12. f = 4y²- Z
Q: 1. A 64 lb object stretches a spring 4 ft in equilibrium. It is attached to a dashpot with damping…
A:
Q: 9. Let R+ denote the set of positive real numbers. Define a relation E on R+ as follows: a Eb if and…
A:
Q: Compute the line integral of the vector field F = (3y, −3x) over the circle x² + y² = 81 oriented…
A:
Q: 1- The purchased and installation cost of some piece of equipment are given as a function of weight…
A:
Q: What is the future value if $6,000.00 is invested for 2 years at 6% compounded quarterly?
A:
Q: If A is a rectangular matrix with more columns than rows and for some r.h.s. b, we can find a…
A:
Q: A surveyor stands some distance from a tunnel. From this point, she can see both entrances and has…
A:
Q: Find the angle (in radians) between the vectors u and v below. u= 0 1 N N V= IE Give exact…
A:
Q: Fill in the missing parts of the tabular method and write the final answer by multiplyi (-3x +…
A:
Q: Find the mass and center of mass of the plate that occupies the region and has the density function…
A:
Q: (1 point) Evaluate the following quantity by applying a change of base. where m = n = log65 (9.72) =…
A:
Q: Find the vectors whose lengths and directions are given. Try to do the calculations without writing.…
A:
Q: Compute the line integral of the vector field F = (3y, -3x) over the circle x² + y² clockwise JcF.…
A:
Q: Σ(1-4). 2 (a) Compute 5 Express your answer as a simplified fraction. 1 1 Σ(-A) 2 (c) Use induction…
A:
Q: • 111,₂³ Round your answer to four decimal places. Evaluate 2xz dV where E = {(x, y, z) | 1 ≤ x ≤ 3,…
A:
Q: Consider the 3 permitations in S.: 2 * = (1 ² 3 4 5 6); ** (123456) 62 2 3 4 " = ( 1 ² ² ± 5 6 )…
A: Given : σ=123456314562 , τ=123456241365, μ=123456524316 To calculate : a στb στ2c σ2μd τσ2e στσ-1
Q: Prove or disprove the following: (a) If X and Y are path-connected, (b) If A CX is path-connected,…
A: Let X and Y be topological spaces. We need to prove or disprove the following: If X and Y are…
Q: A consumer is maximising her utility function: U(x, y) = (x¹/3+y¹/3) ³, subject to the budget…
A: This is the problem of optimization.
Q: The pounds of bananas sold each week at all Metro Seattle Alberstons stores as a function of price,…
A:
Q: Let v = (v1, v2) be a vector in R2. Show that (v2, −v1) is orthogonal to v, and use this fact to…
A:
Q: A company manufactures z units of one item and y units of another. The total cost in dollars, C, of…
A:
Q: B. What is meant by complex conjugate of a complex number? Using an example show how division of…
A: A conjugate of a complex number is another complex number which has the same real part as the…
Q: Find the coordinates of the center of mass of the following solid with variable density. The…
A: We need to find the coordinates of the center of mass of the following solid with variables density.…
Q: Find a quadratic function associated with vertex (h, k) = (1, 0) and point (x, y) = (–3, 4) that the…
A:
Q: Calculate the integral of ƒ(x, y, z) = 2x² + 2y² + zº over the curve c(t) = (cos t, sin t, t) for 0…
A: To find line integral over the parametric curves
Q: Use the theory of Lagrange multipliers to find the point (a,b) on the curve y = ex with the minimum…
A:
Q: 3, 14 gives a basis for W (a) ₁ = (1,1,1,2,3), ₂ = (1,2,-1, -2, 1), uz (3,5,-1, -2,5), u = (1.2,…
A: As both the question are different we shall solve one question only as per the company guidelines.…
Q: Suppose that P(1), P(2),... are statements. Assume that you know only the following: P(3) is true. •…
A:
Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = 4x + 4y + 3z,…
A:
Q: A couple from Baltimore needs $40,717.69 as a down payment for their first home. If they invest the…
A:
Q: Find the present value for a $110,000 investment for 11 years at a compounded continuously at 5%.
