Under the transformation w = :-1 -find the image of the circle E = 1 in the w – plane.

Q: A and B are two points in the xy-plane. If their coordinates are A(2, 3) and B(4,3), which of the…

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Q: Identify the composition of transformations that created circle W, given the circle Q, to show the…

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Q: Which of the following surfaces is the graph of 6x + 3y + 4z = 12 in the first octant? 1. 2.

A: Given:- Equation of plane. 6x+3y+4z=12   To find:- Graph of given plane in first octant

Q: Q2/ By using polar coordinate, graph the curve r=1-2cos 0.

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Q: 6. Given a rule x² + y² = 9, its image rule x? + y² – 2x + 6y +1 = 0 under a translation, state a…

A: To solve the given translation problem.

Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: Find the equation of the circle in standard form satisfying the given conditions: C(7,4) externally…

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Q: draw and identify the graph of the following surfaces a. x² + y² = sin²z, z = [0, π]

A: Any surface in the 3D plane can be represented in the form of f(x,y,z)=0. A graphing utility can be…

Q: 1) Evaluate F dr where F(r,y) = ri and C is the half of the circle %3D ²+y 3 16 lying below the…

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Q: 6. Given a rule x2 + y2 = 9, its image rule x2 + y2 – 2x + 6y + 1 = 0 under a translation, state a…

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Q: et the affine map A : R? → R² be defined by A(x, y) (3x + 4, 2y – 3). Show that the image of a unit…

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Q: Consider the following equation of a circle. x² + y° - 6x + 4y + 9 = 0 Step 1 of 3: Find the center,…

A: The center of the circle having equation of the form y=x2+y2+2gx+2fy+c=0 is (-g,-f).

Q: 6. Evaluate [(x + y²)dx – xdy where C is the circle "x²+y² : = 1" with a counter- clockwise…

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Q: Sketch the given surface

A: Given: x42+y82+z122=1 The given equation is an ellipsoid.

Q: w=f(z)=z/(1-z) under transformation IzI=3 Find the image of the circle?

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Q: Evaluate F dī , where F(x, y) = (e* +x² )î +(e' – xy²)ĵ and C is the circle x² + y2 = 25, oriented…

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Q: Sketch the graph of y = m(r) in Figure 2. %3D 음-3, rS-1 m(x) = 4 %3D 1<r<5

A: Given,          mx=13x-3x≤-141&lt;x&lt;5

Q: Find the exact length of the portion of the curve shown in b r = 0+ 2 2 (i)

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Q: Formulate an verify Green theorem when [P, Q] = [2yx, y² + 2x] and the curve y is the positively…

A: According to the given information it is required to formulate Green theorem. When

Q: (b) Im(2)dz, where C is the circle |z| = 2 traversed once counterclockwise.

A: i have used the parametrization of circle  |z|=2 , z=2e^it where 0&lt;= t &lt;=2pi and the…

Q: Find the equation of the circle with center -2+i and radius 4 units. O (A) (x – 2)* + (y – 1)° = 4.…

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Q: Use the transformation u = x2 –- y²,v = x² + y² to find ff, xydA where R is the region in the first…

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Q: Graph the first-octant portion of each plane. x + y + z = 15

A: Given a Plane, x+y+z=15 We need to graph the above plane.

Q: Let f (2) = 5. Let C be the circle |z| = 2 in the counter-clockwise direction. What is 2ni Tf(2) dz?

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Q: Determine the value(s) of k such that the circle x²+(y-6)²=36 and the parabola x²=4ky will intersect…

A: Consider the provided equations, x2+y-62=36  ....... (1) x2=4ky ...... (2) Determine the value(s) of…

Q: in the figure below, Z is the center of the circle. Suppose that QR=4x-5, ST=7,ZU=8, and ZV=8. Find…

A: Solution

Q: A D E y 50 W V 20 70 В ZDCE= 90 AD = AE = AC = AB by the Hypotenuse Midpoint Theorem + Thus DECB is…

A: The given figure is- Given that AD=AE and AB=AC

Q: Find the equation of the circle with center (–1, 4) and radius of 3. [A] (x+1)² + (y+4)² = 9 [B]…

A: A circle is the locus of points in two-dimensional space which are equidistant from a fixed point.…

Q: _23. What is the equation of the circle that passes through (4, 2) with center (0, -1)? x2 + (y –…

A: Here we find the equation of circle which passes through (4,2) with centre (0,-1)

Q: Evaluate 1+ dz where C is the right half of the circle of radius 2 with counter C clockwise rotation…

A: Given sketch is and integral is ∫C1+x3dx

Q: Example 4: Show that the inverse of a point a with respect to the circle| z - c | = Ris the %3D R 2…

A: Given the inverse of a point wrt circle

Q: Use shifting graph to sketch a) y+2 =|-3+ vx| |3D b) y = -1+ 5sin (2x)

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Exercise 1.2.16 Find the circle x2 +y² +ax+by+c=0 passing through the following points.

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Q: Evaluate (x+ y)ds, where C is the top half of the circle x² + y² = 4, oriented counterclockwise.

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Q: 3. Evaluate ff, (x² + y²)³/²dA, where D is the region in the first quadrant bounded by the x-axis,…

A: Given problem:- Evaluate ∫∫D (x² + y²)3/2 dA, where D is the region in the first quadrant bounded by…

Q: Let f (z) -Let C'be the circle z 10in the counter-clockwise direction. What is 1 -Lf(2) dz? 2ri

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Q: Consider the following. Зx + 2у + 62 3 36 Sketch a graph of the plane.

A: 3x+2y+6z=36 To find x-intercept, put y=0 &amp; z=0, we get 3x+20+60=36⇒3x=36⇒x=12 To find…

Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

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Q: Find the Cartesian equation of the image of the line y = 2 under the mapping z → z 2 Sketch the…

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Q: Example 4: Show that the inverse of a point a with respect to the circle|z -c| = Ris the R2 point c+

A: The statement is given as the inverse of a point a with respect to the circle z-c=R is the point…

Q: iz transformation under z31 15/||

A: Solution: Consider the given equation is; w = izz-1 ⇒wz-1 = iz⇒wz - w = iz⇒wz - iz = w⇒zw-i = w⇒z =…

Q: Find the equation of the circle with center at (−2, 1) and that passes through the point whose…

A: The center of the circle and a point through which the circle passes is given as follows.

Q: 글 fe| 101 dz, where C is the circle |z+ 10i| =1+8, 0<0< 2n . Evaluate 2410i (z+105)

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Q: dz b) C: z|= 4 is a circle calculate the integral .(z-1)(z² +9)

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Q: 1 -dz, C is the circle |z1|= 2 2³ (z-2) C

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Q: Find the Cartesian equation of the image of the line x = 2 under the mapping z → e z.  Sketch the…

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Q: T 1) Reflect quadrilateral ABCD across the y-ar reflection on the coordinate plane to the right. new…

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

Q: Show your soluions Change this general form into standard equation and find its center of the circle…

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Q: Vhat is the equation of a circle with center (3, –7) that goes through the oint (1, 1)? D (x – 3)2 +…

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