It is not difficult to show that E = - (d 2 -r 2)q/rAP 3 - - (25), in other words, the force at P is inversely as the cube of the distance from A.
Sofia dropped her purse on the desk in her cube without removing her sunglasses.
For other speeds the power varies as the cube of the speed.
She popped one water cube but replaced the sugary cube with some hesitation.
22) To find two numbers such that their product their sum gives a cube (IV.
The curve also permits the solution of the problems of duplicating a cube and trisecting an angle.
I haven't been able to get you out of my cube for the past two weeks.
On the other hand, it is worth noticing that the words " quadrature " and " cubature " are originally due to geometrical rather than numerical considerations; the former implying the construction of a square whose area shall be equal to that of a given surface, and the latter the construction of a cube whose volume shall be equal to that of a given solid.
This points to the conclusion that substitution has been effected in one of the cube faces.
The power required to circulate the air through a mine increases as the cube of the velocity of the air current.
It became known as the "Delian problem" or the "problem of the duplication of the cube," and ranks in historical importance with the problems of "trisecting an angle" and "squaring the circle."
That amount, if melted, would form a cube fifty-five feet on each side.
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.
For this purpose four vertical mirrors are arranged round the vertical sides of a cube which is rapidly revolved about a vertical axis.
Lankha shoved another cube in her mouth, then a third.
In general his object is to reduce the final equation to a simple one by making such an assumption for the side of the square or cube to which the expression in x is to be equal as will make the necessary number of coefficients vanish.
End of the temple is the fountain Glauce cut out of a cube of rock, apparently left standing when the material for the temple was quarried around it.
Although bismuth is readily obtained in fine crystals by artificial means, yet natural crystals are rare and usually indistinct: they belong to the rhombohedral system and a cube-like rhombohedron with interfacial angles of 92° 20' is the predominating form.
(If the molecules of air at normal temperature and pressure were arranged in cubical order, the edge of each cube would be about 2.9 X I o - ' cms.; the average diameter of a molecule in air is 2.8X Io - 8 cms.) Further and very important evidence as to the nature of the gaseous state of matter is provided by the experiments of Joule and Kelvin.
The flame appears to lengthen, but if the reflection is viewed in a vertical mirror revolving about a vertical axis or in Koenig's cube of mirrors, it is seen that the flame is really intermittent, jumping up and down once with each vibration, sometimes apparently going within the jet tube at its lowest point.
Yet it appears to be only an approximate relation, and therefore probably accidental, as the volume by the examples is too large to agree to the cube of the length or to the weight, differing 1/20, or sometimes even as 1/12.
He took away her pain first then shoved a water cube between her lips.
The crystals are feebly doubly refracting, and in polarized light exhibit a banded structure parallel to the cube faces.
He has only one symbol (written somewhat like a final sigma) for an unknown quantity, which he calls apc0µ6s (defined as "an undefined number of units"); the symbol may be a contraction of the initial letters ap, as A Y, K Y, D Y O, &c., are for the powers of the unknown (Suvaµcs, square; icu(30s, cube; Svva,uo& va i ccs, fourth power, &c.).
Zeit., 1905, 29, p. 30), assumed the six carbon atoms to occupy six of the corners of a cube, each carbon atom being linked to a hydrogen atom and by single bonds to two neighbouring carbon atoms, the remaining valencies being directed to the unoccupied corners of the cube, three to each, where they are supposed to satisfy each other.
If we denote the critical volume, pressure and temperature by Vk, Pk and Tk, then it may be shown, either by considering the characteristic equation as a perfect cube in v or by using the relations that dp/dv=o, d 2 p/dv 2 =o at the critical point, that Vk = 3b, Pk= a/27b2, T ic = 8a/27b.
Among the contents of this book we simply mention a trigonometrical chapter, in which the words sinus versus arcus occur, the approximate extraction of cube roots shown more at large than in the Liber abaci, and a very curious problem, which nobody would search for in a geometrical work, viz.
Van 't Hoff's formula is equivalent to taking the frequency of dissociation as proportional to the square of the concentration of the molecules, and the frequency of recombination as proportional to the cube of the concentration of the ions.
The discriminant of f is equal to the discriminant of 0, and is therefore (0, 0') 2 = R; if it vanishes both f and 0 have two roots equal, 0 is a rational factor of f and Q is a perfect cube; the cube root being equal, to a numerical factor pres, to the square root of A.
(22) It will be seen that, whereas the couple varies inversely as the cube of the distance, the force varies inversely as the fourth power.
When P is the neutral point, H is equal and opposite to R; therefore M = Hd 3, or the moment is numerically equal to the cube of the distance from the neutral point to a pole, multiplied by the M.
In the preface to this work, which is dedicated to one Dionysius, Diophantus explains his notation, naming the square, cube and fourth powers, dynamis, cubus, dynamodinimus, and so on, according to the sum in the indices.
Others occur in the Metrica where also a method of finding such approximate square, and even approximate cube, roots is shown.
Apart from modifications in the details of sugar refining which have come into use in late years, it should be mentioned that loaf sugar made in conical moulds, and sugars made otherwise, to resemble loaf sugar, have practically disappeared from the trade, having been replaced by cube sugar, which is found to be more economical as subject to less waste by grocers and housekeepers, and also less troublesome to buy and sell.
There is a perfect cleavage perpendicular to the trigonal axis of the crystals: the fact that only two (opposite) corners of the cube-like crystals can be truncated by cleavage at once distinguishes them from true cubes.
Kb(30s, a cube), in geometry, a solid bounded by six equal squares, so placed that the angle between any pair of adjacent faces is a right angle.
In algebra, the "cube" of a quantity is the quantity multiplied by itself twice, i.e.
She ate two more of the sugar cubes and a water cube, eyes lingering on the bloody mess that was her jumper in the corner.
Molly offered her a food and water cube, both of which lessened the pain throbbing through her.
She handed the pale woman a food and water cube and popped two of her own. Standing, she waded into the brush where she'd thrown the knife. It glinted in the morning light. Katie swiped it, glad the trees didn't have a taste for metal as well as Immortal sustenance.
The faces of the cube are striated parallel to one diagonal, and alternate corners are sometimes replaced by faces of a tetrahedron.
The Liber abaci, which fills 459 printed pages, contains the most perfect methods of calculating with whole numbers and with fractions, practice, extraction of the square and cube roots, proportion, chain rule, finding of proportional parts, averages, progressions, even compound interest, just as in the completest mercantile arithmetics of our days.
A famous problem concerning the cube, namely, to construct a cube of twice the volume of a given cube, was attacked with great vigour by the Pythagoreans, Sophists and Platonists.
(b) In determinations of volume which do not admit of a high degree of accuracy the cubic decimetre can be taken as equivalent to the litre; and in these determinations expressions of volumes based on the cube of the unit of linear measure can be substituted for expressions based on the litre as defined above.
The mensuration of the cube, and its relations to other geometrical solids are treated in the article Polyhedron; in the same article are treated the Archimedean solids, the truncated and snubcube; reference should be made to the article Crystallography for its significance as a crystal form.
"You have five minutes to leave my cube, or I'll bite your neck!" she retorted.
There was no way she was sleeping tonight, even if she didn't feel any threat from the phantom.
(i) Cube: side a.
The phantom shook his head in silent objection.
Tying her chosen anchor to one end of the rope, she sat to eat her sugary cube, checked again for the monster, and leaned out of the cave.