the point (-2,1). The gradient is Vp(x,y) = (1.1). 2

Q: Let f: R → R³ be defined by f(x) = (x, 6x², 3x). Is ƒ a linear transformation? a. f(x + y) f(x) +…

A:

Q: can you write this on paper please

A:

Q: Evaluate the following integral, Sszds, where S is the part of the sphere x² + y² + +z² = 49 that…

A: Given that the sphere  that lies above the cone To evaluate the integral where S is the part of the…

Q: A healthy child's systolic blood pressure p (in millimeters of mercury) and weight w (in pounds) are…

A:

Q: Write six different iterated triple integrals for the volume of the tetrahedron cut from the first…

A:

Q: Find the electric flux PE across the part of the cylinder x² + y² = 9,0 ≤ z ≤ 2, in the direction of…

A: Given information:The electric field is given as .The surface is a part of the cylinder defined by…

Q: -10 X = a+ 10 2,0 -10 Write x as a linear combination of a and b. 2.0 b. 18 Hint: The preview shows…

A:

Q: Using the first isomorphism theorem, how would you prove that G/K is isomorphic to G. I already…

A:

Q: Let a, b eN with b>1 and with gcd(a, b) = 1. Then has a terminating decimal expression iff .... Now…

A: Given Information:List of fractions provided as:Objective:Complete the conjecture that the case is…

Q: Factor x4 1 completely in R[x] and then factor it completely in

A:

Q: Let D be the region shown in the figure that lies inside the square with vertices (±3, 0) and (0,…

A: We have to find ∫C2Fdr Using Greens Theorem.

Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A:

Q: 2. Given the following functions f(t), use the formulas to find the Laplace transform c) f(t)=(e²¹ -…

A:

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)=x₂…

A:

Q: The matrix A = [-62 -12] 285 55 A₂ = -5 with eigenvector v2 A EDE¹ where E-¹ is E and D is the…

A: The matrix  has eigenvalue  with eigenvector  amd eigenvalue  with eigenvector .Forming the matrix ,…

Q: Use this equation, b b [ sin² kx dx = cos² kx dx = (b − a) S a a To evaluate the following integral…

A:

Q: Which of the following transformations are linear? Select all of the linear transformations. There…

A:

Q: Follow the steps below to solve the given differential equation using series methods. Assuming the…

A:

Q: Can you answer part c, d and e of the question?

A: As salesman offers to deposit 30% followed by 12 monthly payments of $1150 for Bruce to purchase car…

Q: Find the corner points of the region. (Order your answers from smallest to largest x, then from…

A:

Q: Sketch the level surface of the function for w = 3. w = f(x, y, z) = x² + y²+z² + 2y

A:

Q: For n, ke Z, k0, we denote by A(n, k) the set of integers that are congruent to n modulo k: -2k+n,…

A:

Q: Let V, W be a pair of vector spaces and A : V → W be a linear one image. Then A(V ) is a linear…

A:

Q: You have a chance of a lifetime to creatively design beautiful pieces of artwork, while illustrating…

A: The objective of this question is to understand the relationship between fractions, decimals, and…

Q: Use the method of undetermined coefficients to find a particular solution of DE and solve the given…

A:

Q: Find the equation of the line passing through the point (2, -7) and perpendicular to the line 3y =…

A:

Q: OA. T(A) trace(A) from R3x3 to R OB. T(A) AT from R4x5 to R5x4 2-4 ¹ [²3 3] 6¹]-[² 8 85 0 C. T(A) =…

A: Definition used .

Q: can both parts be written on paper please, if you can only do one then let it be part

A:

Q: Problem #10: Find the flux of F(x, y, z) = yi — xj + 7k across S, where S is the helicoid with…

A: The objective of this problem is to find the flux of the given vector field F across the surface S.…

Q: (a) u(c) u" (c(t)) c'(t) = (B − y) u'(c(t)). For the remainder of this question, the utility…

A: Given: The differential equation  where .To show that the differential equation can be written in…

Q: Consider the functional 1 S[y] = f'da dx √1+x+y¹2, y(0)=A>0, y(1) = B > A. Show that the function…

A:

Q: a. The dimension of the subspace His b. Is {14x² + 12x + 11, 9x² + 8x +7,- (22x² + 20x +17)} a basis…

A:

Q: Your answer is partially correct. State the starting value a, the growth factor b, and the…

A:

Q: (a) S = {(a,b): (b) S = {(a,b): a € Z+, b € Z+, and a b} a € Zt, b € Zt, and 3|(a + b)

A:

Q: Consider the following linear optimization model: (P) max s.t. x1 + 2x₂ -x1+x₂ ≤ 6 x12x2 ≤ 4 X1, X2…

A: Given Information:The Linear programming model is given as follows:Subject to the…

Q: Answer Q-3

A: The addition rule of probability states that the probability of either of two mutually exclusive…

Q: Apply the eigenvalue method to find the general solution and the corresponding particular solution:…

A:

Q: Consider the following line integral. fxy dx + x²y³ xy dx + x²y³ dy, C is counterclockwise around…

A:

Q: olve the system of differential equations given in matrix form for the general solution. We must do…

A: Given that the system of the differential equations i.e.                     Where To find the…

Q: 4 1 ---[[]] } = span ' 2 2 Let H Determine a basis for H which consists of a subset of the given…

A: Given thatWe have to determine a basis for H which consists of a subset of the given vectors.

Q: Let V, W be a pair of vector spaces and A : V → W be a linear image. Then A(V ) is a linear subspace…

A:

Q: An object is thrown vertically upward from the ground with an initial velocity of 25 m/s. Determine…

A: V2 =U2 +2aSwhere V=terminal velocityU=initial velocitya=acceleration of object at any timeS=Total…

Q: Compute the surface integral of the function f(x, y, z) = 2xy over the portion of the plane 2x + 3y…

A:

Q: 4. After exposure to certain live pathogens, the body develops long-term immunity. The evolution…

A:

Q: 1. For the lamina in figure #1 compute the moment of Inertia about the x-axis. The density is p(x,…

A:

Q: Read the SageMath code for understanding, and evaluate the SageCell. Use your findings to provide a…

A: Given Information:To find:The matrix  such that  using sage math code.

Q: Problem #2: Consider the following matrix A and column vectors K₁, K2, and K3. [5 6 6 6 5 6 6 6 5 A…

A:

Q: Solve the following recurrence relations, i.e., find closed-form expressions for an. For each case,…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: [[ 1² dA, where R is region in the third quadrant between the circles of radius 2 and 3 R centered…

A:

Q: Problem #1: Find the value of a for which the following matrix is orthogonal. √a √a· ·√a √a+·…

A: