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: If -4 -5x³x = y² - 2x² then find dy Answer: dy dr (-1,-2) = at the point (-1, -2). Submit Answer at

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Q: (-2/3 + j2) 4. Express in rectangular form.

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Q: The equation y =1-x² can be described parametricall by x = sin t, y = cos² t. %3D اختر احدى الدجابات…

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Q: 3.) Given y=5* (2, 1)? which of the following shows the equation of the line tangent to y at the…

A: To find the equation of the tangent line to the curve   at the point .

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: Prove that the curve y:(-,) → R³ is regular with factor H and determine whether the image y (t) = (2…

A: To determine : the      included in a plane in   or not. Here,…

Q: With respect to the attached figure, line PARALLEL to the line N and passing through the origin, has…

A: We have to find the equation of the line which is parallel to line N and passing through…

Q: Find an equation of the povalbola in standovet form focus at F(-4,0) and divectrix ;X=-4

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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: Show that the line of slope t through (-1, 0) intersects the unit circle in the point with…

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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.