The equation of a circle can be represented as in-h)² + (y – k)² = r², where (h. k)ie center of the circle and r is its radius. For a circle centered at (3, -1) with radius 5, y = A) -1± /25 – (x – 3)2 B) -1± /25 + (x – 3)2 C) 1+ /25 – (x – 3)² D) 1+ /25 + (x – 3)² %3D | | |

Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: Use the method of Characteristic to solve Burger's equation. ut - tuux = 2t, u(x,0) = 3x.

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Q: Let j = and i = Compute the distance from j to the line through u and the 9. origin.

A: Given that y→=-39 and u→=12. To find the distance from y→ to the line through u→ and the origin, we…

Q: Find F. dr for given F and C. (a) (2,4). F = −y sin(x)i + cos(x)] and C is the parabola y = x²…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Find three different parametrizations of the graph of y = x3.

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Q: Let 0 be the angle of inclination for the line through (X1.Y1) as shown in the accompanying figure.…

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Q: The curves 71(t) = (- 5t, t°, 3t*) and r2(t) = (sin(5t), sin(2t), t) intersect at the origin. Find…

A: Answer

Q: Find the distance between x = 10 -3 and y = ㅗ -5

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Q: Find the equation of the tangent plane to the graph of G(u, w) = – cos (uw) at the point (5. ). (Use…

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Q: Express the following points in Cartesian coordinates: (а) Р(1, 60°, 2) (b) Q(2, 90°, –4) (c) R(,…

A: we have to convert cylindrical and spherical co-ordinate system to cartesian system. we know that…

Q: Find the equations of the tangent lines to the circle (x + 2)² + (y + 2)² = 25 at the two points…

A: At x=2; (2+2)2+(y+2)2=25 16+(y+2)2=25 (y+2)2=9 y+2=±3y = 1 or -5Therefore two points at which…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.