canonical formulas of conical sections and their properties

Please see the attached file for the fully formatted problems.

1. Solve the system of equations algebraically. Be sure to find all
solutions!
X^2+y^2=10
2x^2-y^2=17

I got not sure if it's right or missing
x=2.999999976132
Y=0.999999870315

2. Find the coefficient of the term x^5 y^3 in the expansion of (4x-y)^8
3. Put each conic in standard form; identify the conic, , state
vertices, centers, asymptotes where applicable.

1) x^2 = 4y−8

Standard Form:

Identify which Conic Section:

Characteristics applicable:
Center:

Vertices:

Asymptotes:

2) 9(x−2)^2−16(y+1)^2=144
Standard Form:
Identify which Conic Section:

Using first two equations determine 3 possible points that the 2 conic sections that you get from equations meet. Add a third equation figure to out the one point that all three conic sections meet.
First equation is 9(x-squared)+25(y-squared)-72x=81
Second equation is 9(x-squared)-15(y-squared)=9
Graph these two conical

Let [EQUATION1] with [EQUATION2] and [EQUATION3]. The idea is to write each such set in some simple canonical form.
(i) When n = 2, how many distinct knapsack sets are there? Write them out in a canonical form with integral coefficients and 1 = [EQUATION4].
(ii) Repeat for n = 3 with [EQUATION5].
*(For proper equations an

The number of states is expressed as a function of various parameters for three systems below. For each, find an "equation of state" which gives the relationship between p, V, N, and T.
(C and b are constants.)
Please see the attached Microsoft Word document regarding specifics.

A 102-gram airplane is attached to a string with a length of 1.0 meters. if it flies in a circle in which the string is declined at angle (theta) of 39.8 degrees below the horizontal at what speed is the plane flying?

The motion of an object of mass m in two dimensions, in the presence of a gravitational field may be determined from the Lagrangian: (look at attached for better formula representation)
L = 1/2m (x^2+y^2) - mgy
Consider the transformation give by:
x' = x + alpha + beta(t)
y' = y
Where alpha and beta are constants. For

A) Classify and find general expressions for the characteristic coordinates for the equation {see attachment}
b) Use the canonical coordinates {see attachment} and transfer the above PDE into the new coordinates. Solve it in the new coordinates and show that {see attachments} where F and G are arbitrary functions of their ar

Problem attached.
(a) Find the shortest and the largest distance from the origin to the surface of the ellipsoid.
(b) Find the principal axes of the ellipsoid.

Think of two current health care firms.
1. What types of intellectual properties do you think they own?
2. What factors do you think they considered when determining these intellectual properties?
3. How do you think these intellectual properties affect the firm that owns them and competitive health care firms?