What is the surface area, Consider a surface in spherical

What is the surface area

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Reference no: EM132622893

Question 1

You are given 3 vectors: A = -8ax + -9ay + -6az, B = 5ax + 3ay +3az, C = -7ax + 4ay + 0az what is the y component of the operation A + 3B - 2C?

Question 2

You are given 3 vectors: A = -5ax + 3ay + 8az, B = 7ax + 0ay +-3az, and C = 9ax + 5ay + -4az. Find the z component of the operation A*BxC.

Question 3

Determine th line integral of vector F=4.7x lax + 4.5ay + 8.9yaz from point (-1,3,-2) to point (2,4,1) in rectangular space.

Question 4

You are given two vectors.. A = -9ax + 1ay + -1az and B = -6ax + 3ay + -2az. Find the x component of a vector C which is perpendicular to the plane containing Vectors A and B with a length of 8.

Question 5

Determine the line integral of F=3.3rar + 1.5atheta - 1az along a circular path of constant radius 2 between two points in rectangular space (2,0,0) and (0,2,0).

Question 6

Consider a surface defined by r=3, with phi between 8 and 145.3 degrees, and z between 9.8 and 17.6. What is the surface area?

Question 7

Determine the volume of a region between r1=0.1 and r2=17, and phi1=3.6 degrees and phi2=134.3 degrees and z1=0.1 and z2=19.5.

Question 8

A mass is suspended from a string with length of 63 cm it is twirled vertical. It achieves and angle from vertical of 17 degrees. Assuming acceleration due to gravity is 9.78 m/s^2, what is its angular velocity in rpm?

Question 9

Evaluate the line integral of F=2.7ar + 7.9ratheta +8.8raphi between points in rectangular space (0,0,3) and (3,0,0). Also 0 lte theta lte pi/2 and 0 lte phi lte pi/3.

Question 10

Consider a plane which needs to fly due north in order to reach its destination. The airspeed of the plane is 180 mph. The plane is bucking a 33 mph head wind from the north west. What is the angle west of north the plane must fly to reach its destination?

Question 11

Determine the net flux of Vector F=4.75xax + 3.44yay + 3.98az out of the rectangular surface bounded between the xyz axes and x=1, y=2 and z=3.

Question 12

A river flows north to south at a speed of 2.24 mph A boat crosses the river to the west by the most direct route. The maximum speed of the boat without current is 8.26. What is the heading in degrees, north of west that the boat must travel?

Question 13

A truck weighing 4,005 pounds is negotiating a 1,215 foot radius curve with forward velocity of 57 mph. Find the bank of roadway angle which results in no friction between the tires and roadway assuming acceleration due to gravity is 32.2 feet per second squared.

Question 14

Consider a point in rectangular space (3,-5,2). What is the phi component in cylindrical space in degrees?

Question 15

Consider a point in cylindrical space (-5,58,2), where angle phi is in degrees. What is the corresponding x component in rectangular space?

Question 16

Consider 2 vectors at a point in cylindrical space (-7.1,4.5,0.1). Vector A = 1.4ar + 30.1aphi + -1.3az, and vector B = 8.8br + 148.3bphi + 2.6bz. Assume that the angle phi is in degrees, convert it to radians and determine the dot product of A and B.

Question 17

Consider 2 points in cylindrical space. Point 1 is at (7.2,61.5,-2.4) and point 2 is at (2.4,21.3,-1.9). The angles are in degrees. Convert the angles to radians and determine the distance between them.

Question 18

You are given a point in rectangular space. (-5,5,3). Find the r component in spherical space.

Question 19

You are given a point in rectangular space. (8,9,1). Find the phi component in spherical space.

Question 20

You are given a point in spherical space (9.9,-18,-38). Find the x component of the same point in rectangular space.

Question 21

You are given a point in spherical space (2,102,77). Find the y component of the same point in rectangular space.

Question 22

You are given a point in spherical space (3.5,69,92). Find the z component of the same point in rectangular space.

Question 23

What is the direction resulting from the cross prodct of ar X atheta

-aphi

-ar

atheta

Question 24

Consider a surface in spherical space with constant 1.43ar, theta ranging from pi/2 to pi, and phi ranging over the same range. What is the surface area?

Question 25

Determine the line integral of F=9.4rar + 4.3aphi - 9.3az along a circular path of constant radius 1.5 between two points in rectangular space (2,0,0) and (0,2,0).

Question 26

Determine the net flux of the vector F=6.48ar +5.68aphi +6.64zaz. Assume that it is bounded by the xz and yz planes with 0 lte phi lte pi/2 with r=3.37 and z = 6.24.

Question 27

Calculate the net flux from the vector F=9.31ar + 6.76atheta + 7.85raphi out of the surface bounded by the xz and yz planes with r= 5.66, 0 lte theta lte pi/2 and 0 lte phi lte pi/2.

Question 28

Find the x component of the unit vector perpendicular to the plane containing the following vectors. A = -2ax + 7ay + -5az, and B = 1ax + 2ay + 7az

Question 29

Your are given two vectors: A = -6ax + 4ay + -7az, and B = dax + -2ay + 5az. Assume the vectors are perpendicuar, and find the value of d.

Question 30

You are given 2 vectors: A = -3ax + -5ay + 9az, and B = -1ax + 2ay + -8az. What is the magnitude of the projection of B onto A?

Reference no: EM132622893

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