1) Consider the function d to be the “taxicab” distance in the xy plane(R2). The word...
1) Consider the function d to be the “taxicab” distance in the xy plane(R2). The word taxicab refers to only counting distance along vertical or horizontal segments, like a taxi in Manhattan. The “distance” between 2 points p = (x1,y1) and q = (x2,y2) is : d(p,q) = |x1 – x2| + | y1 – y2| Example: d((2,-7),(4,8))= |2-4| +|-7-8| = 2+15 =17.
Prove the taxicab distance is a metric on R2.
Homework Answers
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1) Consider the function d to be the “taxicab” distance in the
xy plane(R2). The word...
Describe in words the neighborhoods below for each of the following metrics. ( 5 points each part) a. For R2 d ( (x1, X2), (Y1 yz) ) = 1 if Euclidean distance > 1 Euclidean distance otherwise N...
Describe in words the neighborhoods below for each of the following metrics. ( 5 points each part) a. For R2 d ( (x1, X2), (Y1 yz) ) = 1 if Euclidean distance > 1 Euclidean distance otherwise N((0,0), ½)
Describe in words the neighborhoods below for each of the following metrics. ( 5 points each part) a. For R2 d ( (x1, X2), (Y1 yz) ) = 1 if Euclidean distance > 1 Euclidean distance otherwise N((0,0), ½)
The charges and coordinates of two charged particles held fixed in an xy plane are q1...
The charges and coordinates of
two charged particles held fixed in an xy plane are q1 = 3.24 μC,
x1 = 4.88 cm, y1 = 0.358 cm and q2 = -3.53 μC, x2 = -2.01 cm, y2 =
1.60 cm. Find the (a) magnitude and (b) direction of the
electrostatic force on particle 2 due to particle 1. At what (c) x
and (d) y coordinates should a third particle of charge q3 = 5.12
μC be placed such that...
Three particles lie in the xy plane. Particle 1 has mass m1 = 6.7 kg and...
Three particles lie in the xy plane. Particle 1 has mass m1 = 6.7 kg and lies on the x-axis at x1 = 4.2 m, y1 = 0. Particle 2 has mass m2 = 5.1 kg and lies on the y-axis at x2 = 0, y2 = 2.8 m. Particle 3 has mass m3 = 3.7 kg and lies at the origin. What is the magnitude of the net gravitational force on particle 3?
The charges and coordinates of two charged particles held fixed in an xy plane are q1...
The charges and coordinates of two charged particles held fixed in an xy plane are q1 = 3.18 μC, x1 = 5.16 cm, y1 = 0.330 cm and q2 = -3.65 μC, x2 = -1.69 cm, y2 = 1.82 cm. Find the (a) magnitude and (b) direction of the electrostatic force on particle 2 due to particle 1. At what (c) x and (d) y coordinates should a third particle of charge q3 = 4.65 μC be placed such that...
The charges and coordinates of two charged particles held fixed in an xy plane are q1...
The charges and coordinates of two charged particles held fixed in an xy plane are q1 = 2.35 μC, x1 = 3.13 cm, y1 = 0.644 cm and q2 = -6.36 μC, x2 = -2.04 cm, y2 = 1.40 cm. Find the (a) magnitude and (b) direction of the electrostatic force on particle 2 due to particle 1. At what (c) x and (d) y coordinates should a third particle of charge q3 = 3.72 μC be placed such that...
The charges and coordinates of two charged particles held fixed in an xy plane are q1...
The charges and coordinates of two charged particles held fixed
in an xy plane are q1 = 3.49 μC,
x1 = 3.80 cm, y1 = 0.165 cm
and q2 = -5.05 μC, x2 =
-2.87 cm, y2 = 2.08 cm. Find the
(a)magnitude and (b) direction
(with respect to +x-axis in the range (-180°;180°]) of the
electrostatic force on particle 2 due to particle 1. At what
(c) x and (d) y
coordinates should a third particle of charge
q3...
The charges and coordinates of two charged particles held fixed in an xy plane are q1...
The charges and coordinates of two charged particles held fixed in an xy plane are q1 = 3.01 μC, x1 = 5.65 cm, y1 = 0.562 cm and q2 = -4.84 μC, x2 = -2.16 cm, y2 = 2.12 cm. Find the (a) magnitude and (b) direction (with respect to +x-axis in the range (-180°;180°]) of the electrostatic force on particle 2 due to particle 1. At what (c) x and (d) y coordinates should a third particle of charge...
The charges and coordinates of two charged particles held fixed in an xy plane are q1...
The charges and coordinates of two charged particles held fixed in an xy plane are q1 = 2.72 μC, x1 = 4.23 cm, y1 = 0.857 cm and q2 = -3.97 μC, x2 = -2.37 cm, y2 = 2.35 cm. Find the (a)magnitude and (b) direction of the electrostatic force on particle 2 due to particle 1. At what (c) x and (d) y coordinates should a third particle of charge q3 = 6.13 μC be placed such that the...
The charges and coordinates of two charged particles held fixed in an xy plane are 91...
The charges and coordinates of two charged particles held fixed in an xy plane are 91 2.66 uc, x1 = 2.85 cm, Y1 = 0.242 cm and 92 = -4.37 uc, x2 = -2.93 cm, Y2 = 1.98 cm. Find the (a) magnitude and (b) direction (with respect to +x-axis in the range (-180°;180°]) of the electrostatic force on particle 2 due to particle 1. At what (C) x and (d) y coordinates should a third particle of charge 93...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above th...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
Describe in words the neighborhoods below for each of the following metrics. ( 5 points each part) a. For R2 d ( (x1, X2), (Y1 yz) ) = 1 if Euclidean distance > 1 Euclidean distance otherwise N((0,0), ½)
Describe in words the neighborhoods below for each of the following metrics. ( 5 points each part) a. For R2 d ( (x1, X2), (Y1 yz) ) = 1 if Euclidean distance > 1 Euclidean distance otherwise N((0,0), ½)
The charges and coordinates of
two charged particles held fixed in an xy plane are q1 = 3.24 μC,
x1 = 4.88 cm, y1 = 0.358 cm and q2 = -3.53 μC, x2 = -2.01 cm, y2 =
1.60 cm. Find the (a) magnitude and (b) direction of the
electrostatic force on particle 2 due to particle 1. At what (c) x
and (d) y coordinates should a third particle of charge q3 = 5.12
μC be placed such that...
The charges and coordinates of two charged particles held fixed
in an xy plane are q1 = 3.49 μC,
x1 = 3.80 cm, y1 = 0.165 cm
and q2 = -5.05 μC, x2 =
-2.87 cm, y2 = 2.08 cm. Find the
(a)magnitude and (b) direction
(with respect to +x-axis in the range (-180°;180°]) of the
electrostatic force on particle 2 due to particle 1. At what
(c) x and (d) y
coordinates should a third particle of charge
q3...
The charges and coordinates of two charged particles held fixed in an xy plane are 91 2.66 uc, x1 = 2.85 cm, Y1 = 0.242 cm and 92 = -4.37 uc, x2 = -2.93 cm, Y2 = 1.98 cm. Find the (a) magnitude and (b) direction (with respect to +x-axis in the range (-180°;180°]) of the electrostatic force on particle 2 due to particle 1. At what (C) x and (d) y coordinates should a third particle of charge 93...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
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