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Computing Values of Functions

Problem involving diff eq'ns

A mass 5kg is attached to a spring suspended from the ceiling. When the mass comes to rest at equilibrium, the spring has been stretched 2m. The mass... Determine the motion of the mass. Decribe its motion in as much detail as possible. Please see attached.

Knapsack Problem : Write in Canonical Form

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

Functions

See attached, ps explain correct answer

Carrying capacity

Suppose that a population develops according to the logistic equation: dP/dt = 0.15P - 0.003P^2 where t is measured in weeks. what is the carrying capacity?

Obtaining a Target Number

Using the numbers 3, 3, 8 and 8 once and only once, obtain the target number of 24. (You have to use 3 twice and 8 twice - 3 x 8 = 24 is not acceptable). You may use only addition, subtraction, multiplication and division (eg. no factorial). Hint: no addition in the equation.

Functions

Find the composition of the following cycles representing permutations on A = {1,2,3,4,5,6,7,8} Answer as a composition of one or more disjoint cycles. A) (1,3,4) . (5,1,2) B) (2,7,8) . (1,2,4,6,8) C) (1,3,4) . (5,6) . (2,3,5) . (6,1)

Exponential Order

Show that a) e^(t^2) is not of exponential order, and b) e^(t^1/2) is of exponential order

Functions with Postal Restriction

Postal Restrictions If a box with square cross section is to be sent by the postal service, there are restrictions on its size such that its Volume is given by V= x²(108-4x), where x is the length of each side of the cross section (in inches). (a) Is V a function of x? (b) If V= V(x), find V(10) and V(20). (c) What restr

Working with iterative methods.

The sequence of value given by the iterative formula is X n+1=2/9-lnXn with initial value X=1,converges to alpha. 1) State an equation satisfied by alpha, and hence show that alpha is the x coordinate of a point on the curve where y=3. 2) Use this iterative formula to find alpha correct to 2 decimal places, showin

The one norm

Prove rigorously that ||x + y||1 <= ||x||1 + ||y||1

Function

A function f is defined on a set of real numbers. Is f one-to-one? Please give explanation so I may understand. (see attached file for function)

Linearization of a function. Attachments in Word.

The distance l from a point at a height h above the Earth's surface to the horizon can be approximated using Pythagoras' theorem by the expression: (Please see the attachment below) (a) Find an expression which serves as a linear approximation for l at h=1000 m. (b) Give two assumptions you think have been made in deriving