Given two pointsA(1,2,3), B(7,6,5), let S be the set of all points in (x, y)–plane such that PA is orthogonal to PB, then
(a) S is empty
(b) S contains exactly one point
(c) S contains exactly two points
(d) S is a line segment
(e) S is a circle
(a) Here is the information about the circuit.
Capacitor = 100 nF
Resistor = 47 kΩ
Supply voltage = 5 V
Investigate the meaning of ‘time constant’ and from your graph estimate a value. Compare this with your calculated one.
An overseas shipment of 5 foreign automobiles contains 2 that have slight
paint blemishes. If an agency receives 3 of these automobiles at random,
find the probability distribution of the random variable X representing the
number of automobiles with paint blemishes purchased by the agency.
Find the mean number of automobiles with paint blemishes.
Also calculate the variation
charging and discharging characteristics of DC
(a) Here is the information about the circuit.
Capacitor = 100 nF , Resistor = 47 kΩ ,Supply voltage = 5 V
Charging characteristic for a series capacitive circuit:
v=v(1 − e−t/RC)
Investigate what the other
terms in this expression mean.
Calculate the time constant for the circuit.
Use a spreadsheet to plot the charging curve over the range 0 to
20 ms (milliseconds).
Investigate the meaning of ‘time constant’ and from your graph
estimate a value. Compare this with your calculated one.
From your graph measure the gradient at 6 ms and compare this with
the calculated value.
(b) Now investigate the discharging characteristic of the circuit but with a 22 kΩ resistor
fitted.
Calculate and estimate the rate of change of voltage when t = T.
The mean value of land and buildings per acre from a sample of farms is $18001800, with a standard deviation of $300300. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 7171.