Physics.

Physics.

As a student of electricity, you will learn that the voltage V (in volts) across a capacitor will gradually diminish to 0 with time t (in seconds). The function relating V to t is: V(t)= e^((-t)/3)  cos??(pt),where p =t  =3?.  What times t does the graph of V touch the graph of y= e^((-t)/(3 ))?When does the graph of V touch the graph of y= -e^((-t)/(3 ))?  When will the voltage V be between -0.4 and 0.4 volts?

Given the polar coordinates (-2, 3p/4 ), find the rectangular coordinates.

Given the rectangular coordinates (8.3, 4.2), find the polar coordinates.

Given 2×2 + 2y2 = 3, write the equation using polar coordinates (r, ?).

Given r2 = cos ?, write the equation using rectangular coordinates (x, y).

A passenger jet maintains a speed of 550 miles per hour headed due north. The Jet Stream is 100 miles per hour in a northeasterly direction. As the navigator, express the velocity va of the jet relative to the air and the velocity vw of the jet stream in terms of i and j. Find the velocity of the jet relative to the ground. Find the actual speed and direction of the jet relative to the ground.

You are a home owner who is interested in solar energy for your home. You learn that the amount of energy collected by a panel depends on the intensity of the sun’s rays and the area of the panel. The vector I represents the intensity in watts per square centimeters. The vector A represents the area in square centimeters whose direction is the solar panel orientation. The total number of watts collected by the panel is given by W = | I ? A |.  Suppose that I = <-0.02,-0.01> and A= <300,400>.  Find || I || and || A ||. Compute W. If the solar panel is to collect the maximum number of watts, what must be true about I and A?

You parked a moving van that has a gross weight of 8000 pounds on a street with a 5% grade. Find the magnitude of the force required to keep the van from rolling down

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