A:
Q: The price of gasoline purchased varies directly as the number of gallons of gas purchased. Suppose…
A:
Q: given
A:
Q: Graph the solution set of the following nonlinear system of inequalities. x² + y² ≥ 36 x² + y² ≤81…
A: We have to draw
Q: Give the solution set to the system of equations -x+y-z=-4 2x-2y+2z=8 x-y+z=4
A:
Q: Use separation of variables to find, if possible, product solutions for the given partial…
A: Given∂u∂x=∂u∂y-------(1) Let u=X(x) Y(y) be the solution of equation Hence…
Q: For the followings problems, consider a function that is twice differentiable. This means that his…
A: 1) At inflection point h'(x) = 0 the interval in which the sign of h'(x) changes from positive to…
Q: Find the centroid of the region bounded by the given curves. y = x³, x+y = 30, y = 0 (x, y) =
A:
Q: (a) Use a graphing calculator to find the correlation coefficient for these data. Round to three…
A: Perform the mentioned steps on TI-83 calculator to obtain the required value. Turn on the calculator…
Q: The price of gasoline purchased varies directly as the number of gallons of gas purchased. Suppose…
A:
Q: A family of functions is given by f(x) = = (kx - b)e, where k ‡ 0. 1. Find the critical points of…
A:
Q: Consider the curve given by the polar equation An sketch of the curve looks as follows: T= cos(30).…
A: The given problem is to find the intervals of the theta for the given r(theta)=cos(3 theta) shaded…
Q: Use Newton's Method to estimate a root of the function f(x)=6x+4−e^x Use the initial estimate…
A: The given function fx=6x+4-ex We have to find the root of the function using Newton's method with…
Q: 13. Prove that if n ≥ 2, then 2 - 1 is not divisible by n.
A:
Q: Find an antiderivative F(x)of the function f(x)=−4x^2−7x+5 such that F(0)=1 F(x) = Now, find a…
A:
Q: Bribe 13. Show that the sequence where Sn = is convergent. 1 (login) loge
A:
Q: Consider a part of a graph of a function f: R → R (see the diagram below). We restrict f to various…
A: To see that graph is injective we have to see for different numbers a and b, the values of f(a) and…
Q: D²y + 2Dy = 4x − 6e-²x -
A:
Q: dy dt + 6y(t) + 9 y(T) dT = 1, y(0) = 0 6y(1) + 9)
A: given dydt+6y(t)+9∫0ty(T)dT=1 Take Laplace Transform on both sides of the differential equation…
Q: A fundamental fact is that if we are working on a closed, bounded inter [a, b], then any continuous…
A:
quadratic surfaces and spherical, cylindrical
Step by step
Solved in 2 steps with 1 images
- 7.3 Compute the curl of the vector field F⃗ =⟨x4,y4,z5⟩F→=⟨x4,y4,z5⟩.curl(F⃗ (x,y,z))curl(F→(x,y,z)) = What is the curl at the point (−4,3,5)(−4,3,5)?curl(F⃗ (−4,3,5))curl(F→(−4,3,5)) = Is this vector field irrotational (curl free) or not?7. (a) Determine the value of k for which (u, v, w) is an orthogonal coordinate system ifx = −(u2 + kv2), y = uv and z = w.(b) Given that F and G are vector fields with G a vector potential of F, prove that G is notunique.(c) Show that a vector field F =(4uv − θ3/√u2 + v2, 2u2/√u2 + v2, (lnθ − 3uθ2/uv), defined in paraboloidalcoordinate system (x = uv cos θ, y = uv sin θ, z =1/2(u2 − v2) is irrotational and hence find its scalar potential.6. (a) Show that a vector field F = (exsiny − yz, excos y − xz, z − xy) is irrotational and hence find its scalar field.(b) For a vector field F =(Rz, 1/R, eR − z2) in cylidrical polar coordinates, show that it is solenoidal and hence find its vector potential G = (G1, 0, G3). (PLEASE ANSWER MY OTHER THREE QUESTION)
