Question 1
Let g(x)=x-3 and h(x)=x^2+6. Find (h o g) (1).
Question 2
Find a quadratic equation function that includes the set of values
(0,6), (2,14), (4,-2).
Question 3
determine if Ax = b has a unique solution for every b in R4
![831_Matrix.jpg](https://secure.tutorsglobe.com/CMSImages/831_Matrix.jpg)
Question 4
Maximize: 4x1 + 5x2
subject to the constraints:
x1 + 2x2 ≤ 10
6x1 + 6x2 ≤ 36
x2 ≤ 4
x ≥ 0, y ≥ 0
Question 5
Let V be the set of all positive real numbers. V is a vector space with the following operations:
x + y = xy (addition)
cx = xc (scalar mutliplication) c ∈ R
Verify each vector space axiom (There are ten listed below)
Definition of a Vector Space
Let V be a set on which two operations (vector addition and scalar multiplication) are defined. if the listed axioms are satisfied for every u, v, and w in V and every scalar (real number) c and d, then V is called a vector space.
Addition:
1. u + v is in V. Closure under addition
2. u+v=v+u Commutative property
3. u + (v + w) = (u + v) + w Associative property
4. V has a zero vector 0 such that for every u in V, u + 0 = u. Additive identity
5. For every u in V, there is a vector in V denoted by -u such that u + (-u) = 0. Additive inverse
Scalar Multiplication:
6. cu is in V. Closure under scalar multiplication
7. c(u + v) = cu + cv Distributive property
8. (c + d)u = cu + du Distributive property
9. c(du) = (cd)u Associative property
10. 1(u) = u Scalar identity
Question 6
Give the equation of the oblique asymptote, if any, of: f(x) = (-6x3 - 7x2 - 6x + 9) / (2x + 1)
a. y = 0
b. y = -3x - 2
c. no oblique asymptote
d. -3x2 - 2x - 2
Question 7
The formula r = 3√3V/4Π gives the radius of a sphere in centimeters for a Volume V given in cubic centimeters. Find r to the nearest tenth of a centimeter if the Volume is 2,744 cubic cm.
Question 8
The coast-down time "y" for a car as it drops 10 mph from an initial speed "x" depends on several factors such as air, drag, tire pressure, and if transmission is in neutral. Use a quadratic regression feature to find the quadratic function "g" that best guts the data. Round to four decimal places.
Initial Speed
|
Coast down time in seconds
|
30
35
40
45
50
55
60
65
|
30
27
23
20
18
16
15
13
|
Use model to predict coast down time at initial speed of 70 mph.
Question 9
Find a polynomial with integer coefficients that has degree 3, and zeros 0 and i.
Question 10
T(x1, x2, x3) = (-2x2 -2x3, -2x1 + 8x2 + 4x3, -x1 -2x3, 4x2 + 4x3)
Determine whether the linear transformation T is one-to-one.