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Charlie has 218 fewer Facebook friends than leana. The number of Deepa's Facebook friends is 28 more than half of Ileana's. Together Charlie, Deepa, and Ileana have 2175 friends on Facebook. How many Facebook friends does each of them have?
the normal form of the differential equation y"-xy'+(4x^2-1)y=?
If the length of both bases and the overall height of an Isosceles Trapezoid is known, is there a formula to determine the interior angles of the shorter base? I know that both angles will be the same. (need to cut a piece of material with a mitre saw and need to use the saw's angle gauge to make the cut) Thank you.
In their 2013 Stanley Cup-clinching game, the Blackhawks had six more shots on goal than the Bruins. Together, they had 56 shots. How many shots did each team have?
If G is an abelian group, then G is cyclic. Is this statement true or false . Also justify your answer.
If G1 and G2 are groups, and f : G1→G2 is a group homomorphism, then
o(G1) = o( G2). Is the statement true or false ? Also justify.
o(G1) = o( G2). Is the statement true or false ? Also justify.
(φ )n = n −1 ∀n∈N , where φ is the Euler-phi function. Is the following statement true? Justify your answer.
Fixing x, show that the Taylor series of e
tx− t
2
2 is given by X∞
n=0
t
nHn(x). (Explain
also why the series converges.)
tx− t
2
2 is given by X∞
n=0
t
nHn(x). (Explain
also why the series converges.)
a) Check whether the following system of equations has a solution.
x+y+3z+w = 5
−x+y+z−5w = 7
x+2y+5z−w = 5 (6)
b) Let T : P2 → P1 be defined by
T(a+bx+cx2
) = b+c+ (a−c)x.
Check that T is a linear transformation. Find the matrix of the transformation with
respect to the ordered bases B1 = {x
2
, x
2 +x, x
2 +x+1} and B2 = {1, x}. Find the
kernel of T.
x+y+3z+w = 5
−x+y+z−5w = 7
x+2y+5z−w = 5 (6)
b) Let T : P2 → P1 be defined by
T(a+bx+cx2
) = b+c+ (a−c)x.
Check that T is a linear transformation. Find the matrix of the transformation with
respect to the ordered bases B1 = {x
2
, x
2 +x, x
2 +x+1} and B2 = {1, x}. Find the
kernel of T.
Show that if A, B ⊆ R^d are closed sets, then A + B is measurable (in fact A + B is an Fσ set). Show, however that A + B may not be closed.
