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Let g(x, y) = y x2+y 2 . (a) Show that g is harmonic in D = {(x, y) : x 2 + (y + 3)2 < 4}. (b) How can the function f(z) = 1 z be used to show that g is harmonic in D?
Assignment 1: Application of static fluid principles
A “Y”-shaped tube is inserted upside down so that the left
foot and right foot are immersed in two kinds of liquid.
After both feet are immersed in the liquid, then the top of
the Y pipe is closed with the finger and pulled upwards,
so that the two legs of the Y pipe are filled with a column
of different high-density liquids. If the density of the first
liquid is 0.80 gram.cm-3 and the second density is 0.75
gram.cm-3, if the first liquid column has a high of 8 cm,
then determine the height difference between the two
liquid columns on U pipe.
All 77 rooms in a motel will be rented each night if the manager charges $40 or less per room. If he charges $(40+z) per room, then 2z rooms will remain vacant. If each rented room costs the manager $7 per day and each unrented room $2 per day in overhead, how much should the manager charge per room to maximise his profit?
The joint PDF of the random variables f(x,y)=8xy,0<x<1, 0<y<x
f(x,y)=8xy,0<x<1, 0<y<x. Find the marginal probability density function of Y.
Assignment 1: Application of static fluid principles
A steel cable holds a 200 kg shark tank 3 meters below
the surface of saltwater. If the volume of water displaced
by the shark tank is 0.1 m^3, what is the tension in the
cable? Assume the density of saltwater is 1025 kg/m^3
Assignment 1: Application of static fluid principles
You have a block of a mystery material, with a length (l)
of m long, 0.11 m wide and 0.25 m thick. Its mass is 1155 grams.
a) What is its density?
b) Will it float in a tank of water, or sink? what
percentage of it is sticking out of the water?
given value: 0.38
Rose wants to buy a car on hire purchase for N$75,000.00 at the rate of 11% p.a. repayable using monthly installments for a period of 3 years and 10 months. (No deposit was required). Use the given information to calculate the:
a. Total amount of money expected to be paid to the Hire Purchase Company over the years. (5)
b. Monthly installment to be paid by Rose (5)
Assignment 1: Application of static fluid principles
A ball of mass 0.05 kg and diameter 1.05 metre is held fully
underwater (density 1000 kg/m3.) Calculate
a. the up thrust on the ball
b. the density of the ball
c. the percentage of the ball above the surface of the
water if it is allowed to float
(6x+yz)dx+(xz-2y)dy+(xy+2z)dz=0
A certain population has a variance of 2.5, and a sample size of 4 is used to obtain the sampling distribution of the sample mean of this population. What is the variance of the sampling distribution of the sample mean?
Write your answer as a fraction in lowest terms.
