Find the outward flux of the vector field F = (x³, y³, z²) across the surface of the region that is enclosed by the circular cylinder x² + y² = 36 and the planes z = 0 and z = 8.

Q: 20. An aquarium contains 10 gallons of polluted water. A filter is attached to this aquarium which…

A:

Q: se the isosceles right triangle and the 30°-60°-90° triangle to complete 45 r √2 - 45 60⁰ 30% √3

A: Part 1 :  For triangle                  For θ=30° It is right-angled triangle.…

Q: Determine the set of x-values where f(x) = 8x² + x - 8 is continuous, using interval notation.

A:

Q: Find the Average Rate of Change of the following function over the interval [2, 5] (That is, from t…

A:

Q: If the value of land in an area is increasing 6.4 percent a year, how long will it take for property…

A: This question can be solved using the concept of compounding.

Q: Find the differential equation for the given family . y = C_{1} * e ^ (2x) + C_{2} * e ^ (4x)

A: The family of a curve is given by y = C1e2x+C2e4x                              ..........1 To…

Q: Use the Chain Rule to find dz/dt. z = tan−1(y/x),    x = et,    y = 5 − e−t

A:

Q: Evaluate the following integral. 6 x (x² + 5)² dx Find the partial fraction decomposition of the…

A:

Q: (a) If the point (1, 7) is on the graph of an even function, what other point must also be on the…

A: Topic- functions for even function if (x,y) is on the graph then (-x,y) is also on the graph for odd…

Q: Use Green's Theorem to evaluate 90 O O -384 O -48 fayd r²y² dr + (yr³+ y²) dy where C' is shown…

A: As we know from Green's theorem: ∫cMdx+Ndy=∫∫R∂N∂x-∂M∂ydA Where, ∬dA=∬dxdy or ∬dydx And We know the…

Q: Use the final value theorem, the final value of f(t) = 6. (et +2) - 10 is .....

A: final value theorem

Q: 5T A positive angle less than 47 that is coterminal to 4 Part: 1/2 Part 2 of 2 is 57 A negative…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y = x and y = √√x about the…

A: In this question, we need to find the volume of the solid.

Q: A function is given. Determine the average rate of change of the function between the given values…

A:

Q: Find the integral. (Use C for the constant of integration.) t (294 - t2)3/2 dt

A:

Q: Find the differential equation by eliminating the arbitrary constant/s. y = = Aex cos x + Bex sin.x…

A: We differentiate the number times as the number of arbitrary constants present in the equation and…

Q: Let the points B, C be perpendicular to the bases O and A (13,0), respectively, on the line 5x-12y +…

A: Given equation of line: 5x-12y+65=0 Coordinates of point A: (13,0)  Coordinates of point O: (0,0)

Q: C. Find the standard form of the equation of a circle given the following conditions. 12. Center at…

A: Find the equation of the circle whose centre is at (2,m), radius is twice the y co ordinate of the…

Q: Express (5x + 7y, 8x + 5y, 0) as the sum of a curl free vector field and a divergence free vector…

A:

Q: What is the general solution to the the differential equation3y" - y'- 2y = 10e *?

A:

Q: 2. Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x…

A: given goaph of f'(x)

Q: Parameterize the line through P = (-4,-4) and Q = (0, 3) so that the points P and Q correspond to…

A:

Q: Find a formula for the nth term of the sequence in terms of n. 3² 3³ 34 1 3 3 - 4' 6 8 " 10 " 12

A:

Q: a) Complete the table below given f(x)=sin(3x)/x Round your answers to six decimal…

A: Compute the table for f(x)=sin(3x)x

Q: C. Find the standard form of the equation of a circle given the following conditions. 10 10. Passes…

A: We can solve it by various method but i solved it as shown below.

Q: im -3 1 x+5 8 x-3 ►

A:

Q: 7. Find all constants a, b that make f continuous at x = 2. (Use limits and definition of…

A:

Q: H] Example: If an amount of $5000 is invested at 3% compounded quarterly, what is the amount after 3…

A: Note:- since part f incomplete to find value of x we need equations of revenue function and cost…

Q: B] Find the domains of the following relations. Write them in interval notation. 1) f(x)=√x-9 2)…

A:

Q: Find the equation of tangent at x = In 5: ln 2x a) y = ²x + 1 e to :

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Because of the curvature of the earth, the maximum distance D that you can see from the top of a…

A: I am attaching image so that you understand each and every step.

Q: Assume that is an acute angle. If sec8=6, find the exact value of sin 8. Write your answer as an…

A:

Q: average

A:

Q: y=ae³x + be-3; y"-9y=0 -3.x.

A:

Q: If f(x) = 7 and g(x) 4x + 3 (fog)(1): (gof)(1) = = √√45x + 4, compute the compositions (fog)(1) and…

A: Given , f(x)= 7 / (4x+3) And g(x)=√(45x+4)

Q: www Given the function defined by f(x)=3x−1, find f(-

A:

Q: For the differential equation ty' - y = t²e-¹, 1. Draw a direction field for the differential…

A: Solution

Q: Write a function of the form f(x) = csc (Bx-C) for the given graph. 3 2 1 0 -1 -2 -3 F 12 5п 12 3πI…

A:

Q: D] Find composite functionsf(g(x)) and g(f(x)) for given f and g 1) f(x) = 3x + 1, g(x) = 2x² 2)…

A:

Q: y= 희. dx (2x+1)4 (4x + 1)5

A: we have to find dy/dx

Q: 10. Use the squeeze theorem to find lim f(x) if 2x+2 ≤ f(x) ≤ x² +3. x-1

A: Given: Use the squeeze theorem to find limx→1f(x) if 2x+2≤f(x)≤x2+3

Q: speed x HOSX< 1000 if Graph Ffor 0 sx s 100. F sxs F 1000 (100, 1000 (100, 1000

A: We have to make the function from given data and graph the function.

Q: 3. Find the area of the region enclosed by the curves y = x² + 2, y = -x, x = 0, and x = 1. (a) (c)…

A:

Q: What about the graph, where to plot the both lines ???

A: As S denotes the number of bowls of salad and P denotes the number of pizza slices .Also given that…

Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

A:

Q: 4. Verify that the solution of the DE d²x dt² + k²x = 0 is x = sin(kt).

A: To verify that the solution of the DE d2xdt2+k2x=0 is x=sinkt.

Q: Find the set of all solutions of each of the following differential equations.  y" =32.

A:

Q: average

A:

Q: the derivative. 28) y = x5/6 A) 5x7/6 B)x1/5 a C)/x-5/6 D) Ex-1/6

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the distance from the point (1, 5, 5) to the line x = 0, y = 5 + t, z = 5 + 5t.

A: