1.
Reduce the quadratic form 2x2 – 6xy + y2 to standard form. Use the
new...
1.
Reduce the quadratic form 2x2 – 6xy + y2 to standard form. Use the
new form to sketch the graph of this quadratic form. What is the
angle by which the standard axes are rotated to the standard form
orientation
2. find the principal stresses and directions of the stress
state given by the matrix
Part A: Express the quadratic function in standard form (vertex
form). ?(?) = 1 − 12? − 4? 2
Part B: Find the quotient and remainder using synthetic
division. ?^4 + 2?^3 − 10? all over ? − 3
Part C: A stone is thrown upward from the top of a building. Its
height (in feet) above the ground after t seconds is given by the
function ℎ(?) = −16?^2 + 96? + 48. a. What maximum height does the...
Write the following quadratic function in standard form and then
sketch its graph. Clearly mark on the graph the vertex and all
intercepts.
f(x)=-2x^2+6x+15
Note: if you could include step by step explanations so I’ll
be able to understand the process and learn this concept that would
be great!!
Suppose g(x) is in Standard Form of Quadratic with a positive
leading coefficient. Answer the following:
A) What is the vertex of g(x)?
B) What is the Domain of g(x)? Why?
C) What is the Range of g(x)? Why?
D) Is the vertex a maximum or minimum? Why?
Solve for x using the quadratic formula. Be sure to check
solution(s). 2x2-4x +1=0
Solve for x using the quadratic formula. Be sure to check
solution(s). 3x2-2x+4=0
How many and what type of solutions will you have with
4x2-7x+11=0
2 Real solutions
2 complex solutions
1 real solution
Fit a quadratic function of the form ?(?)=?0+?1?+?2?2 f ( t ) =
c 0 + c 1 t + c 2 t 2 to the data points (0,−1) ( 0 , − 1 ) , (1,8)
( 1 , 8 ) , (2,−7) ( 2 , − 7 ) , (3,−6) ( 3 , − 6 ) , using least
squares.
1. For both systems below form the augmented matrix, reduce
the augmented matrix to echelon form
(zeros below the diagonal), and give the solution to the
system.
(a) x – 2y + z = 0; 2x + 3y – z = 16; 3x – y – 3z = 23.
(b) 2x – 3y + z = -3; x + 2y – 5z = -29; 3x – y + 2z =
-2
Differential Geometry
3. Evaluate the 1-form f = x2 dx - y2 dz
on the vector fields V = xU1 + yU2 + zU3, W = xy (U1 - U3) + yz (U1
- U2), and (1/x)V + (1/y)W.
Evaluate or solve the following
A) dy/dx=
-(2x2+y2)/(2xy+3y2)
B)dy/dx=(1+y2)/(1+x2)xy
C) (x2+1)dy/dx+2xy=4x2 given that when
x=3,y=4
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Many games involve the use of dice. The singular form of dice is
die. A standard die is a cube, i.e. a polyhedron with six sides.
Each side of a die has a number of dots (or pips) on it; each side
of a die is unique and contains a number of pips from 1 through 6.
A die is rolled or tossed such that it comes to rest with one side
randomly facing up. The die is said to...