Find parametric equations for the line through the point

(0, 2, 3)

that is perpendicular to the line

x = 2 + t, y = 2 − t, z = 2t

and intersects this line. (Use the parameter t.)

(x(t), y(t), z(t)) =

Let G = (AN , AT , S, P) be a context-free grammar in Chomsky normal form. Prove that if there exists a word w ∈ L(G) generated by a derivation that uses more than |P| + |AT | steps, then L(G) is infinite.

Prove that if G is a simple graph with |V (G)| = n even, where δ(G) ≥ n 2 + 1, then G has a 3-regular spanning subgraph.

let A= {1,2} and C={8,9}. for each i=1,2, construct sets B sub i as well as functions f sub i: A to B sub I, 1<=i<=4, with the following properties:
1) g sub 1 ° f sub 1 is onto C but f sub 1 is not onto B sub I.
2) g sub 2° f sub 2 is one-to-one but g sub 2 is not one-to-one.

Hello, I have a question about the heat equation with Non-homogeneous Boundary Conditions in Differential Equations. u_t = 4u_xx u(0, t) = 2 u_x(3, t) = 0 u(x, 0) = x. If available, could you explain the solution in detail? Thank you.

a) In how many ways n distinct ball can be given to k children so that no child gets more than 3 balls?

b) What happens if the balls are indistinguishable?

1. The equation 8?2 − 3?? = 0 has three roots. Find:

(i) The first root, which is between -1 and 0, by the bisection method;

(ii) The second root, which is between 1 and 2, by Newton’s method;

(iii) The third root, which is between 3 and 4, by both the bisection method and Newton’s method.

All the answers should be correct to 2 decimal places.

*Functions and applications:

Toms terrific table company produces and sells dinning room tables. On a good day Toms can produce 10 tables at a cost of $6300. On a slow day Toms can produce 4 tables at a cost of $5400.

a. write the cost function C(x) where x represents the number of tables produced

b. what is the marginal cost, and what does it represent ?

c. what is the fixed cost and what does it represent ?

d. Tom sells the tables for $950. How many tables need to be produced and sold each day for Toms to break even?

e. on a slow day only 4 tables are produced and sold . What is Toms profit/loss?

f. On a good day 10 tables are produced and sold. What is Toms profit/loss ?

1. Let a < b. (a) Show that R[a, b] is uncountable

EITHER illustrate Turing’s claim that something practical might go wrong if one has an inconsistent deductive system OR defend Wittgenstein’s claim that the problem would not be a logical one.