- 2-What is the size of the vector space consisting of polynomials of degree not exceeding n? A) 0 B) 2n+1 C) n-1 D) n+1 E) n1. The distance of a point in the 3-D system from the origin a. is defined by the absolute value of the vector from the origin to this point. b. is the square root of the square of the sums of the x-, y- and z-values. c. is the square root of the sum of the squares of x-, y- and z-values. d. can either be negative or positive. e. None of the above. 2. In parametrizing lines connected by two points in 3-D plane, a. there is only one correct parametrization. b. symmetry equations may not exist. c. a, b, and c must not be equal to 0. d. the vector that connects the two points is a scalar multiple of the vector containing the direction numbers. e. None of the above. 3. A plane in 3D-space system a. is generated by at least three points. b. can lie in more than one octant. c. must have a z-dimension. d. must have a point other than the origin. e. None of the above. 4. A quadric surface a. must have either x2, y2, or z2 or a combination of those, on its general expression. b. must have a…Divergence Theorem for more general regions Use the DivergenceTheorem to compute the net outward flux of the following vectorfields across the boundary of the given regions D. F = ⟨x2, -y2, z2⟩; D is the region in the first octant between theplanes z = 4 - x - y and z = 2 - x - y.
- Divergence Theorem for more general regions Use the DivergenceTheorem to compute the net outward flux of the following vectorfields across the boundary of the given regions D. F = ⟨x, 2y, 3z⟩; D is the region between the cylindersx2 + y2 = 1 and x2 + y2 = 4, for 0 ≤ z ≤ 8.2. (a) Let r = (x, Y, z) and r = ||r||. Assuming r cannot equal 0, is there a value of p for which the vector field f(r)=r/r^P is solenoidal? You must fully justify your answer. (b) Show that if f and g are twice differentiable scalar fields then V²(f g) = ƒ V^2g+ g V²f + 2Vƒ · Vg . 3. (a) Show that any vector field of the form h(x, Y, z) = f(x) i+g(y)j+h(z) k, where f, g, h are differentiable functions, is irrotational. (b) Determine whether there is a vector field g such that V x g = xi+yj+zk.1) Consider the conservative vector field given by: F(x, y) = (exy3 + 2e2xy, e2x + 3exy2) A potential function that generates the vector field F corresponds to: A) f(x, y) = exy + exy3 B) f(x, y) = 3exy2 +(e2x/2)+(exy4)/4 C) f(x, y) = e2xy + exy3 D) f(x, y) = exy + e2xy3 2) Consider the vector field F(x, y, z) = (y - z sinx, x, 2z + cosx). The work that performs the F field to displace a body, from point A (3π, −1, 1) to point B (π, 2, 0) corresponds approximately to: A) 28, 45 JB) 32, 42 JC) 15, 71 JD) 13, 72 J
- 1) Of the following vector fields, the one that is conservative corresponds to: (See the answers in the images for question 1) 2) If f is a potential function for the vector field F = (−2y + 2xyz, −2x + x2z, x2y + 8z), then the value of f(3, −4, 1) is: A) −12B) 14C) −8D) 10A two-dimensional vector field describes ideal flow if it has both zero curl and zero divergence on a simply connected region.a. Verify that both the curl and the divergence of the given field are zero.b. Find a potential function φ and a stream function ψ for the field.c. Verify that φ and ψ satisfy Laplace’s equationφxx + φyy = ψxx + ψyy = 0. F = ⟨x3 - 3xy2, y3 - 3x2y⟩calc 3 13.7 #5 Evaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xy i + yz j + zx kS is the part of the paraboloid z = 2 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has upward orientation.
