Evaluate |-y dx+x dy , where C consist of the curves along the horizontal line from (-4,4) to (-2,4) and along the C parabola y =x² from the point (-2, 4) to the point (0, 0). [Hint: Follow the direction of the curves and S =[ +J 1

Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

A:

Q: - 6y Find the tangent plane to the equation z at the point (12,24,4) z =

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Q: The tangent line to the graph of y = In(2x) is perpendicular to z + 4y = 1 at the point where Select…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

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Q: Verify that Green's Theorem is true for S,3(y? – x) dx + (x2 - y)dy given that the curve C is formed…

A: We have to solve the given integral by Green's theorem.…

Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

A: If be a positively oriented,  closed curve  enclosing the region D Then for a vector field F→=P,Q…

Q: (B) The length of the curve r(t)=(1+1)i+(1-1j+r/2k from the point t=- to the point r= is 2. -IN

A: The length of the curve means the arc of the length of the curve . The arc of the length of a curve…

Q: Do the curves ri(t) = (t² + 3, t+1, t² – 5) and rž(s) = (4s, 2s – 2, s + 1) intersect? If so, at whi…

A:

Q: 2. Prove that the following curves are intersecting with a right angle: 5y-2x+ y –x*y =0 2y+5x+x*…

A: Given curves are  5y-2x+y2-x2y=0and2y+5x+x4-x3y2=0

Q: Find the plane thst passes through the equation of. the point P(6,0,-2) ¢ = 1+t, z=2 -t entains the…

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Q: Which of the following is the equation of the tangent plane to the surface z = 3x2 +x-y²+y at the…

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Q: Let f: R2 R be the function with f(xy) = x3 + y3. Determine all points € R2 such that the tangent…

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Q: Express the curve by an equation in x and y given x(t) = e' and y(t) = 7 – e2'. a) O-x2 + y = 7, x 2…

A: simplify the equation and choose correct equation.

Q: y = x², x = y? X = about the line x = -1 can be computed using the method of disks or washers via an…

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Q: Find . F dR such that F(x, y) = (2y, xy – 2x) And I is the curve in the 3rd quadrant from the point…

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Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

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Q: (d) The curve y = x – x² from r = 0 to r = 2

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Q: 2) Consider the oriented curve C given by C = C1uC2, where C2 is obtained by intersecting the…

A: We will first parametrize the curves C1 & C2 then substitute the x,y,z values into the line…

Q: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

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Q: Express the curve by an equation in x and y given x(t) = sin(t) and y(t) = 8 + cos² (t). a) O-x² +y…

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Q: Find the equation for the tangent plane and the normal line at the point Po(3,3,1) on the surface x…

A: To find an equation for the tangent plane and the normal line at the point (3,3,1).

Q: ) Find the gavea d the rgion enclased by the line x-In3 and the curves y= ex and y=ex

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Q: Find the tangent plane to the equation z = x + 3y – 5y at the point ( – 5, – 5, 125) 2 Z =

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Q: Find the equation for the tangent plane and the normal line at the point Po(3,2,3) on the surface 2x…

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Q: At what point on the paraboloid  y= x^2 +z^2is the tangent plane parallel to the plane x+2y+3z=1 ?

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Q: Find the points on the graph of f(x, y) = 3x 2 - xy - y 2 at which thetangent plane is horizontal.

A: Given that, fx, y=3x2-xy-y2z=3x2-xy-y2

Q: 2. Let F(x,y) = (cos(x – 2y), –2 cos(x – 2y)). Find curves C and C2 so | that, F. dr = 0 F. dr = 1

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Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x)) and C is the curve in the third quadrant from…

A: Given

Q: Find the coordinates of the point(s) on the curve 2y = 10 – a² that are closest to the origin. а) О…

A: Given that

Q: |Verify that Green's Theorem is true for S,3(y2 – x) dx + (x² – y)dy given that the curve C is…

A:

Q: Find the equation of the plane that passes through the point (2, 1,2) and is tangent to the surface…

A:

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

A:

Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: Find the length of the curve r(t) = (√2t)i + (√2t)j + (1 - t2)k from (0, 0, 1) to (√2, √2, 0)

A: given, r(t)=(2t)i +2tj+1-t2kwe have to find the length of the  given curve from (0,0,1) to 2,2,0

Q: Let C be any curve.

A:

Q: (b) F. dr, C is the line segment from (1, 1) to (5, 1), F = (y, -x). 3 of 7 (c) Set up but do not…

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Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

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Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y²-x²y = 0 2y +…

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Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

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Q: The value of [F.dr where F= x'y2 i + y j and C is the curve y? = 4x in the XY-plane from (0, 0) to…

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Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

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Q: ind the equation of the plane in the figure, which is tangent to the graph f(x, y) = 0.2x + 1.4y –…

A: Equation of tangent plane to the surface x=f(x,y) at point (a,b) is…

Q: nclosed between the curves y= r'and x= y? 18 16 14 12 12 14 16 18 -1 -1 O 02 04 0.8 0.6 0.4 0.2 0.6…

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Q: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

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Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

Q: EX Find the point the curve y=x3+x²-l where the tamjent on is parallel to the X-oaxis

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Q: Find an equation for the tangent plane to z = 9x? – 8y² at the point (1, 1, 1). - = 0.

A: Here we find the equation of tangent plane.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.