A rectangle is to be inscribed in the ellipse with the following equation x² y² + 81 144 Determine the maximum possible area of this rectangle. Enter answer using exact v = 1.

Q: Find the value or values of c that satisfy the equation the given function and interval. f(x) = 7x +…

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Q: find the critical points

A: given function

Q: A particle starts out from the origin. Its velocity, in miles per hour, after t hours is given by…

A: We have to use the concept of integration

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Q: Evaluate the line integral e F. dr where F H ScF. dr = (5 sin x, 5 cos y, 5xz) and C is the path…

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Q: A restaurant frequently offers a special prix fixe meal and has been charging $170 per person for…

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Q: Find af ах af ду af дz Әх af af af af and I Әх ду дz Find their values at (0, -1, 1) if possible.…

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Q: The polynomial C(t) = -0.006t4 +0.140t³ -0.53t² +1.79t measures the concentration of a dye in the…

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Q: As with discrete-time dynamical systems, equilibria can act strange when the slope of the…

A: We have to graph a rate-of-change function that has a slope of 0 at the equilibrium but the…

Q: _g(x) = 4x3 (1 – x4)²

A: The given function .The aim is to find the series representation of the given function.

Q: lim f(x)=-5, lim g(x)=3, and lim h(x) = 3. Given x→a x→a xa the limit does not exist, explain why.…

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Q: A) Consider the vector field F(x, y, z) = (yz, -9xz, -8xy). Find the divergence and curl of F.…

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Q: 1. Vector field F is given by F(r) = (x, y, and surface A is the locus of points satisfying ≈ + x² +…

A: The objective of this question is to evaluate several integrals related to a given vector field and…

Q: Suppose that SpaceX launches a rocket at t = 0 seconds and that its height, in meters above…

A: Given the height of rocket is

Q: Find the distance (m) traveled by a particle in the x-y plane with position (x, y) for the time…

A: Find the distance (m) traveled by a particle in the x-y plane with position (x, y) for the time…

Q: Compute the curl of the vector field F = -2z7+5yj - 8x k. curl =

A: To find the curl of the vector field .

Q: Find the critical points of the function f(x,y) = 8 + 76xy + 38x^2 + 240y + y^4/4

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Q: Find a parametric equation for the line through the point (1,3,-3) and perpendicular to the plane 3x…

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Q: Using n = 2 equal-width subintervals, approximate the area of the region bounded by the graph of,…

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Q: The time it takes an object to hit the ground, if air resistance is ignored, is a function only of…

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Q: Sketch the graph of the function. f(x)=x²-x² -2 -2 Find the area of the region bounded by the graph…

A: Since you have posted multiple questions. According to bartleby guidelines, only first question will…

Q: X = = 3 sin(t), y = 4 cos(t), 0 < t < 2π (a) Eliminate the parameter to find a Cartesian equation of…

A: Consider the parametric equation

Q: Find a parametric representation for the lower half of the ellipsoid 2x2 + 6y2 + z² = 1. (Enter your…

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Q: Prove that the equation is an identity. (sin 0 - cos 0)² + 2 cos 0 sin 0 = 1 Working from the…

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Q: The demand function for a certain book is given by the function x = D(p) = 50e-0.004p. Find the…

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Q: The parametric equations and parameter intervals for the motion of a particle in the xy-plane are…

A: x=4cos⁡(2t),y=4sin⁡(2t),0≤t≤π

Q: Find the domain of the following function. √√x-5 X+2 G(x) =

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Q: Find the domain of the function. f(x) = -5x + 3

A: f(x)=-5x+3

Q: Use polar coordinates to calculate A = ²³² dA where D is the region in the first quadrant - bounded…

A: The given integral  where D is the region in the first quadrant bounded by To find value of

Q: Find the gradient field of the function, g(x,y,z) = e²z - In (2x² + y²). The gradient field is Vg =…

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Q: Sketch the curve with the polar equation r = 2 + 2 cos(0). What is the name for the shape of the…

A: Given that the polar equation

Q: A particle starts out from the origin. Its velocity, in miles per hour, after t hours is given by…

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Q: A gardener has 920 feet of fencing to fence in a rectangular garden. One side of the garden is…

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Q: A certain company produces potting soil and sells it in 50 lb bags. Suppose that 100,000 bags are to…

A: The given problem is an example of the Economic Order Quantity (EOQ) model.The EOQ model determines…

Q: The grid on the right shows the graphs of several functions f(x) whose slope at 8x each x is Find…

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Q: Find a power series representation of for f(x) = convergent, find its sum. x+2

A: f(x)=x2x+2We know the power series of 11+x11+x=∑n=0∞(−1)nxn

Q: Let u = (5,-4) and v= (-4,7). Find the (a) component form and (b) magnitude (length) of the vector.…

A: The vectors are given by(a) The component form of the vector  can be obtained as follows:

Q: Suppose f(x) = 3x -2. Find f (x+²) 3 (x+2) 3 (Simplify your answer.)

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Q: Problem #7: Evaluate the surface integral f FdS where F(x, y, z) = xyi - y²j-9zk and S is the sphere…

A: Calculate F.dS where  F(x, y, z)  =  xyi − y2 j − 9zk  and  S is the sphere  x2 + y2 + z2  =  9…

Q: Find the Taylor series for f(x) = ln(x) about a=2. Find the interval of convergence.

A: Taylor series of ln⁡(x) around a=2A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: 7 The rate of change of a population with emigration is given by P'(t) = 300 population in millions,…

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Q: Find F as a function of x and evaluate it at x = 5, x = 7, and x = 9. F(x) = F(5)= F(7) = F(9) =…

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Q: 3 40 32 24 16 8 4 5 Evaluate the definite integral * 3 6 (4x + 10)dx =

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Q: 2- -2- -3 12 B + 45 6 + 7 + 8 9 10 t

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Q: 1 A 3 2 1 a 1 To find the blue shaded area above, we would calcula b f(x) dx = area Where: a = 1…

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Q: The hull speed (in knotts) of any watercraft is given by V = 1.34-L¹/2 where L is the length of the…

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Q: Suppose the equation 1 40 y = 22 models the height of an arrow where is the horizontal distance in…

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Q: For Questions 1 and 2, region R is bounded by f(y)=y²-14 and g(y) = 2y + 1. Which of the following…

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Q: 2η 3. Σ. 1 n=1 nn

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Q: Find inflection point(s) for f(x), if any. f(x) = 27x - x³ A. f(x) has an inflection point at x = -3…

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