Use graphing software to graph the function. Select a viewing window that reveals the key features of the function. 1. Graph the lower half of the circle defined by the equation x2 + 2x = 4 + 4y - y2.

Q: 11) The number of gallons of water in a swimming pool t minutes after the owner begins to drain it i...

A: “Since you have asked multiple question, we will solve the first question for you. If you want any s...

Q: you are standing abore the point 13, 1) ot the surtace 2=10-(2x+242) a) which direction shonld in ve...

A: Given surface

Q: In Exercises 23–24, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = 1 + xy2 - 2z2 24. ƒ(x, y, z) = xy + yz ...

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Q: Let S be the cylinder x2 + y2 = a2, 0<=z <=h, together with its top, x2 + y2 <=a2, z = h. L...

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Q: Find the areas of the regions . 1. Shared by the circles r = 2 cos u and r = 2 sin u 2. Shared by th...

A: 1. Area of the region shared by the circles r = 2 cos u and r = 2 sin u Replace the variable u by θ ...

Q: Find the circulation and flux of the fields F1 = x i + y j and F2 =-y i + x j around and across each...

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Q: Suppose a triangle has vertices A, B and C and has the following measurements: m/C = 91° AC = 39.9 c...

A: Given,  

Q: Can you help with 8 please?

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Q: A function f is given, and the indicated transformations are applied to its graph (in the given orde...

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Q: Profit Function for Sports Watches  The total profit function P (in thousands of dollars) for the Si...

A: Hi, the first term in the given function is not clear. Please use appropriate brackets in future to ...

Q: Find the area of the surface. The portion of the plane y + z = 4 that lies above the region cut from...

A: Given:

Q: At what points (x, y) in the plane are the functions continuous? a. g(x, y) = sin (1/xy ) b. g(x, y)...

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Q: Find the area of the cap cut from the sphere x2 + y2 + z2 = 2 by the cone z = sqrt(x2 + y2).

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Q: verify that wxy = wyx . w = x sin y + y sin x + xy

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Q: Find the centroid of the surface cut from the cylinder y2 + z2 = 9, z>= 0, by the planes x = 0 an...

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Q: Consider the triangle shown in the diagram below. ZB ZA Suppose that m/A= 84°, a = 6.46, and b = 4.3...

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Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2 i ...

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Q: How do you integrate a scalar function over a parametrized surface? Of surfaces that are defined imp...

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Q: Which fields in Exercises 1–2 are conservative, and which are not? 1. F = y i + (x + z)j - y k 2. F ...

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Q: Make a table of values for the function F(x) = (x + 2)/(x - 2) at the points x = 1.2, x = 11/10, x =...

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Q: Find parametrizations The cone z = 1 + sqrt(x2 + y2), z <=3

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Q: Give the derivative formula for the function. j(x) = 4 In x – e67 j'(x)=

A: To give the formula of the given function.

Q: Suppose that ƒ is an odd function of x. Does knowing that lim x-->0+ ƒ(x) = 3 tell you anything a...

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Q: (b) Find the derivative of f (1) = (12 +6) (4z – 9) by using the product rule. Let g (z) = 12 + 6 %3...

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Q: Find an equation of the tangent line to the graph of the following function f at the specified point...

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Q: Find the area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

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Q: graph the function ƒ to see whether it appears to have a continuous extension to the origin. If it d...

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Q: Find a field F = M(x, y)i + N(x, y)j in the xy-plane with the property that at each point (x, y) ≠ (...

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Q: A bug crawls on the surface z = x2 - y2 directly above a path in the xy-plane given by x = ƒ(t) and ...

A: We are given that the bug crawls on the surface z = x2 - y2 and x = ƒ(t) and y = g(t).  So,         ...

Q: Find the general solution to the given differential equation. (Use C for the constant of integration...

A: Consider the given differential equation.  

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Q: Let S be the portion of the cylinder y = ln x in the first octant whose projection parallel to the y...

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Q: Find the point(s) on the graph of f where the tangent line is horizontal. f(x) =  x x2 + 36

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Q: Find a field F = M(x, y)i + N(x, y)j in the xy-plane with the property that at each point (x, y) ≠ (...

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Q: Find the mass and center of mass of a wire of constant density d that lies along the helix r(t) = (2...

A: Given information:

Q: Integrate H(x, y, z) = x2sqrt(5 - 4z), over the parabolic dome z = 1 - x2 - y2, z>=0.

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Q: Find all the second-order partial derivatives of the functions 41. h(x, y) = xe^y + y + 1 42. s(x, y...

A:   “Since you have asked multiple question, we will solve the first question for you. If you want any...

Q: 4P 22) The pressure P, volume V, and temperature T of a gas are related by PV = n(RT + aP - DF), whe...

A: To find the derivative of P.

Q: Find the flux of the field F = y2i + xzj - k outward (normal away from the z-axis) through the cone ...

A: Definition:

Q: please help with b and show all work

A: Consider the curve Further solve by use of partial fraction,

Q: use a parametrization to express the area of the surface as a double integral. Then evaluate the int...

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Q: sketch the interval (a, b) on the x-axis with the point c inside. Then find a value of d > 0 such...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Find the flow of the velocity field F = (y + z)i + xj - yk, where velocity is measured in meters per...

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Q: Graph the rational functions . Include the graphs and equations of the asymptotes and dominant terms...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Integrate G(x, y, z) = x + y + z over the surface of the cube cut from the first octant by the plane...

A: Definition used:

Q: Find the general solution to the given differential equation. (Use C for the constant of integration...

A: Given differential equation

Q: Find the derivative of the function. g(t) = (2t-2)2/(3t+6)4

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Q: use the formal definition of limit to prove that the function is continuous at c. g(x) = 1/(2x), c =...

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.