Math Answers

Let the electric equipotential lines (curves of constant potential) between two concentric cylinders with the z-axis in space be given by u(x,y) = x^2:+:y^2 = c (these are circular cylinders in xyz-space). Using the method in the text, find their orthogonal trajectories (the curves of electric force).

Write an equation for the set of all points in the plane equidistant from (0,–6) and y= –10.

Write your answer in vertex form. Simplify any fractions.

U=u(x1,x2)=(x1+2)^2(x2+3)3

find the marginal utility of each commodity

In a large restaurant 2 out of 5 customers ask for water with their meals .A random sample of 12 customers is selected . Find the probability that exactly 8 customers ask for water with their meal.

Determine the length of the curve 𝑥 = 𝑦^2 /2 for 0 ≤ 𝑥 ≤ 1/2 . Assume 𝑦 positive.

Let a and b be two cardinal numbers. Modify Cantor’s definition of a < b to define a ≤ b. (Hint: Examine what happens if you drop condition (a) from Cantor’s definition of a < b.) 2. Prove that a ≤ a. 3. Prove that if a ≤ b and b ≤ c, then a ≤ c. 4. Do you think that a ≤ b and b ≤ a imply

a = b? Explain your reasoning. (Hint: This is not as trivial as it might look.)

Given a die it has 6 faces in which gas either dot of x = 1, 2,3, 4, 5,6. Consider the sample of size n= 3. Illustrate the sampling distrubution and the central limit theorem.

Find an approximate value of the double integral below where 𝑅 is the rectangular region having

vertices (−1, 1) and (2, 3). Take a partition of 𝑅 formed by the lines 𝑥 = 0, 𝑥 = 1, and 𝑦 = 2, and take (𝑢𝑖

, 𝑣𝑖) at the

center of the 𝑖th sub region.

∬(3𝑦 − 2𝑥

2)𝑑𝐴

𝑅

Solve this Diffrential equation (1-x^2)y"-2xy'+n(n+1)y=0 using Power Series Method

Suppose we roll two dice and let X be the maximum of the two numbers obtained and let Y be their minimum. Write down the distribution tables of X, Y and Z = (X, Y ).