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Page "Examples of differential equations" ¶ 10
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We and solve
We have proved so able to solve technological problems that to contend we cannot realize a universal goal in the immediate future is to be extremely shortsighted, if nothing else.
`` We must solve the problems which have forced these people to depend upon ADC for subsistence '', Martin said.
We can solve for the temperature of the compressed gas in the engine cylinder as well, using the ideal gas law.
We may solve this by separation of variables ( moving the y terms to one side and the t terms to the other side ),
We can solve both problems using a more abstract definition of the exponential map that works for all Lie groups, as follows.
Bishop John Tong Hon of Hong Kong used it with regard merely to an openness to dialogue with others, saying: " We are guided by the spirit of Vatican II: only dialogue and negotiation can solve conflicts.
We can solve the differential equation using separation of variables:
We thus say that in order to solve this problem, the computer needs to perform a number of steps that grows linearly in the size of the problem.
We can use the three-dimensional theory to solve this problem if we regard u as a function in three dimensions that is independent of the third dimension.
We can solve this by using a weighted average of the quartiles and the interquartile dataset:
Lloyd George was also helped by John Maynard Keynes to write We can Conquer Unemployment, setting out Keynesian economic policies to solve unemployment.
We can solve the differential equation in the coordinate basis, using a spectral method.
" One of the projects of Jemison's foundation is The Earth We Share ( TEWS ), an international science camp where students, ages 12 to 16, work to solve current global problems, like " How Many People Can the Earth Hold " and " Predict the Hot Public Stocks of The Year 2030.
We have to solve this system for to construct the interpolant The matrix on the left is commonly referred to as a Vandermonde matrix.
We wish to solve the forced, transient, nonlinear Burgers ' equation using a spectral approach.
" Ultimately, security and material items are cited as the solution to any problem in the country " We want to remind people that there is no problem this country can throw at you that you can ’ t solve with electric fencing and a pedicure.
We want to solve
We can solve for thermodynamic beta by considering it as a central difference without taking the continuum limit:
We can then solve this using the formula for the integral of secant cubed.
In 2007, the Ottawa Citizen reported that Hellyer is demanding that world governments disclose alien technology that could be used to solve the problem of climate change: " I would like to see what ( alien ) technology there might be that could eliminate the burning of fossil fuels within a generation ... that could be a way to save our planet ... We need to persuade governments to come clean on what they know.
We will solve for each independently:
We are told that counselling, medical treatment and travel have all failed to solve the problem and now his son has turned the house into a prison to keep the old man away from the law courts.
We are interested in the query complexity, which is the number of oracle calls needed to solve the problem.
We have an ongoing gun crisis including firearms-related homicides lately in Toronto, and a law registering firearms has neither deterred these crimes nor helped us solve any of them.

We and transformed
We note that y = 0 is not allowed in the transformed equation.
We said to them, " You will be transformed into despised apes.
We have already remarked that the institution of the Office of Compline transformed the Lucernarium by taking from it something of its importance and symbolism, the latter at the same time losing its original sense.
: ( 3 ) We would be much better off if X were done away with, or at least radically transformed.
The Eastern Orthodox Church Synod of Jerusalem declared: " We believe the Lord Jesus Christ to be present, not typically, nor figuratively, nor by superabundant grace, as in the other Mysteries, ... but truly and really, so that after the consecration of the bread and of the wine, the bread is transmuted, transubstantiated, converted and transformed into the true Body Itself of the Lord, Which was born in Bethlehem of the ever-Virgin Mary, was baptised in the Jordan, suffered, was buried, rose again, was received up, sitteth at the right hand of the God and Father, and is to come again in the clouds of Heaven ; and the wine is converted and transubstantiated into the true Blood Itself of the Lord, Which, as He hung upon the Cross, was poured out for the life of the world.
The mission statement of the diocese is: " We, the Catholic people of the Diocese of Stockton, transformed by Jesus Christ through Baptism ; empowered by the Holy Spirit ; nourished by the Eucharist ; faithful to the mission of Christ ; commit ourselves to be God ’ s heart of mercy and love, God ’ s voice of hope and truth, God ’ s hands of justice and healing to all people.
' We should pass on to future generations the opportunity to enjoy these places and not have them transformed into ordinary places ,' Wayburn said when he was notified of the honor.
We provide integrated education through which people's minds and hearts can be transformed into their highest potential for the benefit of others, inspired by an attitude of universal responsibility.

We and equation
We make several assumptions to derive the momentum balance equation for an acoustic medium.
We know that is opaque and thus follows that is opaque, so in the above equation, each operator can be written as a convex combination:
We now know that the above equation is true modulo integer multiples of, but Cotes missed the fact that a complex logarithm can have infinitely many values due to the periodicity of the trigonometric functions.
We can show a waveform is periodic by finding some period T for which the following equation is true:
We have arrived at the equation:
We may substitute the first equation into the second and, using the trigonometric identity
We also note that a two-body Dirac equation composed of a Dirac operator for each of the two point particles interacting via the Coulomb interaction can be exactly separated in the ( relativistic ) center of momentum frame and the resulting ground state eigenvalue has been obtained very accurately using the Finite element methods of J. Shertzer.
We know that Euler's equation is true because every time a human mind derives the equation, it gets the same result, unless it has made a mistake, which can be acknowledged and corrected.
We may write the time-independent Schrödinger equation,
We wish to find a point which is on both planes ( i. e. on their intersection ), so insert this equation into each of the equations of the planes to get two simultaneous equations which can be solved for and.
We can prove the cancellation law easily using Euclid's lemma, which generally states that if an integer b divides a product rs ( where r and s are integers ), and b is relatively prime to r, then b must divide s. Indeed, the equation
We now use the assumption that is large compared to other scales in the problem ; we therefore neglect the last term in the equation, and get a 1-dimensional diffusion equation:
We re-arrange the equation into:
We can then simplify the Phong equation to:
We can re-write the equation to:
We can rewrite the equation as:
We arrive at the following equation from equation 1 and 2
We may assume that the function is non-negative, since only its absolute value enters in the equation.

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