4. Let C be the the circle ² + y² = 4 and Calculate the work(W = [,F dr when C is traversed in the counter-clockwise direction.

Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: Calculus Question

A: Substitution is the method in which a variable is substituted with its equivalent expression to…

Q: Guide Plot. label and connect the following coordinates F (-5, -4), G (-2, 4) & H (3, -4) on the…

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Q: Create the formula for circles with center on the line y = -x and passes through the origin

A: Introduction The equation of circle gives an algebraic approach to define a circle given its centre…

Q: 5. Is the point (2, 7) on the circle defined by (x – 2) + (y – 7)2 = 4?

A: Given equation of the circle is: (x-2)2+(y-7)2=4 Given point is: (2,7) Substituting,x=2,y=7 in given…

Q: Evaluate 12x-7 dz where (2213) (2-1)² Cis the circle Z = 2

A: Approach to solving the question:  Detailed explanation:

Q: Evaluate (r2 + y?)ds, C is the left half of the circle with radius 4 centered at (0,0) and is…

A: We calculate this by using concepts of line Integrals !

Q: Find the distance between two points (1, 2) and (3, −1).

A: We want to find the distance between the given two points. We use formula for finding the distance…

Q: Find the image of (4,-1) obtained by translating 4 units up, followed by a reflection over the…

A: We have to find the image of (4,-1) obtained by translating 4 unit up and then reflection over y…

Q: Transform the function y=6x-1rlght 3, down 4 , and reflected over the x-axis

A:

Q: 8c. Graph the line y = x +3 for -8 < x < 6 and then use geometry to calculate + 3) dr.

A: Answer is 35. Solution is given below....

Q: 8. Is the point (2, –7) on the circle defined by (x + 6) + (y + 1) = 100?

A: Given the equation of a circle, x+62+(y+1)2=100                   ...(1)

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

A:

Q: Evaluate F. dr along the line segment C from Pto Q. F = -8 xi+5y j; P(-1,0), Q(7, 0) F. dr i

A:

Q: 3. Use the Secant method on the circle function (x + 1)²+(y – 2)²= 16 to %3D find the intersection…

A:

Q: 2. Let be the part of the circle x² + y² = 9 from (-3,0) to (0, 3) in the upper left quadrant.…

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Q: Q6. Evaluate (2yx² - 4x)ds, where C is the lower half of the circle centered at the origin of radius…

A: check belowExplanation:Step 1:Step 2:Step 3: Step 4:

Q: 3. Find the equation of a circle with center at (2, 3) and tangent to the line 3x – 5y = 8. а. 2х2 +…

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Q: Find XY in the triangle below. 12/2 45°

A: