Ax Sentence Examples
He swung the ax again.
He swung the ax once more, now only half a body length away.
Again she swung the ax, and this time it went half way through the log.
She relinquished the ax for the glass of tea.
Glancing over his shoulder at his advancing pursuer, he knew he'd have to drop far enough and rapidly enough to pass Shipton before the killer could swing out with his deadly ax.Advertisement
He shrugged and offered her the ax.
Thus what have been called seminvariants are not all of them invariants for the general substitution, but are invariants for the particular substitution xl = X11 + J-s12, X 2 = 112 Again, in plane geometry, the most general equations of substitution which change from old axes inclined at w to new axes inclined at w' =13 - a, and inclined at angles a, l3 to the old axis of x, without change of origin, are x-sin(wa)X+sin(w -/3)Y sin w sin ' _sin ax y sin w a transformation of modulus sin w' sin w' The theory of invariants originated in the discussion, by George Boole, of this system so important in geometry.
To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.
There is no linear covariant, since it is impossible to form a symbolic product which will contain x once and at the same time appertain to a quadratic. (v.) is the Jacobian; geometrically it denotes the bisectors of the angles between the lines ax, or, as we may say, the common harmonic conjugates of the lines and the lines x x .
The linear invariant a s is such that, when equated to zero, it determines the lines ax as harmonically conjugate to the lines xx; or, in other words, it is the condition that may denote lines at right angles.Advertisement
Thus, to solve the equation ax e +bx+c = o, we consider, not merely the value of x for which ax 2 +bx+c is o, but the value of ax e +bx+c for every possible value of x.
In this they were completely successful, for they obtained general solutions for the equations ax by = c, xy = ax+by+c (since rediscovered by Leonhard Euler) and cy 2 = ax e + b.
A particular case of the last equation, namely, y 2 = ax e + 1, sorely taxed the resources of modern algebraists.
Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.
Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..Advertisement
The Diophantine analysis was a favourite subject with Pell; he lectured on it at Amsterdam; and he is now best remembered for the indeterminate equation ax 2 +1 = y 2, which is known by his name.
Now µx 2 is very small compared with Ax, so that x is nearly equal to F/X, and as an approximation, F=Ax+µF 2 /A 2, or x=F/A - µF 2 /A 3.
To prove this let AB, AB' be the tangents from any point on the line AX.
Warm mineral springs of note are found at Ax, Aulus and Ussat.
In the geometry of plane curves, the term parabola is often used to denote the curves given by the general equation a' n x n = ym+n, thus ax= y 2 is the quadratic or Apollonian parabola; a 2 x = y 3 is the cubic parabola, a 3 x = y4 is the biquadratic parabola; semi parabolas have the general equation ax n-1 = yn, thus ax e = y 3 is the semicubical parabola and ax 3 = y 4 the semibiquadratic parabola.Advertisement
Denoting these limits by Pi, Pa we have P1/W=L1H/HK=sin (aX)/cos (0+X),
An important property of the diagram is that if points X and x are taken dividing the link CB and the whole acceleration of B about C, namely, cb in the same ratio, then Ax represents the acceleration of the point X in magnitude and direction; cb is called the acceleration image of the rod.
Timid by nature, aware of his impending doom, and ax times justly dissatisfied with himself, he tries all means of reconciling himself to the idea of suicide.
In 1844 Minas published a work, avowedly from a MS. with the superscription Galenus, entitled FaXrlvo13 Eiaa'yw yi, &aX€Krucii.
The only roads are bridle-paths, and one municipal road by the Balira valley, connecting Andorra with the high road to Seo de Urgel and Manresa; but in 1904 France and Spain agreed to build a railway from Ax to Ripoll, which would greatly facilitate traffic.Advertisement
Considering the equations ax +by +cz =d, a'x +b'y +c' z =d', a"x+b"y+cnz=d" and proceeding to solve them by the so-called method of cross multiplication, we multiply the equations by factors selected in such a manner that upon adding the results the whole coefficient of y becomes = o, and the whole coefficient of z becomes = o; the factors in question are b'c" - b"c', b"c - be", bc' - b'c (values which, as at once seen, have the desired property); we thus obtain an equation which contains on the left-hand side only a multiple of x, and on the right-hand side a constant term; the coefficient of x has the value a(b'c" - b"c') +a'(b"c - bc") +a'(bc' - b'c), and this function, represented in the form a, b,c, a' b'c', a" b" c" is said to be a determinant; or, the number of elements being 32, it is called a determinant of the third order.
In 1907 the sanctuary of Athena "of the Brazen House" (X aX KlocKos) was located on the Acropolis immediately above the theatre, and though the actual temple is almost completely destroyed, fragments of the capitals show that it was Doric in style, and the site has produced the longest extant archaic inscription of Laconia, numerous bronze nails and plates and a considerable number of votive offerings, some of them of great interest.
