Профессиональной коммуникации АнглийСкий язык reading numerals and formulas методический материал для чтения и перевода текстов, знаков, символов на английском языке Пермь 2010

 Название Профессиональной коммуникации АнглийСкий язык reading numerals and formulas методический материал для чтения и перевода текстов, знаков, символов на английском языке Пермь 2010 страница 4/7 Дата 27.11.2012 Размер 0.52 Mb. Тип Документы
 Lateral area of a prism The lateral area of a right prism is equal to the product of the perimeter of the base and the height. Sector The area of a sector is equal to one-half the product of the radius and the length of the arc. Regular polygon The area of a polygon is equal to one-half the product of the perimeter and apothem. Rhombus The area of a rhombus is equal to one-half the product of the two diagonals. Circumscribed polygon The area of a circumscribed polygon is equal to one-half the perimeter times the radius of the inscribed circle. Ellipse The area of an ellipse equals times the product of the long and short diameters, or times the product of the long and short radii. Surface of a sphere The surface of a sphere is four times the area of a circle of the same diameter.Volumes Rectangular solid The volume of a rectangular solid is equal to the product of its length, width and height. The volume of a rectangular solid is equal to the area of the base times the height. Prism or cylinder The volume of any right prism is equal to the product of the base and altitude. The volume of any right cylinder is equal to the product of the base and altitude. The volume of any parallelepiped is equal to the product of the base times the altitude. Oblique prism or cylinder The volume of any oblique prism is equal to the product of a right section and the slant height. Pyramid or cone The volume of a pyramid (cone) is equal to one-third the product of the base and altitude. Frustum of a pyramid or a cone The volume of a frustum of a pyramid is equal to one-third the altitude multiplied by the sum of the area of the lower base, the area of the upper base and the square root of the product of the two bases. Spherical sector The volume of a spherical sector is equal to one-third the product of the area of the zone and the radius of the sphere.TRIGONOMETRIC FORMULAS In any oblique triangle the square of any side is equal to the sum of the squares of the other two sides diminished by (minus) twice their product times the cosine of the included angle (The law of cosines). In any triangle the difference of any two sides is to their sum as the tangent of one half the difference of their respective opposite angles is to the tangent of one half of the sum of these angles (The law of tangents). a plus b over a minus b is equal to c plus d over c minus d. a cubed is equal to the logarithm of d to the base c. 1) of z is equal to b, square brackets, parenthesis, z divided by c sub m plus 2, close parenthesis, to the power m over m minus 1, close square brackets; 2) of z is equal to b multiplied by the whole quantity: the quantity two plus z over c sub m, to the power m over m minus 1, minus 1. The absolute value of the quantity sub j of t one, minus sub j of t two, is less than or equal to the absolute value of the quantity M of t1 minus over j, minus M of t2 minus over j. j = 1, 2, … n) k is equal to the maximum over j of the sum from i equals one to i equals n of the modulus of of t, where t lies in the closed interval a b and where j runs from one to n. The limit as n becomes infinite of the integral of f of s and of s plus delta n of s, with respect to s, from to t, is equal to the integral of f of s and of s, with respect to s, from to t. sub n minus r sub s plus 1 of t is equal to p sub n minus r sub s plus 1, times e to the power t times sub plus s. L sub n adjoint of g is equal to minus 1 to the n, times the n-th derivative of a sub zero conjugate times g, plus, minus one to the n minus 1, times the n minus first derivative of a sub one conjugate times g, plus … a sub n conjugate times g. The partial derivative of F of lambda sub i of t, with respect to lambda, multiplied by lambda sub i prime of t, plus the partial derivative of F with arguments lambda sub i of t and t, with respect to t, is equal to 0. The second derivative of y with respect to s, plus y, times the quantity 1 plus b of s, is equal to zero. ( arg z = ) f of z is equal to sub mk hat, plus big O of one over the absolute value of z, as absolute z becomes infinite, with the argument of z equal to gamma. D sub n minus 1 prime of x is equal to the product from s equal to zero to n of, parenthesis, 1 minus x sub s squared, close parenthesis, to the power epsilon minus 1. K of t and x is equal to one over two , times the integral of K of t and z, over w minus w of x, with respect to w along curve of the modulus of w minus one half, is equal to rho. (a > 0) The second partial (derivative) of u with respect to t, plus a to the fourth power, times the Laplacian of the Laplacian of u, is equal to zero, where a is positive. (c > 1) D sub k of x is equal to one over two , times integral from c minus i infinity to c plus i infinity of dzeta to the k of w, x to the w divided by w, with respect to w, where c is greater than 1. 4 c plus W third plus 2 m first a prime plus R a-th equals thirty-three and one-third. A is equal to one half mu by r p-th omega L second omega L first over (by) the square root out of R second round brackets opened R first plus omega square L first square by r p-th round brackets closed. Capital M is equal to R sub one multiplied by x minus capital P sub one, round brackets opened, x minus a sub one, round brackets closed, minus capital P sub two, round brackets opened, x minus a sub two, round brackets closed. is equal to B divided by six point four five multiplied by two point five four. Capital F is equal to capital C sub s, A, I L sine theta Tangent r is equal to, dash (line of division), tangent i over (by) e. A v-th is equal to mu omega m omega square L square (divided) by r p-th square brackets opened omega square m square plus R second round brackets opened R first plus omega square L square (divided) by r p-th round and square brackets closed. Therefore cotangent r is equal to e cotangent i. Therefore M sub t is equal to G theta, dash d to the fourth power divided by thirty-two. P critical is equal to square E I divided by four 1 square.AXIOMS Axiom of extensionality Two sets are equal if and only if they have the same members.Axiom of the null set There exists a set with no members (the empty set). Axiom of unordered pairs If x and y are sets, then the (unordered) pair is a set.Axioms of the sum set or union If x is a set of sets, the union of all its members is a set. For example, if , then the union of the (two) elements of x is the set ).

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