Math Answers

Find the extreme values of z

 on the surface 2x

2

+3y

2

+z

2

−12xy+4xz=35

The joint probability density function of 𝑋 and 𝑌 is given by 𝑓(𝑥, 𝑦) = { 𝑥 + 𝑦 3 0 ≤ 𝑥 ≤ 1, 0 ≤ 𝑦 ≤ 2 0 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒 Find the two lines of regression.

The joint probability density function of 𝑋 and 𝑌 is given by

𝑓(𝑥, 𝑦) = {

𝑥 + 𝑦

3

0 ≤ 𝑥 ≤ 1, 0 ≤ 𝑦 ≤ 2

0 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒

Find the two lines of regression.

Determine values of the constants A and B such that an = An + B is a solution of

recurrence relation an = 2an−1 + n + 5. Hence, find the solution of this recurrence

relation with a0 = 4.

A manufacturing process costs RM 6500 to set up for one year’s use. If items cost RM 85 each to produce and other costs amount to 3.5 x2, where x is the production in hundreds, find the level of production that will minimize the cost per item over the year. What will the total cost amount to at this level of production?

Solve the following differential equations in series.

x²d²y/dx + xdy/dx +(x²-4)y=0

Show that a norm on a vector space X is a sublinear functional on X

reduce the following equation onto canonical form

u_x+2xyu_y=x

Apply separation of variable to solve

x²u_xy+9y²u=0

Solve the Cauchy Problem,

xu_x+(x+y)u_y=u+1 with u(x,y)=x² on y=0