The heaviside function h is defined by h(t)={0 if t< 0, 1 if t≥0 it is used in the study of electric circuits to represent the sudden surge of electric current, or voltage, when a switch is instantaneously turned on. sketch the graph of the voltage v(t) in a circuit if the switch is turned on at time t=5 seconds and 240 volts are applied instantaneously to the circuit. write a formula for v(t) in terms of h(t). (note that starting at t=5 corresponds to a translation.)

Explanation:

The heaviside function is defined as:

so we see that the Heaviside function "switches on" when, and remains switched on when

If we want our heaviside function to switch on when , we need the argument to the heaviside function to be 0 when

Thus we define a function f:

The term inside the heaviside function makes sure to displace the function 5 units to the right.

Now we just need to add a scale up factor of 240 V, because thats the voltage applied after the heaviside function switches on. ( when , so it becomes just a 1, which we can safely ignore.)

Therefore our final result is:

I have made a sketch for you, and added it as attachment.  

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​