### Hyperbola : Vertices and Foci

Find the coordinates of the vertices and the foci of the hyperbola and sketch the graph. 9y^2/25 - x^2 = 1

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Find the coordinates of the vertices and the foci of the hyperbola and sketch the graph. 9y^2/25 - x^2 = 1

1) 9x^2+4y^2+36x-24y+36=0 The answer is as following: Vertices: (-2,6), (-2,0) Foci: (-2, 3+or -√5) Eccentricity: √5/3 I have listed the answers for no. 1 above, but don't understand the steps. Please explain. 2) x^2+5y^2-8x-30y-39=0 Center: (4, 3) Vertices: (-6, 3), (14, 3) Foci: (4 + or -

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Let be a vector space and a subset of such that implies and for Define a partial order on by defining to mean . A linear functional on is said to be positive (with respect to ) if for . Let be any subspace of with the property that for each there is an with . Assume that , where Then each positi

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Two opposite vertices of a square are P(3, 2) and Q(-5, -10). Find the length of: a) a diagonal of the sqaure b) a side of the sqaure

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Using the given vectors how do I find the specified dot product u=3i-8j;v=4i+9j find u.v

- In space, given 3 points M (1,0,0), P (0,2,0), Q (0,0,3). Let C be the contour... (See attached file for full problem description).

3. Two vectors Xand Y are said to be orthogonal (perpendicular) if the angle between them is r/2. (a) Prove that X and V are orthogonal if and only if X . Y = 0. Use part (a) to determine if the following vectors are orthogonal. (b) X =(?6,4.2) and Y =(6,5,8) (c) X=(?4,8,3) and Y=(2,5,16) (d) X = (?5. 7, 2) and Y = (4, 1, 6

Important Formulas and their Explanations (III): Gradient, Divergence and Curl Gradient of a constant Gradient of a con

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If v = i - j and w = i + j, find the dot product v * w and the cosine of the angle between v and w.

If v=3i-4j, find ||v||

4) A vector field F is shown. Use the interpretation of divergence derived in this section to determine whether div F is positive or negative at P1 and P2 a.) Are the points P1 and P2 so sources or sinks vector field F shown in the figure? Give an explanation based solely on the picture. 5)Use the divergence Theorem to c

B. A region is surrounded by two infinitely long concentric cylinders of radii, a1 and a2 (a2>a1). The concentric cylinders are charged to potentials phi1 and phi2 respectively. Determine the potential and electric field vector everywhere in the region. Please see the attached file for the fully formatted problem.

For each of the following vector fields F type in a potential function f (please see attached for full question). See the attached file.

Show ... is independent of path for any central force F....

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See the attached problem.

Please see the attached files for the fully formatted problems.

(a) Consider a vector function with the properly ... = 0 everywhere on two closed surfaces S1 und S2 and in the volume V enclosed by them (see the figure). Show that the flux ol F through S1, equals the flux of F through S2. In calculating the fluxes, choose the direction of the normals as indicated by the arrows in the figure.

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Suppose that E is a one-dimensional normed linear space. Prove that E is complete and that each linear functional on E is continous.

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Suppose that T is a topologocal vector space. Prove that a linear functional f on T is continuous if and only if ker(f) is closed.