Let t and s ( t > s ) be the sides of the two inscribed squares in a right triangle with hypotenuse c. Then s < sup > 2 </ sup > equals half the harmonic mean of c < sup > 2 </ sup > and t < sup > 2 </ sup >.

: Let ’ s lay off the excessive groaning.

: Let ’ s deal with the common benefits first off,

Proof: Let d be the position of the leftmost ( most significant ) nonzero bit in the binary representation of s, and choose k such that the dth bit of x < sub > k </ sub > is also nonzero.

Let It Be < nowiki >'</ nowiki > s release had attracted attention from the major record labels, and by late 1984 several had expressed interest in signing the Replacements.

* " Identity " / " Let ’ s Submerge " ( July 1978: EMI International, INT 563 )-No.

Let ’ s tell them the truth, that there are no gains without pains, that we are now on the eve of great decisions.

Let ’ s leave it to the gods to set his mind on that.

Traditional Bayram ( Turkey ) | Bayram wishes from the Istanbul Metropolitan Municipality, stating " Let us love, Let us be loved ", in the form of mahya lights stretched across the minaret s of the Sultan Ahmed Mosque ( Istanbul ) | Blue Mosque in Istanbul

It was: Let ’ s try to do something together.

Let c, h, s be the sides of three squares associated with the right

While their next release, " Never to be Forgotten " brought a regional hit, the band ’ s next single, " Let Her Dance " brought the band ’ s first national hit, barely missing the Billboard Hot 100 at 133, though bringing in a Top 40 hit.

Let ’ s first imagine a cube with sides of length 2, and its center positioned at the axis origin.

Given an integer n, choose some integer a < n. Let 2 < sup > s </ sup > d = n − 1 where d is odd.

Many episode titles parodied the titles of Bond films, e. g. “ Live and Let ’ s Dance .”

As well as the songs he would go on to perform on the day, his list included “ All Things Must Pass ” (“ with Leon ”, apparently ) and “ Art of Dying ” − both from All Things Must Pass − and “ Bangla Desh ”’ s B-side, “ Deep Blue ”; Clapton ’ s song “ Let It Rain ” appeared also, implying that the guitarist was expected to have his own solo spot ; while the suggestions for Dylan ’ s set were “ If Not for You ”, “ Watching the River Flow ” ( his recent, Leon Russell-produced single ) and “ Blowin ' in the Wind ”.

Let q be a prime number, s a complex variable, and define a Dirichlet L-function as

While each concert was professionally mastered, the recordings capture everything that happened onstage and for preservation's sake the band chose not to edit anything out, singer / guitarist Guy Picciotto explained to the New York Times "“ We liked this idea of, ‘ Let ’ s just let it be everything ,’ “ Mr. Picciotto said.

Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

Let us for simplicity take m = k as an example.

Let f and g be any two elements of G. By virtue of the definition of G, = and =, so that =.

Let the directrix be the line x = − p and let the focus be the point ( p, 0 ).

Let be a non-negative real-valued function of the interval, and let < math > S =

Let us assume the bias is V and the barrier width is W. This probability, P, that an electron at z = 0 ( left edge of barrier ) can be found at z = W ( right edge of barrier ) is proportional to the wave function squared,

If V is a real vector space, then we replace V by its complexification V ⊗< sub > R </ sub > C and let g denote the induced bilinear form on V ⊗< sub > R </ sub > C. Let W be a maximal isotropic subspace, i. e. a maximal subspace of V such that g |< sub > W </ sub > = 0.

LET x = rnd * 20! Let the value ' x ' equal a random number between ' 0 ' and ' 20 '

LET y = rnd * 20! Let the value ' y ' equal a random number between ' 0 ' and ' 20 '

Let A =

:: Let n = 0

:: Let repeat = TRUE

Let ( S, f ) be a game with n players, where S < sub > i </ sub > is the strategy set for player i, S = S < sub > 1 </ sub > × S < sub > 2 </ sub > ... × S < sub > n </ sub > is the set of strategy profiles and f =( f < sub > 1 </ sub >( x ), ..., f < sub > n </ sub >( x )) is the payoff function for x S. Let x < sub > i </ sub > be a strategy profile of player i and x < sub >- i </ sub > be a strategy profile of all players except for player i. When each player i < nowiki >

Let X = " to make something that its maker cannot lift ".

* Let TQBF =

* The ring of continuous functions from the real numbers to the real numbers is not Noetherian: Let I < sub > n </ sub > be the ideal of all continuous functions f such that f ( x ) = 0 for all x ≥ n. The sequence of ideals I < sub > 0 </ sub >, I < sub > 1 </ sub >, I < sub > 2 </ sub >, etc., is an ascending chain that does not terminate.

# Let p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >) and q = ( q < sub > 1 </ sub >, q < sub > 2 </ sub >) be elements of W, that is, points in the plane such that p < sub > 1 </ sub > = p < sub > 2 </ sub > and q < sub > 1 </ sub > = q < sub > 2 </ sub >.

Let A be a complex unital Banach algebra in which every non-zero element x is invertible ( a division algebra ).

Let M be a smooth manifold and let x be a point in M. Let T < sub > x </ sub > M be the tangent space at x.

Let M be a smooth manifold and let x be a point in M. Let I < sub > x </ sub > be the ideal of all functions in C < sup >∞</ sup >( M ) vanishing at x, and let I < sub > x </ sub >< sup > 2 </ sup > be the set of functions of the form, where f < sub > i </ sub >, g < sub > i </ sub > ∈ I < sub > x </ sub >.

Let g be a smooth function on N vanishing at f ( x ).

Let x, y, z be a system of Cartesian coordinates in 3-dimensional Euclidean space, and let i, j, k be the corresponding basis of unit vectors.

Let G denote the set of bijective functions over A that preserve the partition structure of A: ∀ x ∈ A ∀ g ∈ G ( g ( x ) ∈ ).

Let X be a topological space, and let x < sub > 0 </ sub > be a point of X.

Let x < sub > 0 </ sub >, ...., x < sub > N-1 </ sub > be complex numbers.

Let now x ' and y ' be tuples of previously unused variables of the same length as x and y respectively, and let Q be a previously unused relation symbol which takes as many arguments as the sum of lengths of x and y ; we consider the formula