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The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
ft/s 3.2808 The metre per second is the unit of both speed (a scalar quantity ) and velocity (a vector quantity , which has direction and magnitude) in the International System of Units (SI), equal to the speed of a body covering a distance of one metre in a time of one second .
For instance, if the one solving the math word problem has a limited understanding of the language (English, Spanish, etc.) they are more likely to not understand what the problem is even asking. In Example 1 (above), if one does not comprehend the definition of the word "spent," they will misunderstand the entire purpose of the word problem.
Also, let Q = (x 1, y 1) be any point on this line and n the vector (a, b) starting at point Q. The vector n is perpendicular to the line, and the distance d from point P to the line is equal to the length of the orthogonal projection of on n. The length of this projection is given by:
An ant starts to crawl along a taut rubber rope 1 km long at a speed of 1 cm per second (relative to the rubber it is crawling on). At the same time, the rope starts to stretch uniformly at a constant rate of 1 km per second, so that after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc.
Surprisingly, the answer is 2 π m or around 6.3 metres (21 ft). In the second phrasing, considering that 1 metre (3 ft 3 in) is almost negligible compared with the 40,000 km (25,000 mi) circumference, the first response may be that the new position of the string will be no different from the original surface-hugging position.
By carefully writing the above equations as matrix equations, we obtain its dual problem: [15] {, () + () + (,) and by the duality theorem of linear programming, since the primal problem is feasible and bounded, so is the dual problem, and the minimum in the first problem equals the maximum in the second problem.
Converts measurements to other units. Template parameters [Edit template data] This template prefers inline formatting of parameters. Parameter Description Type Status Value 1 The value to convert. Number required From unit 2 The unit for the provided value. Suggested values km2 m2 cm2 mm2 ha sqmi acre sqyd sqft sqin km m cm mm mi yd ft in kg g mg lb oz m/s km/h mph K C F m3 cm3 mm3 L mL cuft ...