Math Answers

Consider the equation and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”. For example, “(0, 3) R (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation can also be read as “the point (x, y) is on the circle of radius 1 with center (0, 2)”. In other words: “(x, y) satisfies this equation , if and only if, (x, y) R (0, 2)”.

Does this equation determine a relation between x and y?

Can the variable x can be seen as a function of y, like x=g(y)?

Can the variable y be expressed as a function of x, like y= h(x)?

If these are possible, then what will be the domains for these two functions?

What are the graphs of these two functions?

Are there points of the coordinate axes that relate to (0, 2) by means of R?

Let D be a convex region in R2 and let L be a line segment of length I that connects points on the boundary of D. As we move one end of L around the boundary, the other end will also move about this boundary, and the midpoint of L will trace out a curve within D that bounds a (smaller) region R. Using the corollary to Green’s Theorem for finding area, find an expression that relates the area of R to the area of D in terms of the length I of the line segment. [You might start with some simple regions, but you must show this generally.] 

The symbol.___________________ means"is similar to"and the symbol_________id the abbreviation for the word angle

compute a two sided 95% Cl for the true mean serum-creatinine level

A population consist of the numbers 3,5,10,11 and 6. Let us list all possible samples of size 3 fr this population and compute the mean of each sample

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

The run time for written C-Programmes for Gauissian elimination follows a normal distribution with a mean of 36 minutes and a standard deviation of 11 minutes. For a C-Programme chosen from Gaussian elimination files at random, find the probability that the run time will be

a)        less than 51 minutes                                                                                       

b)        more than 60 minutes                                                                                    

c)        between 41 and 56 minutes                                                                           

d)        between 12 and 26 minutes 

Locate the critical points and identity the stationary points of 4x^4-16x^2+17

a. Construct a truth table for (~p ˄ r) ˅ (q ˄ ~r).

b. Use the truth table that you constructed in part to determine the truth value of (~p ˄ r) ˅ (q ˄ ~r), given that

p is false, q is true, and r is false.

The number of claim per hour at the WBA Insurance Company has a Poisson distribution with mean 3 claim per hour. Find the probability that in any given hour there will be.

a)        exactly none claims   

b) exactly one claim                                                                                           

c)        exactly two claims                                                                                       

d)        three or more class                                                                                        

e)        exactly four claims in 2 hours