Consider the map F:x 3x on the circle S' = R/Z. • Find all fixed points of this map. • Find all points of period 2.

Q: If the circle x2+y2+ax+by-12=0 has the centre  at (2,3) then find a , b and radius

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Q: Sketch a contour map for the graph of the equation z = 2² + y². Include level curves corresponding…

A: In question we need to draw a contour map.

Q: 5. Center: (0, 7); Point on the Circle: (-7, 6) 6. Center (9, -12); Tangent to the line x = 15

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Q: If a unit circle C is traced by R(t), R(0) = (0, 1) and (0) = (2,0), then the circle

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Q: 65. Let A and B be the points where the ray of angle 6 intersects the two concentric circles of…

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Q: (4) Find the circle a(x² +y³)+b(x+y) = 1, which best fits the following data. (0, –1), (–1,0),…

A: Given that a(x2+y2)+b(x+y)=1 satisfy the given data (0,-1),(-1,0),(1,-1),(1,1)  that is it gives…

Q: Find the point(s) of intersection of two circles, one centered at the origin and, the other,…

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Q: For each point given in rectangular coordinates, write three different polar representations of the…

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Q: Find the equation of the circle if the circle is tangent to the line x + y = 1 at the point (0,1)…

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Q: The result of a transformation of circle A using the rale (a,y)+ (+4,y-1). followed by a dilation of…

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Q: nd the equation of the circle having center at (2,3) and which touches x+y=1.

A: Provided that the (2,3) is the center of circle and this circle touches the line x+y=1 .We can…

Q: Graph the curve given by the parametric equations below, and show its orientation. c=-t², y=-3t,…

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Q: Find the composition rule of transformations that maps circle F onto Circle F'. X -10 -8 -6 LL F F2…

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Q: 3) y = Vx – 5 4) y= Vx - 4

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Q: what is the  reflection about the line y=x

A: what is the  reflection about the line y=x

Q: The equation of a circle centered at (4, 5) with a radius of 3 is given by which of the following…

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Q: ,draw the circle given by the equation (x+4)² + (y –6)² = 16. THIN BLACK 13- 12- 11+ 10 9- 8- -거 6-…

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Q: Write standard equation and center and radius for all 7 circles

A: The standard equation of the circle helps to find the required equations of the circle. The…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.