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An inductor of 2 henries, resistor of 16 ohms and capacitor of 0.02 farads are connected in series with a battery of
e.m.f E = 100sin33t. At t=0, the charge on the capacitor and current in the circuit are zero. Find the charge and
current at time t.
J. A spring with a mass of 2 kg has natural length m. A force of 25.6 N
perform this using the linear differential equation of higher order in operator form: (D2 + 3D + 2) (e^-2x + 3x²)
Tank A initially contains 200, litres of brine containing 225 N of salt. Eight litres of fresh water per A and the mixture, assumed uniform, passes from A to b. initially .containing 200 litres of fresh water, at 8 litres per minute. The resulting mixture, also kept uniform, leaves B at the rate of 8 litres/min. Find the amount of minute enter salt in tank B after one hour.
perform this using the linear differential equation of higher order in operator form: (D2 + 3D + 2) (e-2x + 3x²)
Suppose that a population yy grows according to the logistic model given by formula:
yy = LL
1 + AAee−kkkk .
a. At what rate is yy increasing at time tt = 0 ?
b. In words, describe how the rate of growth of yy varies with time.
c. At what time is the population growing most rapidly?
Verify that the function u(x,y,z)=1/(√x^2+y^2+z^2) is a solution of the three-dimensional Laplace equation Uxx + Uyy +Uzz = 0.
An object moves along a straight line so that after t minutes, its distance from its starting point is𝑠(𝑡)=2𝑡3+4𝑡2+6meters .
At what speed is the object moving at the end of 3minutes?
Draw 25 samples from a distribution of IQ scores that are normally distributed with a mean of 100 and standard deviation of 15. What is the probability that the mean of 25 randomly drawn IQ scores will exceed 103 points?
State the Pigeonhole Principle. In a result sheet of a list of 60 students, each marked “Pass” or “Fail
“. There are 35 students pass. Show that there are at least two students pass in the list exactly nine
students apart. (for example students at numbered 2 and 11 or at numbered 50 and 59 satisfy the
condition).
State the Pigeonhole Principle. A chess player wants to prepare for a championship match by playing
some practice games in 77 days. She wants to play at least one game a day but no more than 132
games altogether. Prove that there is a period of consecutive days within which she plays exactly 21
games
#339914 on Dec 2023