Q. Let S = {(x,y), 2² + y? = 1} C R?, then S is homeomorphic to a. {(x, y), 22 -y2 = 1} b. {(x,y), x+y = 1} c. {(x, y), 4a2 +9y? = 36} d. R2 %3D %3D O b O d

Q: Q2. (a) Find the overlapping area of two equations also give its geometrical representation: u? + v?…

A: Since, these equations are of the form  (x - a)2 + (y- b)2 = r2  which means both the equations are…

Q: -4 and C = 7 A = y В 1 3. Let Find x, y, z 2 -3 such that AB =C.

A: The matrix multiplication of two square matrices is performed as follows. Let P=ab cd and Q=ef gh .…

Q: T1 :3x + 2y+5z = 4 2: Contains the points A(1, 2, 1), B(0, –1, –4), C(3, 5, 2)

A:

Q: 2+2 c(z+1)²(z²+1)' 3. Determine dz, C: CCW rectangle with vertices (+2,+2), (±2,F 2).

A:

Q: Q. Let S = {(x, y), 2² + y? = 1} CR, then S is homeomorphic to a. {(x, y), a? – y? = 1} b. ((2,y), 2…

A: Here the a option is the same set ehich is given in the question.

Q: y uf f(x,y) = -+2 then find y %3D ду? O a. 02f 2x %3D dy? .3 O b. 22f %3D dy? y3 O c. a2f dy? y? 2x…

A:

Q: 8. The distance between the planes 2r-y-2z 5 and 2r – y - 2z = 7 is A C 2 9 dn 24

A:

Q: 1- Sz x?e*y dxdy 2 exy 3

A: Since you have posted multiple questions I can do first question as per our company guidelines…

Q: 1. Let F(x, y,z) = (x + y², y + z²,z + x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: Consider the provided question,

Q: 12. What is the radius and center for (x – 2)2 + y? 16? O A. r = 16; center is (2,0) O B. r = 4;…

A: Given equation is x-22+y2=16find radius and center

Q: Incorrectly, we usually say that when we multiply any number by ten we “add” a zero to the number.…

A: a) Jushua is wrong because the correct answer is 10×1.3=13 b) If a whole number is multiplied by 10…

Q: 5 Let V1 -B-A-el and y = = 8 A B = For what value (s) of his y in Span{v₁, V₂}? (E) h = None of the…

A:

Q: L? + y) da + (x + y?) dy ; C: AB, A = [1,3] → B = [3, 0] C: AB , A = [1, 3] → B = [3,0]

A:

Q: Q.2: Find u x v, where a: u = (1,–3,4) & v = (3,4, 7), ats b: и %3D (1,2,3) &v %3D (1,5, 2).

A: Given: a u=1, -3, 4 and v=3, 4, 7b u=1, 2, 3 and v=1, 5, 2 To Find: u×v=?

Q: Which of the following equations is variable separable? O a y+2zy O b. (z2 + y²)da – aydy = 0 O .…

A:

Q: a. Let C = C, U C2 where C, is the line segment from (2,0,0) to (3,4,5) and C2 is the line segment…

A: c1: Line segment from (2,0,0) to (3,4,5)The equation is…

Q: Evaluate . F dr where F(x, y, z) = zi + x²j + yk and C is the line segment from (1,2,3) to (4,3,2).…

A: Given Fx,y,z=zi^+x2j^+yk^. We have to evaluate ∫CF⋅dr, where C is the line segment from 1,2,3 to…

Q: 10. Given X(7,3) and Y(-6,2), find the coordinates of any point Z such that XZ XY = 41. .

A:

Q: A. y(x² + y²)dx + x(3x² – 5y²)dy = 0; whenx = 2,y = 1.

A:

Q: 2. Which of the following is the domain of y sec(x)? %3D A. [-1,1] B. R- (n+ 1) C. IR D. [-1,0}

A:

Q: Which of the following functions satisfy x²dy+ y(x + y)dx=0 with y(1) = 1 ?

A: A detailed solution is given below.

Q: Find fyzy. 9,8 f(x, y) = x°y³ – 8x*y + x f yry yxY ||

A:

Q: 2. Which of the following lines in standard form is equivalent to y OA. 2x+y=1 OB. x + 2y = 1 Oc.…

A: We have given that y = 2x + 1

Q: Evaluate (x – 2y + z) dS. S: z = 8 – x, 0 <x< 8, 0 < y< 7

A: Given I=∬S(x−2y+z)dSS:z=8−x,0≤x≤8,0≤y≤7

Q: Find the eu. f line through the Pont (-2,3,4) and Parallel to e Planes: 2x +3y +42-5, 3X+4y+52 - 6…

A:

Q: 5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a)…

A:

Q: J₁ R - x + 3y = 0, x + 3y Round your answer to 4 decimal places. Find - x + 3y -dA, where R is the…

A:

Q: x2+3y2 + dx dy 2ху = 0 Ans: In(x+ y) + = C (x+y)² 3x2+y2

A: substitution method to find the solution of the differential equation.

Q: 4. Find the values of x and y as shown below if three lines are parallel. (5y-4) 3y (2x+13)

A:

Q: df find dz

A:

Q: Q. Let S = {(x, y), x² + y? = 1} C R2, then S is homeomorphic to a. {(x, y), a² – y? = 1} b. {(x,y),…

A: Homomorphism

Q: (yæ² + æ*) dy – (y³ + 2 y² a 3 3 y x²) dx = 0 - - –

A:

Q: Find f, and f and evaluate each at the given point. F(X, v) = arctan). (2, -2) f,x, y) = %3D X, v) =…

A:

Q: 1. (t. xp- 2x 1 а. 3 /x. + C b. (1+x)³ + C 3 X + C с. 2x(1+x) d. None of the above

A: Given integral is, ∫1+x2xdx.   It is integrated as follows:   ∫1+x2xdx=∫1x+2+xdx

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.