Delcass, the French minister for foreign affairs, and on the I 8th of August r904 a convention was signed providing for the construction of (1) the Huesca-Oloron line, (2) a line from Ax les Thermes in the Arige to Ripoll in Catalonia, (3) a line from St Girons in the Arige to Sort, and thence to Lrida.
Diagrammatic longitudinal section of cone, showing the axis (ax) bearing the bracts (br) with peltate sporangiophores (sp) springing from their axils; sm, sporangia.
Part of cone, showing the axis (ax) bearing peltate sporangiophores (sp) without bracts; sm, sporangia.
Diagrammatic longitudinal section of the cone, showing the axis (ax) bearing alternate whorls of bracts (br) and peltate sporangiophores (sp) with their sporangia (sm).
The dorsal segments are sterile, corresponding to the bracts of Sphenophyllum Dawsoni, while the ventral segments constitute peltate sporangiophores, each bearing four sporangia, just as in a ax FIG.
Penny said, glaring at the officer as she tapped the handle of a sinister looking ice ax.
Shipton continued to chop, as if deciding this and not a direct blow from the ice ax was a far better way to remove this annoying impediment to his foolproof plan.
The leg wound from Shipton's flailing ice ax had been an eight-stitcher of no permanent consequence but the clump of frozen mountain Dean caught on the head kept him fuzzy and blurred his vision for a day and a half, necessitating the stay.
This 40 x 40 ft rock looks as if God took an ax and split the rock in half.
Another Chetnik sexually assaulted women and killed internees, in some cases using an ax to the head.
He tells them that he has got to have an ax and a hickory stake.
In a burst of fear and rage, I ran at it wielding the ax as hard as I could.
Typing ps ax on Saturday usually gave me a half dozen processes to kill.
Consider the general quadratic equation ax 2 + bx + c = 0 where a 0.
Back to top T ax and Indemnities A key question in assessing the value of a settlement deal concerns the impact of tax.
F-Zero ax machine parts Cheats Successfully complete the game in story mode on the hard difficulty setting to unlock the F-Zero AX machine parts.
Square matrices A and B are congruent if there exists a non-singular X such that B = X T ax.
Page 25 No need to do Activity 4. Page 25 Graphs of the form ax + by = c.
To see how many processes there are, type ps ax.
When using a billhook, slasher or ax, always make sure there is a clear path to swing the tool.
A silver birch, burnt then chopped at with an ax, still looking a bit like a silver birch.
However, the red Escort was soon to blot it's copybook by failing Ax with no less than three punctures!
Trees were free fuel for poor cottagers, every one of whom had an ax.
A few tragic accidents have resulted from people not wearing crampons or using an ice ax.
The price does not include any accommodation, food or the hire of ice ax crampons, winter boots or any personal winter clothing.
Steve had read a magazine and been shopping; he was experimenting with an ax and ice dagger combination!
I felt I was reading a diatribe from someone with a personal ax to grind, rather than a scholarly or well researched biography.
Finally, the fourth ax of educational quality and inclusive education development is related with pedagogical differentiation, the main content of this paper.
Course Description Solving linear systems Ax = b or finding the eigenvalues of a matrix may appear to be trivial tasks.
Every moment I expect to see the executioner arrive with his ax.
Unique service for disabled faces ax A cash crisis is threatening the future of a pioneering city counseling center for the disabled.
It is a small, socketed ax head with a loop underneath it for binding it to a wooden haft.
This comes from the Fairy Feller in the foreground, his ax poised on high, ready to chop a giant hazelnut in half.
Do you need an ax to split an infinitive?
An ax may b e kept near a chopping block to make kindling.
He is the legendary lumberman, who supposedly stood at 42 ax handles tall!
There are less noble weapons that you can wield, such as an executioner's ax or spiked maces.
She'd prefer the ax murderer to Troy Marsden, the weird guy who lived on the property up the track.
The giant ogre was smashing the gate with his huge ax each time iron cracked off sending sparks into the air.
At its heart was a sharp iron ax of the weight of seven pounds twelve ounces.
Another man enters clutching a live rooster, presents the protagonist with an ax, then leaves the room.
Then there are night races and blinding sandstorms to struggle through not forgetting the odd throwing ax or javelin that may come your way.
The axeman was present, his ax freshly sharpened.
He told the story of the young man who wanted his ax ground.
The firemen's uniform consisted of a helmet, belt, badge and ax.
Referred to the centre this becomes Ax e +2Hxy+By 2 +C =o; and if the axes of coordinates be the principal axes of the curve, the equation is further simplified to Ax e - By 2 = C, or if the semi-transverse axis be a, and the semiconjugate b, 'x' 2 /a 2 - y 2 /b 2 = I.
