Math Answers

The dimensions of a box are b, b+1, b+4. Find how fast the volume increases as b increases

Find 2×2 matrix A that maps (1,3)^T and (1,4)^T into (-2,5)^T and (3,-1)^T, respectively

For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ x 2 − 25}.

1. f : R → R defined by f(x) = 3x3.

2. g : R + → R defined by g(x) = ln(x).

3. h : R → R defined by h(x) = x − 9.

Let f : Z → Z be defined by f(a) = 2a 2 − a and g : Z → Z be defined by g(x) = x(2x − 1). Determine whether f is equal to g. Justify your answer.

For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ x 2 − 25}.

1. f : R → R defined by f(x) = 3x3.

2. g : R + → R defined by g(x) = ln(x).

3. h : R → R defined by h(x) = x − 9.

Absolute extrema in closed interval

a. h(x)=x²-2x, [0,4]

b. f(x)= (2x+5)/3, [0,5]

Suppose a recurrence relation

an=2an−1−an−2

where a1=7 and a2=10

can be represented in explicit formula, either as:

Formula 1:

an=pxn+qnxn

              or  

Formula 2:

an=pxn+qyn

where 

x

and

y

are roots of the characteristic equation.

Determine p and q

 Answer:

p :

q :

Suppose that G is a connected multigraph with 2k vertices of odd degree. Show that there exist k subgraphs that have G as their union, where each of these subgraphs has a Euler path and where no two of these subgraphs have an edge in common.

1. Proof that an undirected graph has an even number of vertices of odd degree.

Describe at least one way to generate all the partitions of a positive integer n.