Example elements in R are
("abc","abcd"), ("ab","abcd"), ("a","abcd")
Example elements NOT in R are
("abc","def"), ("abc","de"), ("abc","defg")

(I point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be x =- (a) Find a point P-(zo, 30, zo) where F is parallel to 1. Find a point Q (which F and I are perpendicular. Q= and l are perpendicular Give an equation for the set of all points at which F and l are perpendicular. equation:
(I point) Let F=21+(z...
For each of the following problems, decide whether the set A is
regular. If the set is regular, give a FSM that recognizes it; if
the set is not regular, prove it using the pumping lemma. 1.
A={s11s | s∈{0}∗} Thus the strings 00011000 and 000001100000 are
elements of A, but 00100 and 001100000 are not. 2. A={r11s |
r,s∈{0}∗} Thus the strings 001100 and 0110000 are elements of A,
but 00111100 and 000010 are not. 3. A={w∈{a,b}∗ | w...
1) Show that two lines are skew x+1 y+2 z+3 4:x=y=z and L: +7=5 2) Find the general equation of the plane containing the point P (1,2,3 ) and L, . 3) Find the point Q-the point of intersection the plane found in 2) and the line L. 4) Find the distance from the point (1,-1,2) to the line Lą.
Let L = {x|x = yz, y ∈ {a} ∗ ,z ∈ {Λ,b,bb}} Let L1 = {x|x ∈ L,|x| ≤ 4}. List all the strings in L1. List all the strings of the following language: L = {x|x ∈ {0,1} ∗ and |x| = 4 and x contains 01 as substring}
Let L= {x[x = yz,y € {a}",z € {A, b, bb}} Let L1 = {x|x E L,[x] <4}. List all the strings in Lj.
Verify that Prn (cos θ) solves sin θΟθ (sin ea, Θ) + (E(1 + 1) sin2 θ-m2) Θ 0. Use that pr(z)-(1-z2 )T (4), Pr(r) with Pr(z) a Legendre polynomi 1
Verify that Prn (cos θ) solves sin θΟθ (sin ea, Θ) + (E(1 + 1) sin2 θ-m2) Θ 0. Use that pr(z)-(1-z2 )T (4), Pr(r) with Pr(z) a Legendre polynomi 1
Question 4. Take the curve y cosh r in the r-y plane, and revolve it around the z axis. The resulting surface of revolution S is called a catenoid. Show that it is a smooth surface in two different ways, as follows. (1) Give an atlas of regular surface patches for S. Describe S as the level set of a function f : R3 → R such that ▽f S. 0 on
Question 4. Take the curve y cosh r...
Let T є L(C3) be defined by T(r, y, z)-(y-2-2c, z-2-2y,1-2y-22). (a) Is span((1,1,1)) invariant under T? (b) Is U = { ( (c) Is U = {(x, y, z) : x + y + z = 0} invariant under T? (d) Is λ 2 an eigenvalue of T? Is T-21 injective? (e) Find all eigenvectors of T associated to the eigenvalue λ =-3. 4. r, y,r-y) : x, y E C} invariant under T?
Question 4 Consider the lines L, D=1+2, y = 2 – 3t, z = 2+t and L2 X = 3 - 4s, y=1+ 48, z = -3 + 48. We will use these lines for the questions 4 and 5. Are these lines parallel? Explain your answer below. B IV A - A - Ix E - C o o x G You HTML 11 x Ⓡ 5E T To 12pt Pan Question 5 9 pts Determine where these lines...
Consider the Mundel-Fleming small open economy model: Y=C(Y-T)+1(1) + G Y = F(K,L) (M/P) L(r+z® Y) Goods Money C = 50+0.8(Y- T) M 3000 I = 200-20r r*=5 NX = 200-508 P = 3 G=T= 150 L(Y, r) Y - 30r 1- find the IS* equation (hint : y as a function of e) 2- find the LM* equation (hint, also relates y and maybe e) 3-draw the IS-LM curve I y 4- find the equilibrium interest rate (trick question!)...