For the quadratic aoxi +2a i x i x 2 +a 2 x, we have (i.) ax = 7/1x1+2aixix2-I-7/24, (ii.) xx=xi+xzi (ab) 2 =2(aoa2 - ai), a a = a o+712, _ (v.) (xa)ax= i'?- (a2 - ao)xix2 - aix2.
One carried a gun, one had a pitchfork, and the third had an ax.
He was armed with a musketoon (which he carried rather as a joke), a pike and an ax, which latter he used as a wolf uses its teeth, with equal ease picking fleas out of its fur or crunching thick bones.
Tikhon with equal accuracy would split logs with blows at arm's length, or holding the head of the ax would cut thin little pegs or carve spoons.
He had a musketoon over his shoulder and an ax stuck in his girdle.
A single fragment of bronze, probably part of a socketed ax, was recovered with the aid of a metal detector.
The final nightmare is missing a nice close-up of the father 's head spewing frothy blood from his ax wound.
Instead, if you are hit by an ax, or are shot, you get a blood splatter across the screen.
As Beaker staggered backward, he dropped the ax and tried to pull the chicken body off his face.
Every time I wanted to swing the ax I was blinded by snow and the wind pushed me off balance.
Then we learned to traverse icy slopes using crampons, kicking steps in snow or hacking them out in ice with an ax.
Use your trusty pick ax, ropes and dynamite and go on a glorious hunt for treasure.
The firemen 's uniform consisted of a helmet, belt, badge and ax.
On the left, the upstream passage is Ax Wars Inlet.
He carries a working flashlight in his hand and a fireman 's ax made from padded velour fabric is fixed to his belt.
Where would you wield the ax in order to save the Library?
Suddenly, they heard the clean chopping strokes of the woodcutter 's ax.
An old, woodsman 's ax has been left | within reach.
He finally quit after smoking for forty-five years, although he said in the first few days after quitting he "felt like an ax murderer."
Many shows felt the ax in the 2008-2009 television season, due in no small part to financial reasons.
Among them are The Birdman of Alcatraz with Burt Lancaster, Escape from Alcatraz with Clint Eastwood, The Rock, and So I Married an Ax Murderer.
Dean leaped on Shipton, clawing away at the soft snow, pummeling him like an eighth grade schoolyard brawler while Shipton, still clutching his ice ax in one hand, swung at Dean, catching him on the cheek and face with the side of the solid handle.
I suppose you've got a good reason why you tried to beat the brains out of a guy holding an ice ax, in the middle of the street with a bunch of people watching.
He swung his ice ax into the wall in front of him, dug in the toes of his crampons and began to ascend toward Dean.
Shipton swung his ice ax again, inching up closer to Dean.
Shipton's ax bit the ice scarcely a foot below Dean as the man glared up at him, a snarl on his face.
Shipton flailed out at him with his ax, missing his head by inches as Dean leaned sideways and frantically fumbled with his line to drop again.
But his cry came an instant too late as Shipton plummeted past him, his ice ax swinging in a rip across Dean's calf as he plummeted backward into space, and down to the rocks and churning river below.
The leg wound from Shipton's flailing ice ax had been an eight-stitcher of no permanent consequence.
His muscular back glistened with perspiration as he swung the ax, expertly splitting a chunk of wood.
She gripped the ax handle.
Taking a few steps back she gripped the ax half way down on the handle and slammed it down against the block of wood with a dull whack.
The ax blade went about an inch into the wood.
This time the ax sank about four inches into the wood - in another spot.
After a full minute of tugging and grunting she managed to dislodge the ax from the wood.
He lifted the ax, taking aim at a new block of wood.
Such curves are given by the equation x 2 - y 2 = ax 4 -1bx 2 y 2 +cy 4 .
The number of partitions of a biweight pq into exactly i biparts is given (after Euler) by the coefficient of a, z xPy Q in the expansion of the generating function 1 - ax.
It may be written in the form n n-1 2 ax 1 +bx1 x2 +cx 1 x 2 + ...; or in the form n n n=1 n n-2 2 +(1)bx x2+ ?
From the three equations ax = alxl+ a2x2, b.= blxl+b2x2, cx = clxi+c2x2, we find by eliminating x, and x 2 the relation a x (bc)+b x (ca) +c x (ab) =0.
The two forms ax, bx, or of, 0, may be identical; we then have the kth transvectant of a form over itself which may, or may not, vanish identically; and, in the latter case, is a covariant of the single form.
If the forms be ax, b2, cy,...
When C vanishes j has the form j = pxg x, and (f,j) 3 = (ap) 2 (aq)ax = o.
The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and integral function of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5.
When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does f.
So they filled a small boat with the things that he would need the most--an ax, a hoe, a kettle, and some other things.
He hefted the ax to his shoulder and grinned down at her.