If the force required to remove the coatings is plotted against film thickness, a graph as illustrated schematically in Fig. 5 may characteristically result.

If x and y are real numbers, and if the graph of y is plotted against x, the derivative measures the slope of this graph at each point.

If the function f is not linear ( i. e. its graph is not a straight line ), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.

If f is a continuous function, meaning that its graph is an unbroken curve with no gaps, then Q is a continuous function away from.

If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).

If this triangulated graph is colorable using four colors or less, so is the original graph since the same coloring is valid if edges are removed.

If there is a graph requiring 5 colors, then there is a minimal such graph, where removing any vertex makes it four-colorable.

If the graph G is connected, then the rank of the free group is equal to 1 − χ ( G ): one minus the Euler characteristic of G.

If the graph does not contain any cycles ( i. e. it's an acyclic graph ), its girth is defined to be infinity.

If the graph is directed, the direction is indicated by drawing an arrow.

If A is nonzero, then the x-intercept, that is, the x-coordinate of the point where the graph crosses the x-axis ( where, y is zero ), is − C / A.

If B is nonzero, then the y-intercept, that is the y-coordinate of the point where the graph crosses the y-axis ( where x is zero ), is − C / B, and the slope of the line is − A / B.

* If asked to imagine the graph of the relationship y = ax < sup > 2 </ sup >, one typically visualizes a range of values of x, but only one value of a.

( If the graph has no weights, 1 indicates an edge, 0 indicates no edge.

If no path exists between two cities, adding an arbitrarily long edge will complete the graph without affecting the optimal tour.

If a variable undergoes regular oscillations, and a graph of the system is drawn with the oscillating variable as the vertical axis and time as the horizontal axis, the amplitude is visually represented by the vertical distance between the extrema of the curve and the equilibrium value.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.

If it is constrained to bury the cable only along certain paths, then there would be a graph representing which points are connected by those paths.

If there are n vertices in the graph, then each tree has n-1 edges.

If x and y are vectors, then the best linear approximation to the graph of f depends on how f changes in several directions at once.

If this fragment is part of a larger graph, then any Hamiltonian cycle through the graph must go in or out of the top vertex ( and either one of the lower ones ).

* The Lusternik – Schnirelmann theorem: If the sphere S < sup > n </ sup > is covered by n + 1 open sets, then one of these sets contains a pair ( x, − x ) of antipodal points.

If the tree contains data, we can simply simultaneously store it in a consecutive array in preorder.

If the cord is twisted up tightly on itself and then the bucket is released, it begins to spin rapidly, not only with respect to the experimenter, but also in relation to the water it contains.

In the words of Henry Chadwick, " If the Consolation contains nothing distinctively Christian, it is also relevant that it contains nothing specifically pagan either ... is a work written by a Platonist who is also a Christian, but is not a Christian work.

If the ideals A and B of R are coprime, then AB = A ∩ B ; furthermore, if C is a third ideal such that A contains BC, then A contains C. The Chinese remainder theorem is an important statement about coprime ideals.

If each pixel on the display actually contains three rectangular subpixels of red, green, and blue, in that fixed order, then things on the screen that are smaller than one full pixel in size can be rendered by lighting only one or two of the subpixels.

If the sheet contains regions where the number of atoms in a ring is different from six, while the total number of atoms remains the same, a topological defect has formed.

If the frame contains areas where nothing has moved, the system simply issues a short command that copies that part of the previous frame, bit-for-bit, into the next one.

If both copies are damaged, the Purkinje layer ( a part of the cerebellum that contains better-connected neurons than any other ) develops abnormally, runting is more common, and pups die within weeks due to inadequate lung development.

If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.

If a project plan contains a significant portion of LOE, and the LOE is intermixed with discrete effort, EVM results will be contaminated.

If an explosive molecule contains just enough oxygen to convert all of its carbon to carbon dioxide, all of its hydrogen to water, and all of its metal to metal oxide with no excess, the molecule is said to have a zero oxygen balance.

If a map contains a reducible configuration, then the map can be reduced to a smaller map.

If the packet contains options, this field contains the option type of the next option.

# If V is a set of strings then V * is defined as the smallest superset of V that contains λ ( the empty string ) and is closed under the string concatenation operation.

The inscription on his tomb contains Persian words penned which state: اگرفردوس روی زمین است همین است و همین است و همین است ( If there is a paradise on earth, it is this, it is this, it is this!

If the picture contains an area of the same color, it can be compressed without loss by saying " 200 red dots " instead of " red dot, red dot, ...( 197 more times )..., red dot.

If each group contains less than half the population, then some of the population is exactly equal to the median.

If S contains two elements that are not pairwise orthogonal ( in particular, the set of all quantum states includes such pairs ) then an argument like that given above shows that the answer is no.

If each additional layer contains less oil, the final painting will crack and peel.

# If he contains and sustains all things, would he not be existence itself?

If it is made from durum wheat, the pasta contains protein and gluten.