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the radius of some planet is miles use the formula for the radius r of a sphere given its


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1.Show that the force field vec F =(2xy-4- 1 2 sin( x 2 )sin( y 2 )) hat i +(x^ 2 + 1 2 cos( ...

cos( x 2 )cos( y 2 )) hat j is conservative and obtain the potential function. Evaluate the work done by vec F in moving a particle along the curve C which is the portion of the circle centered at origin with radius 2 in the first quadrant with counter clockwise orientation, without using line integrals.
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2.Jupiter’s mass is 320 times that of the Earth and its radius is 11.2 times the Earth’s. The Earth’s surface gravitational ...

h’s surface gravitational field strength is 9.81Nkg−1. Calculate the gravitational field strength close to the surface of Jupiter.
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3.Q1) (15 points) In the diagram below, M1 = 50 Kg, M2 = 20 Kg, mass and radius of the ...

g and 30 cm each, respectively. Both M1 and M2 rest on frictionless surfaces and the system starts from rest. (a) Draw the fbd for each of M1, M2 and the pulley. (b) Write the equations of motion for each of M1, M2 and the pulley. (c) Calculate the linear acceleration of the two masses, as well as the angular acceleration of the pulley. (d) Calculate the angular velocity of the pulley after M1 and M2 have been displaced linearly by 2 m. Q2) (10 points) A basketball is thrown with an initial speed v0 of 10.8 m/s at 400 above horizontal, and it enters the hoop from above. The ball is released at 2.00 m above the ground. The hoop is 3.05 m above the ground and 10.0 m away from the player. (a) Find the time at which the ball passes through the hoop. (b) Find the ball’s velocity (express in component form) just when it enters the hoop. (c) Find the ball’s maximum height. Q3) (5 Points) An object is thrown up from the top of a building of height of 400 m with an initial velocity of 20 m/s. (a) Find the position and the velocity of the object 5 s later. (b) With what velocity will it hit the ground? (c) At the same time the first object is thrown up, a second object is thrown up from the ground at 100 m/s. Will the two objects collide? If yes, calculate when and where,
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4.Circle properties that relate: • a tangent to a circle and the radius of the circle • a chord in a circle, ...

in a circle, its perpendicular bisector, and the centre of the circle • the measures of angles in circles
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6.I am trying to figure out the optimal radius that will give the lowest surface area of a cylinder. I ...

have done the calculus which reveals that the surface area is at a minimum when height is double the radius. I am now trying to find an equation for the relationship between the amount of wasted surface area as a percentage of the minimum surface area and the ratio between height and radius. If I were to plot it on a graph, the y axis would be the percentage of excess materials needed as a percentage of the minimum possible surface area, and the x axis would be height divided by radius. Since the surface area is minimized when height=2(radius), I know that when x=2, y=0. The website explains what I am trying to do quite well and shows the graph below. I am trying to find the equation for this graph, but am unsure how to go about it.
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7.A cell membrane has capacitance per unit area of 11.1 mF/m^2. . (a) cell has radius of 5.0 μm. Calculate surface area. ...

lculate surface area. (b) Calculate total capacitance presented by the cell membrane. (c) cell membrane has a resistance of 10 MΩ. Calculate τ (d) interior of the cell has an initial potential of Vi = 0 V, a potential of Vo = 100V is applied to the outside of the cell. Calculate how long it takes for the potential inside the cell to reach 50 V.
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8.Dung beetles are renowned for building large (relative to their body size) balls of dung and rolling them on the ...

them on the ground. A dung beetle can roll (without slipping) a ball of dung with radius 4.70 cm at a linear speed of 8.90 cm/s. Through what angle does the ball roll as the ball moves a distance of 10.0 cm?
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics