Math Answers

a) A thin metal plate bounded by the 𝑥-axis and the lines 𝑥 = 0 and 𝑥 = 1 and

stretching to infinity in the 𝑦-direction has its upper and lower faces perfectly

insulated and its vertical edges and edge at infinity are maintained at the constant

temperature 0 °𝐶, while over the base temperature of 50 °𝐶 is maintained. Find

the steady state temperature 𝑢(𝑥,𝑡).

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b) If 𝑓(𝑥𝑦^2, 𝑧 − 2𝑥) = 0 then prove that 𝑥 𝑧x −1/2𝑦 𝑧𝑦 = 2 𝑥

Solve (𝐷^2 − 3𝐷 + 2)𝑦 = 𝑥^2 + sin 𝑥 where 𝐷 =𝑑/𝑑𝑥

Given x'=x(-20-x+2y)

y’=y(-50+x-y) identify the type of interaction represented by the system

A random sample of 16 pigs showed an average increase of weight of 20 kg when a new diet is administered. Assuming

that the increase in weight is normal with variance 4, find 95% confidence interval for average increase in weight due to

new diet. ( ) ( ) )

the intensity (I) of illumination given by a projector varies inversely as the square of the distance(d) of its lamp from the screen if the projector is 20m from the screen when the intensity is 2.5 find the distance when the intensity is 62.5 a if r varies inversity as the aquare of h and r =6 when h = 4 

A furniture manufacturer makes two products - tables and chairs. Processing of these products is done on two types of machines A and B. A chair requires 2 hours on machine type A and 6 hours on machine typeB. A table requires 5 hours on machine type I and no time on Machine type II. There are 16 hours/day available on machine type A and 30 hours/day on machine type B. Profits gained by the manufacturer from a chair & a table are Birr 2 and Birr 10 respectively.What should be the daily production of each of the two products?Use graphical method of LPP to find the solution.

Three applicants are to be choosen at random out of 4 boys & 6 girls.what is the probability of selecting 1)all girls 2)all boys 3)at least one boy

A marble is drawn at random from a box containing 10 red,30 white,20 blue& 15 orange marbles .find the probability that it is 1)orange or red 2)not red or blue

A drawer contains 50 bolts & 150 nuts ,half of the bolts are rusted,if one item is choosen at random .what is the probability that it is rusted or a bolt?

Suppose the average number of calls received by an operator in one minute is 2. What is the probability of receiving 10 calls in 5 minutes?