Find all points on the y-axis that are a distance 8 from P(7, 5).
Please solve using the distance formula, not Lagrange
multipliers.
5. (11 points) Find the shortest distance from the point P (0, 4,1) to the cone z = Vx2y2
5. (11 points) Find the shortest distance from the point P (0, 4,1) to the cone z = Vx2y2
7. A positive charge, Q1 , is placed on the +y axis, a distance d from the origin. A negative charge, Q2, is placed on the +x axis, also a distance d from the origin. Find the magnitude of the net electric potential at the origin if Q1 = +25 nC, Q2 = -10 nC, and d = 1.5 cm. A B C D E 13,732 V 5,025 V 8.990 V 20,977 V 7,676 V
All the charge in a ring of charge Q is the same distance r from a point P on the ring axis. a) Electric charge Q is distributed uniformly around a thin ring of radius a (Fig. 23.20). Find the potential at a point P on the ring axis at a distance x from the center of the ring. b) Find the electric field at P using the appropriate denotative relationships
Find a formula for the distance from the point P{x,y,z) to each of the following planes. a. Find the distance from P(x,y,z) to the xy-plane. b. Find the distance from P(x,y,z) to the yz-plane. c. Find the distance from P(x,y,z) to the xz-plane. a. Choose the correct formula for the distance from the point P(x,y,z) to the xy-plane. O A. Iz OB. Mx2 + y2 OC. Vz OD. x² + y² + 2? b. Choose the correct formula for the...
Q14 Find the distance from x=3 to x = 8 on the graph of y als Find the area of the surface generated by rotating y = 25*56 about the y-axis. Bonus: (1) Draw the region that is represented by the following definite integral which represents the volume of a solid generated by rotating the region about some axis. Be sure to label the curves and the axis of revolution: 2 (2 - y)- y)dy
005 10.0 points Acharge of 8 is on the y axis at 2 cm, and a second charge of-8 μC is on the y axis at .2 cm. 28 HC 4 AC -1 + 1 2 3 4 5 6 7 8 9 2-8 C Find the force on a charge of 4 μC on the r axis at r 6 cm. The value of the Coulomb constant is 8.98755 x 10 N m2/C Answer in units of N.
5. (8 points) The region in the first quadrant, bounded by the graphs of y-eye, and the y-axis is rotated around the y-axis to form a container. All units in the xy-plane are in feet. The container is entirely filled with a liquid of density 70 lbs/ft3 SET UP an integral equal to the work required to pump all the liquid to the top of the container.
5. (8 points) The region in the first quadrant, bounded by the graphs...
5. Find the vector 5 that is parallel to vector a = 27 -7 and has the length of 5. 6. Find the distance between two points (-1,-3,6) and (0,3,0). 7. Find the distance from the point (-5,3,-2) to a. the origin b. the x-axis c. the xz-plane 8. Let P; be the midpoint of the line segment between P.(-3,4,1) and P2(-5,8,3). Find the coordinate of the midpoint between P, and P3. 9. Knowing = (2,-3,1), 7 = (-2,0,5), and...
Find an equation for the surface consisting of all points P forwhich the distance from P to the x-axis is twice the distance from P to theyz-plane. Identify the surface.
Find all points on the x-axis 5 units away from the point (2, −4).