Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6)

Q: Find the following for the given equation. r(t) = (e-t, 3t², 4 tan(t)) (a) r(t) = (b) r(t) = (c)…

A: Topic = Derivative

Q: Find the smallest angle in the right triangle with a hypotenuse of length 175 and a leg of length…

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Q: A bottle rocket is shot directly upward into the air at an initial velocity V, of 80 feet per…

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Q: (2n - 1)! (2n + 1)!

A: Given: we have ax=2n-1!2n+1!

Q: = 3. Let R be the region between the functions y x²2 and y = 8 x². Set up the iterated double…

A: To  sketch the region R and then set up the iterated double integral

Q: Consider a two variable function z = x³ + 2xy + y² + 4y. Z= Find partial derivatives zy, ży Find all…

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Q: How long will it take for the population to reach 65286528 fish, according to this model?

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Q: What is the slope of the line 0 = ? (Use decimal notation. Give your answer to three decimal…

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Q: 28. Write the expression as a sum and/or difference of logarithms. Express powers as factors. log 2…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: B. Determine the general solution for each given higher order differential equation. Write your…

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Q: Evaluate the following iterated in -1 1 075 (3x+y)dy dx

A: Topic:- application of integration

Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

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Q: 9. (True/False) If F is a conservative vector field, then V x F = 0.

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Q: 44. y' - 2y = 0

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Q: To prove that: n²= 5k or 5k+1 or 5k+4 we use the following method: Division into cases. We need 3…

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Q: Use implicit differentiation to find an equation of the tangent line to the graph at the given…

A: The tangent is a straight line so it will be of the form y = mx +c  We can get  m  by finding the…

Q: 5) .  Find an explicit formula for the general term an of the sequence.  −1,   1 3, −  1 5,

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Q: 35. Find the exact value of the expression. (3)] Select the correct choice and fill in any answer…

A: We can answer the question as below.

Q: What is the area under the curve of the following positive function y = 10x4 + 3x2 between x = −1…

A: Given: y = 10x4 + 3x2 between x = −1 and x = 2 Area=∫-1210x4+3x2dx         =∫-1210x4dx+∫-123x2dx…

Q: Analyze the following equation and graph it. 36 9-8 sin 9 r= Identify the conic that the polar…

A: Solution is given below:

Q: Find the limit of the sequence using L'Hôpital's Rule. bn = 6   n ln  1 +  1 n   lim n→∞ bn =…

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Q: Find, in its simplest form, the quadratic equation with the following pair of solutions: 3/5 ± 3i

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Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

A: Given,  a=4i-j+8k, b=16j+8k

Q: Fill in the blank. (Enter your answer in terms of t.) {} ( s7 - 6s + 13.

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: 1. Using the graph of f(x), what is lim, -f(x)? A. - 00 B. 0 C. -2 D. Does not exist E. 00 A

A: The graph of f(x) is represented by two infinite curves.

Q: Find the vector v with the given magnitude and the same direction as u. Direction u = (-6, 4, 0) V =…

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Q: 1 17. If the function x² - 4 constants A and B respectively are: 1 1 4 A. A: = B. A = 1 4 B B 1 4 is…

A: Use partial decomposition

Q: Determine whether the planes are parallel, orthogonal, or neither. 4x 3y + z = 6 x + 4y + 8z = 1 O…

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Q: The weight (in kilograms) of a certain species of animal can be predicted by W(t) = 508.2…

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Q: Identify the following quadric surface. 11 + O hyperboloid of one sheet O ellipsoid O hyperboloid of…

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Q: Let g(x) = x³ 3x². What is the absolute minimum of g(x) in the interval [-2, 4]? Answer: -

A: Given :gx=x3-3x2

Q: Consider the following. u = −8i – 2j – 4k, v = 4j + 4k (a) Find the projection of u onto v. (b) Find…

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Q: 3. The production cost, in dollars, per week of producing x bottles is given by: C(x) =…

A: To find out the marginal cost, marginal revenue, and marginal profit.

Q: Find dx dt dx dt at x = = 2 if y= 2x² - 1 and dy dt - 3.

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Q: Using geometry only, find the area under the curve. Include a sketch of graph for each region. Give…

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Q: Find the unit tangent vector T(t). r(t) = t²i + tj + 20 T(5) = (10, 1) ✓101 eBook k. P(25, 5, 20/3)…

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Q: Convert the integral into spherical coordinates. Int[-3,3]  Int[0,sqrt(9-x^2)]…

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Q: 7

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Q: Use linear approximation, i.e. the tangent line, to approximate 3.9³ as follows: Let f(x) = x³. The…

A: We have to approximate 3.93 using linear approximation, i.e. the tangent line. Given fx=x3. The…

Q: Use Lagrange multipliers to find the maximum value of f(x, y) = 6x + 6xy +y where x >0 and y>0…

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Q: Find the regression line associated with the set of points. (Round all coefficients to four decimal…

A: Select the line which passes through all the given points.

Q: We are given the following homogenous differential equation and pair of solutions on the given…

A: Given differential equation x2y''-7xy'+15y=0We have to verify that given function x3 and x5 form a…

Q: The given family of functions is the general solution of the differential equation on the indicated…

A: By using the general solution and the initial conditions we can find the particular solution of the…

Q: 16. Solve dx (a²+x²)

A: NOTE: As per our guidelines, I have solved one problem. If you want the answers of rest, kindly post…

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

A: Topic = DIFFERENTIAL EQUATION

Q: The barometric pressure y (in inches of mercury) at an altitude of x miles above sea level decreases…

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Q: The linear approximation at and where B is: = = 0 to sin(9x) is A + Bx where A is:

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Q: For the sequence, determine if the divergence test applies and either state that lim n→∞ an does not…

A: Answer: The solution is as given below: