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Page "Formula" ¶ 31
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If and physical
If a nation wished to get a head start in physical fitness over all other nations, it would start its kindergarten students on a program of gymnastics the day they entered and thus eliminate a large number of the problems that plague American schools.
If you have an annual or regular physical examination program, is it worth what it is costing you??
If the fourth dimension is a physical concept and not purely metaphysical, through what medium does it extend??
If the replica had all the same experiences, traits, and physical appearances of the first person, we would all attribute the same identity to the second, according to Hick.
If that steady-state signal was interrupted, it indicated one of two things: either the operator was about to start transmitting, or something else had happened to break the connection — such as a physical break in the telegraph line.
If a man owed and he could not pay, he and his wife, children or servants were forced into " debt slavery ", until the creditor recouped losses via their physical labour.
If numerical iterative methods have to be employed, the aim is to iterate until full machine accuracy is obtained ( the best that is possible with a finite word length on the computer, and within the mathematical and / or physical approximations made ).
If untreated, it results in mild to severe impairment of both physical and mental growth and development.
:: If patients fail to experience the healing power of Christian Science, and think they can be benefited by certain ordinary physical methods of medical treatment, then the Mind-physician should give up such cases, and leave invalids free to resort to whatever other systems they fancy will afford relief.
If a physical object statement is to be translatable into a sense-data statement, the former must be at least deducible from the latter.
If physical reality is totally finite, then the Copenhagen interpretation might be an approximation to an information processing system below the Planck scale.
If not to make a direct change, this movement is in place to raise awareness about the effects that take place because of the physical things around us.
If an ' extreme ' foul is committed, such as physical contact or unsportsmanlike behavior, a player may receive a 10 minute penalty or even a match misconduct.
If the physical material that will be used in production is derived from bones, dilute acid solutions are used to remove calcium and similar salts.
If there are few androgen receptors ( people with androgen insensitivity syndrome ) or too much androgen ( females with congenital adrenal hyperplasia ), there can be physical and psychological effects.
If no value of the rotation parameter is successful and theory is not within observational error, a modification of physical law is considered.
If the particles have the same physical properties, the n < sub > j </ sub >' s run over the same range of values.
If the teacher asked whether the learner might suffer permanent physical harm, the experimenter replied, " Although the shocks may be painful, there is no permanent tissue damage, so please go on ".
If matter and energy are seen as necessary to explain the physical world, but incapable of explaining mind, dualism results.
If MNT were realized, some resources would remain limited, because unique physical objects are limited ( a plot of land in the real Jerusalem, mining rights to the larger near-earth asteroids ) or because they depend on the goodwill of a particular person ( the love of a famous person, a live audience in a musical concert ).
If the material is kept still there is often nothing ( such a physical vibration ) to trigger this change, and supercooling ( or superheating ) may occur.
If there were a large ( possibly infinite ) number of universes, each with possibly different physical laws ( or different fundamental physical constants ), some of these universes, even if very few, would have the combination of laws and fundamental parameters that are suitable for the development of matter, astronomical structures, elemental diversity, stars, and planets that can exist long enough for life to emerge and evolve.
: If a person traveling with a yardstick, measures the length of such yardstick, the physical quantity of length would be written as
If a measurement indicated that a dimensional physical constant had changed, this would be the result or interpretation of a more fundamental dimensionless constant changing, which is the salient metric.

If and formula
If it is assumed that the formula given by Lodge of cosec Af applies, the pressure difference along the major axes can be calculated from the angle of inclination of the major axis, and from this the interfacial tension can be calculated.
If we wish to implement this filter as a digital filter, we can apply the bilinear transform by substituting for the formula above ; after some reworking, we get the following filter representation:
If one integrates this picture, which corresponds to applying the fundamental theorem of calculus, one obtains Cavalieri's quadrature formula, the integral – see proof of Cavalieri's quadrature formula for details.
If we allow both, the problem is called the quantified Boolean formula problem ( QBF ), which can be shown to be PSPACE-complete.
If the answer is " no ", the formula is unsatisfiable.
If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).
If φ is C < sup > k </ sup >, then the inhomogeneous equation is explicitly solvable in any bounded domain D, provided φ is continuous on the closure of D. Indeed, by the Cauchy integral formula,
If these conditions do not hold, the formula describes a more general affine transformation of the plane provided that the determinant of A is not zero.
Since mathematics is related to logic, he cites an example from mathematics: If we have a formula like ( a + b )( a-b )= a²-b² it does not tell us how to think mathematically.
If empirical data reach significance under the appropriate statistical formula, the research hypothesis is supported.
If some specific deductive system of first-order logic is sound and complete, then is it " perfect " ( a formula is provable iff it is a semantic consequence of the axioms ), thus equivalent to any other deductive system with the same quality ( any proof in one system can be converted into the other ).
If every formula in R of degree k is either refutable or satisfiable, then so is every formula in R of degree k + 1.
" If I have learned a formula in gibberish which in any way jogs my memory so as to enable me in each single case to act as though I had a general idea, what possible utility is there in distinguishing between such a gibberish ... and an idea?
If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points.
If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.
If ΔW is the amount of work performed during a period of time of duration Δt, the average power P < sub > avg </ sub > over that period is given by the formula
If G is a finite group and S and T are subgroups of G, then ST is a subset of G of size | ST | given by the product formula:
If the slope m of a line and a point ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) on the line are both known, then the equation of the line can be found using the point-slope formula:
If the respective impedances of the branches of the hybrid that are connected to the conjugate sides of the hybrid are known, hybrid balance may be computed by the formula for return loss.
If the observer is close to the surface of the earth, then it is valid to disregard h in the term, and the formula becomes
If h is significant with respect to R, as with most satellites, then the approximation made previously is no longer valid, and the exact formula is required:
* If 4a < sub > 0 </ sub > = −, the above formula yields ũ < sup > 2 </ sup > = 0.
* If 4a < sub > 0 </ sub > > −, the above formula yields ũ < sup > 2 </ sup > > 0.

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