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A plane curve with length I has its end points at (0,0) and another point (a,...
Consider an arbitrary curve of fixed length C that connects the origin and a point a...
Consider an arbitrary curve of fixed length C that connects the origin and a point a fixed distance L < C away on the x-axis in the Cartesian x − y plane. Use the method of Lagrange multipliers to show that the area between the curve and the x-axis will be maximized if the curve forms the arc of a circle. (This shows, by the way, that a circle is the shape that encloses the largest area in a plane...
36a and 37 12:41 - A A) a a lies between the points (0,0) and (1,1)....
36a and 37
12:41 - A A) a a lies between the points (0,0) and (1,1). If your CAS has trouble evaluating the integral, make a substitution that changes the integral into one that the CAS can evaluate. 33. Sketch the curve with equation x2/3 + y2/3 = 1 and use symmetry to find its length. 34. (a) Sketch the curvey - x (b) Use Formulas 3 and 4 to set up two integrals for the are length from (0,0)...
8.7. A conducting strip of infinite length lies in the xy plane with its length oriented...
8.7. A conducting strip of infinite length lies in the xy plane with its length oriented along the x axis, and where – b/2<y<b/2 defines its width along y. Current I flows down the strip in the positive x direction and is uniformly distributed over the width. Above the strip and parallel to it at z=d is an infinitely long current filament that carries current I in the positive x direction. Find the force of attraction between the two currents...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,1), (0 , 1). Find the area of the image of R in the ry plane? (b) Find the area of R by computing the Jacobian of the transformation from uv-space to xy-space Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice...
e 09, 201 (6) 2 points An equation for the level curve of f(z, y) = In(z+y) that passes through the point (0, e2) i...
e 09, 201 (6) 2 points An equation for the level curve of f(z, y) = In(z+y) that passes through the point (0, e2) is A. z + y = e2 B. I+y e C. z+y 3. D. None of the above (7) 2 points The gradient of f(z,y, z) = ep at the point (-1,-1,2) is A. (2e2,e2,2e2). B. (-e,-e,2e2). C. (-2e2,-2e2, e) D. (-2e2,-e,-e) (8) 2 points Let f be a function defined and continuous, with continuous first...
Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined...
Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined by y=e" between y-1 and y-e. (a.) Set up, but do NOT evaluate, an integral with respect to y for the arc length of C. (b.) Set up, but do NOT evaluate, an integral with respect to x for the arc length of C. Set up, but do NOT evaluate, an integral for the area of the surface obtained by rotating C about the...
Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 ...
need help
Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 Find the length of parametized curve given by a(t) -0t3 -3t2 + 6t, y(t)1t3 +3t2+ 0t, where t goes from zero to one. Hint: The speed is a quadratic polynomial with integer coefficients. A curve with polar equation 14 7sin θ + 50 cos θ represents a line. Write this line in the given Cartesian form Note: Your answer should be...
Suppose is a closed curve in the plane and that -Y dr + 2? + y2...
Suppose is a closed curve in the plane and that -Y dr + 2? + y2 2 dy = 671 z? + y2 How many self-intersection points must have, at least? By "self-intersection point", I mean a point where the curve intersects itself other than its endpoints. For example, a simple closed curve has zero self-intersection points, and a figure 8 has one self-intersection point. Hint: If a curve has self-intersection points, then it can be divided up into a...
Qa 2 A semi-infinite line of charge of charge per unit length 1 is placed on...
Qa 2 A semi-infinite line of charge of charge per unit length 1 is placed on the positive î-axis. A semicircular arc of charge of radius a is joined to it at the origin, with its centre on the ġ-axis, at a distance a away, as shown. The total charge on the semicircle is Q. a. [5 points] Determine the electric field at a point i = yỹ (y > 0) due to the straight line. b. [3 points] Show...
Please answer all parts with full, clear solutions so i can understand :) :) Q2 (6 points) If C is a smooth plane curve...
Please answer all parts with full, clear solutions so i can
understand :) :)
Q2 (6 points) If C is a smooth plane curve with parametrization r r(t),t E [a, b], then the curvature K(t) of C at the point r(t) is defined to be the magnitude of the rate of change -ll dT of the unit tangent vector with respect to the arc length. That is, = ds () [2p] Show that K(t) = ||F (C) xr" (t)|| r...
36a and 37
12:41 - A A) a a lies between the points (0,0) and (1,1). If your CAS has trouble evaluating the integral, make a substitution that changes the integral into one that the CAS can evaluate. 33. Sketch the curve with equation x2/3 + y2/3 = 1 and use symmetry to find its length. 34. (a) Sketch the curvey - x (b) Use Formulas 3 and 4 to set up two integrals for the are length from (0,0)...
8.7. A conducting strip of infinite length lies in the xy plane with its length oriented along the x axis, and where – b/2<y<b/2 defines its width along y. Current I flows down the strip in the positive x direction and is uniformly distributed over the width. Above the strip and parallel to it at z=d is an infinitely long current filament that carries current I in the positive x direction. Find the force of attraction between the two currents...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,1), (0 , 1). Find the area of the image of R in the ry plane? (b) Find the area of R by computing the Jacobian of the transformation from uv-space to xy-space Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice...
e 09, 201 (6) 2 points An equation for the level curve of f(z, y) = In(z+y) that passes through the point (0, e2) is A. z + y = e2 B. I+y e C. z+y 3. D. None of the above (7) 2 points The gradient of f(z,y, z) = ep at the point (-1,-1,2) is A. (2e2,e2,2e2). B. (-e,-e,2e2). C. (-2e2,-2e2, e) D. (-2e2,-e,-e) (8) 2 points Let f be a function defined and continuous, with continuous first...
Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined by y=e" between y-1 and y-e. (a.) Set up, but do NOT evaluate, an integral with respect to y for the arc length of C. (b.) Set up, but do NOT evaluate, an integral with respect to x for the arc length of C. Set up, but do NOT evaluate, an integral for the area of the surface obtained by rotating C about the...
need help
Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 Find the length of parametized curve given by a(t) -0t3 -3t2 + 6t, y(t)1t3 +3t2+ 0t, where t goes from zero to one. Hint: The speed is a quadratic polynomial with integer coefficients. A curve with polar equation 14 7sin θ + 50 cos θ represents a line. Write this line in the given Cartesian form Note: Your answer should be...
Suppose is a closed curve in the plane and that -Y dr + 2? + y2 2 dy = 671 z? + y2 How many self-intersection points must have, at least? By "self-intersection point", I mean a point where the curve intersects itself other than its endpoints. For example, a simple closed curve has zero self-intersection points, and a figure 8 has one self-intersection point. Hint: If a curve has self-intersection points, then it can be divided up into a...
Qa 2 A semi-infinite line of charge of charge per unit length 1 is placed on the positive î-axis. A semicircular arc of charge of radius a is joined to it at the origin, with its centre on the ġ-axis, at a distance a away, as shown. The total charge on the semicircle is Q. a. [5 points] Determine the electric field at a point i = yỹ (y > 0) due to the straight line. b. [3 points] Show...
Please answer all parts with full, clear solutions so i can
understand :) :)
Q2 (6 points) If C is a smooth plane curve with parametrization r r(t),t E [a, b], then the curvature K(t) of C at the point r(t) is defined to be the magnitude of the rate of change -ll dT of the unit tangent vector with respect to the arc length. That is, = ds () [2p] Show that K(t) = ||F (C) xr" (t)|| r...
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