Math Answers

Find the extreme values of z on the surface 2x^2 + 3y^2 + z^2 – 12xy + 4xz = 35.(DO NOT USE LAGRANGE MULTIPLIERS)

A house which is valued at 2,600, 000 appreciated at rate of 12% per year

I. What will be its value after two and half years?

ii. After how long will its value be 4200,000

Find z1/n; for n=3, z = 1-i in C (, the Argand Plane).

Write each of these statements in the form “if p, then q” in English.

a) It snows whenever the wind blows from the northeast.

b) The apple trees will bloom if it stays warm for a week.

c) That the Pistons win the championship implies that they beat the Lakers.

d) It is necessary to walk eight miles to get to the top of Long’s Peak.

e) To get tenure as a professor, it is sufficient to be world famous.

f ) If you drive more than 400 miles, you will need to buy gasoline.

g) Your guarantee is good only if you bought your CD player less than 90 days ago.

h) Jan will go swimming unless the water is too cold.

i) We will have a future, provided that people believe in science.

Write each of these statements in the form “if p, then q” in English.

a) It snows whenever the wind blows from the northeast.

b) The apple trees will bloom if it stays warm for a week.

c) That the Pistons win the championship implies that they beat the Lakers.

d) It is necessary to walk eight miles to get to the top of Long’s Peak.

e) To get tenure as a professor, it is sufficient to be world famous.

f ) If you drive more than 400 miles, you will need to buy gasoline.

g) Your guarantee is good only if you bought your CD player less than 90 days ago.

h) Jan will go swimming unless the water is too cold.

i) We will have a future, provided that people believe in science.

Solve differential equation

(D^3-6D’D+11D’^2D-6D’)z=cos(2x+y)+e^(2x+y)-y

find the general solution of the homogeneous linear equations

1.(2D²-5D-3)y=0

2. (9D²-6D+1)y=0

3. (D⁴-2D²)y=0

4. (D⁵+8D³+16D)y=0

5. (D³+8)y=0

Reduce 2++x²+2x₂x4x−2x4, into canonical form. Find the rank,

index, signature and its nature.

A company calculates its expected profits as a function of the quantity of the items it can sell. How much are their expected profits if the company’s profit function is P(q)=q³−2000q+500 and their current sales quantity, q, is 60?

Specifications for mass-produced bearings of a certain type require among other things, that the standard deviation of their outside diameters should not exceed 0.0050cm. Use the level of significance 0.01 to test the null hypothesis σ=0.0050 against the alternative hypothesis σ>0.0050 on the basis of a random sample of n=12 for which s=0.0077cm. What would be the decision for the test of hypothesis for this problem?