Compute the gradient vector fields of the following functions: A. f(x, y) = 1x² +10y² Vf(x, y) =i+ j B. f(x, y) = x³y5, Vf(x, y) = i+ j C. f(x, y) = 1x + 10y V f(x, y) =i+j

Q: Find the general solution of the differential equation. y (4) - y = 8t+cost. NOTE: Use C₁, C2, C3,…

A:

Q: Question 4 Solve the rational inequality: 2x²-8x+15 xâ450+ ≤0, using a factor table...

A: Given problem:-

Q: A force of 880 newtons stretches a spring 4 meters. A mass of 55 kilograms is attached to the end of…

A:

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i - 8j as…

A: Suppose ABCD is the parallelogram with AB=i+j & BC=i-8j. So, the diagonals are AC and BD.

Q: A rectangle is inscribed in a right triangle, 5 by 12 by 13 units. What are the dimensions of the A…

A: We have to find if the box can be constructed in Php 300.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: 2. Determine the parent function and equation of the transformed function of the graph shown below.…

A: Let's find function equation.

Q: Solve the given initial-value problem. d²y dt² y(t) = 4d dt - 5y = 0, y(1) = 0, y'(1) = 4

A:

Q: 5. Determine whether 3x 4 is a factor for each polynomial. Show all your work! 3 a. 6x 6x³ - 26x²…

A: Solution is given below:

Q: Tutorial Exercise Use the method of cylindrical shells to find the volume V of the solid obtained by…

A:

Q: 7. A cylindrical tank, buried on its side, has radius 3 feet and length 10 feet. It is filled…

A:

Q: 9 -25 -49 + 8 = 2*+* 3X 2X - 2X Ans: y = c + czxe + cze L 25 -3X e + x + x + ½

A: See this solution in below

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y"" -…

A: Here, the given DE is: y'''-16y'=te-4t+5cos(4t) So, the auxiliary equation is:…

Q: A ship is just off the shore of New York City. A sighting is taken on the Statue of Liberty, which…

A: Given  Height = 305 feet  Base = 950 feet  We need to find the angle of elevation

Q: The sonar of a navy ship detects a submarine that is 4000 feet from the ship. The angle between the…

A:

Q: Find the general solution of the differential equation. y (4) - y = 8t+cost. NOTE: Use C₁, C2, C3,…

A: We need to solve D.E.

Q: f(x) = { cos x, xpi  which lim does not exist

A:

Q: Let P(n) be the statement. n is a multiple of 3 and Q(n) be the statement. n is a multiple of 5.…

A: We have to find the true statement.

Q: Convert the point (x, y, z) = (-4,- 4, 4) to cylindrical coordinates. Give answers as positive…

A:

Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4ex - 3 y(x) =

A: We need to solve D.E.

Q: A population is growing according to the logistic model 5500 1+ 4.8 1.9t N = where t is the time in…

A:

Q: Solve the given differential equation by using an appropriate substitution. The DE is of the form dy…

A:

Q: Find k, given f(x, y) = k(y² + xy) and [[ f(x, y) dxdy = 54 R R=0<x<y<2

A:

Q: ylindrical coordinates for the rectangular equation y = x² Entry Tip #1: To enter 0, type "theta".…

A:

Q: Find the general solution of the given second-order differential equation. y" - 6y' + 10y = 0 y(x) =

A:

Q: Use the integration capabilities of a graphing utility to approximate to two decimal places the area…

A:

Q: Find a function of the form y = A sin(kx) + Cor y = A cos(kx) + C whose graph matches the function…

A:

Q: Find parametric equations (not unique) for the following circle and give an interval for the…

A: Here we have to find the parametric equation of the required circle

Q: 3. An air ambulance is travelling from Barrie to Toronto. Toronto is located 90 km [S5°E] of Barrie.…

A:

Q: Determine whether the series converges or diverges. Select the correct answer. O diverges Oneither O…

A:

Q: Solve the given differential equation by undetermined coefficients. y"" - y" - 25y' + 25y = 6 - ex +…

A:

Q: Find the general solution to the following problems: 1. (D² + 4D + 5)y = 50x + 13 e³x 2. (D² - 1)y =…

A: 1. Its AE is: D2+4D+5=0 D=−4±16−202=−2±i Thus  CF​=e−2x(c1​cosx+c2​sinx) Here X=50x+13e3x Lets find…

Q: Find an equation of the line that passes through the point and has the indicated slope. Point slope…

A:

Q: Find the area inside the limacon = 7+ 6 sin 0. OA) 134T - 84 B) 67T + 84 OC) 67 T OD) 134T

A:

Q: The notion of an asymptote can be extended to include curves as well as lines. Specifically, we say…

A: a) The given function is: y=x2-3x-3. We have to find a simpler function gx, that the given function…

Q: Tutorial Exercise Find the slope and y-Intercept (if possible) of the line. 11x - 12y = 60 Step 1…

A:

Q: Consider the following. u= (-10, 0, 4) v=(3, 3,0) Find u x v. (12.12.30) Determine if u x v is…

A:

Q: Find the general solution of the given higher-order differential equation. + 16d2y + 4y = 0 dx² y(x)…

A:

Q: 5x *(2,3)=ze4%. yer. Then Vf= and Duf(1, -1) in the direction of the vector (1, 1) is

A:

Q: Find the inverse LaPlace transform F(s) = 5s 2 s² +9

A:

Q: A baseball team plays in a stadium that holds 64000 spectators. With the ticket price at $10 the…

A: In this question we have to find the ticket price that would maximize the revenue.

Q: (a) Evaluate the double integral Je emax{z²,y²} where R = {(x, y) |0 ≤ x ≤ 1,0 ≤ y ≤ 1} is the unit…

A:

Q: Antidifferentiate: f3e²x dx 0e²x +C O 3e² + C

A: To antidiffferentiate the given.

Q: =(4,-1, 7) along b = (6, 6, -7) and the vector component of v Find the vector component of v =…

A: Given vector,v = 4, -1, 7b = 6, 6, -7Vector component of v orthogonal to b.

Q: yP=A ex+Bex шкатур

A:

Q: Find area bounded by the carves. (Round answer to 2 decimal places) y = 7x² −2x _y=x³ -7x+4 +

A:

Q: Find the surface area of the torus generated by revolving the circle given by r = 2a about the line…

A:

Q: m -3m- 8m (a) Find the work required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use…

A:

Q: Find the first four nonzero terms in a power series expansion of the solution to the given initial…

A:

Q: x) = y" - y² + ²y = 4 + = 4 + ex/2

A: We will solve  the given differential equation.