# 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 3/7 Дата 27.11.2012 Размер 0.52 Mb. Тип Документы
 Subscripts and Superscripts ' a prime b'' 1) b double prime; 2) b second prime; 3) b twice dashed 1) c first; 2) c sub one 1) d sub zero; 2) d zero-th 1) f prime, sub one; 2) f sub one, prime 1) f prime, m-th; 2) f m-th, prime 1) capital A, r-th; 2) capital A, sub r capital L 1) capital P sub m minus two, prime; 2) capital P prime, sub m minus two first derivative of y second derivative of y h triple prime 1) c sub q 2) c q-thExponents 1) a square; 2) a squared; 3) a to the second; 4) a to the second power; 5) a raised to the second power; 6) the square of x; 7) the second power of x 1) b cube; 2) b cubed; 3) b to the third; 4) b to the third power; 5) b raised to the third power; 6) the cube of b; 7) the third power of b c to the sixth Note: The variants given below are possible with all the exponents. 1) d to the y-th; 2) d to the y-th power; 3) d raised to the y-th power; 4) the y-th power of d m to the minus first n to the minus seventh c to the m-th two to the pi-th x to the minus q-th c to the power m minus n 1) z to the power m over (divided by, by) n; 2) z to the m by n-th power; 3) z to by (power) k to the power m over n minus q minus capital B to the n minus one 1) the quantity five minus a over b to the fourth…; 2) parenthesis five minus a over b close parenthesis to the fourth; 3) round brackets opened, five minus a over b round brackets closed to the fourthRoots the square root (out) of two the square root (out) of a the cube root (out) of b the seventh root (out) of d the q-th root (out) of a to the m-th power five times the fourth root (out) of three two-thirds times the square root (out) of b capital C is equal to the square root (out) of x square plus y square the twelfth root (out) of p cube plus q cube the fourth root (out) of (dash, line of division) capital A first (sub one) plus capital B over (by, divided by) three a second (sub two) b double prime (twice dashed) the minus m-th root (out) of p to the fourth (power)Variables, Functions and Limits 1) f of x; 2) a function of x Note: Not f times x capital F first (sub one) of x 1) a function of (two variables) x and y; 2) f of y and y 1) a function of x, y and z; 2) f of x, y and z 1) a function of the quantity x plus delta x; 2) f of the quantity x plus delta x 1) the limit of f of x is equal to l; 2) the limit of a function of x is equal to l the limit of x as x tends to (approaches) is equal to l the limit of z, as v approaches l, is equal to a the limit of f of x, as x tends to infinity (x increases without bound, x becomes infinity) is equal to l The point P with coordinates x and y 1) The point A with coordinates minus two and minus three; 2) The point A whose abscissa is minus two and ordinate minus threeEXAMPLES OF READING FORMULAS Algebraic Formulas The square of the sum of two numbers (a binomial) is equal to the square of the first term, plus twice the product of the first and last terms, plus the square of the last term. The square of the difference of two numbers (of a binomial) is equal to the square of the first term, minus twice the product of the first and last terms, plus the square of the last term. The product of the sum and difference of two numbers is equal to the difference of the squares of the numbers. The product of two binomials having a common term is equal to the product of the first two terms, plus the sum of the last terms multiplied by the common term, plus the product of the last terms. The square of the sum of three numbers (a trinomial) is equal to the sum of the squares of each term of the trinomial and twice the product of each term by each of the other terms. The sum of two cubes is factored into the sum of the cube roots and the incomplete square of the difference. The difference of two cubes is factored into the difference of the cube roots and the incomplete square of the sum. x The derivative of a function is the limit of the ratio of the increment of the function to the increment of the independent variable, when the latter varies and approaches zero as a limit.SOME GEOMETRICAL FORMULAS Notation Used in Formulas A area a apothem a, b, c sides of a triangle b and b’ bases or areas of bases C circumference d diameter h height, altitude l length w width p perimeter r radius s slant height s half the perimeter of a triangle = 3.1416 V volumeFormulas for lines Right triangle The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides (the Pythagorean theorem). Circle The circumference of a circle is equal to times the diameter. Triangle The altitude drawn to one side of a triangle is equal to the product of either one of the two other sides and the sine of the angle adjacent to it. Areas Square A = b2 The area of a square equals the length of the side of the square multiplied by itself, that is, the side squared. Rectangle A = bh The area of a rectangle is equal to the product of its base and altitude. Parallelogram A = bH The area of a parallelogram is equal to the product of the base and altitude. A = ab sin A The area of a parallelogram is equal to the product of the two sides and the sine of the included angle. Triangle The area of a triangle is equal to one-half the product of the base and altitude. The area of a triangle is equal to one-half the product of two sides and the sine of the included acute angle. Circle The area of a circle is equal to one-half the product of the circumference and the radius. The area of a circle is equal to times the square of the radius. Trapezoid The area of a trapezoid is equal to one-half the sum of the parallel bases times the altitude. Zone The area of a zone is equal to its altitude multiplied by the circumference of a great circle. Lateral area of a cone The lateral area of a right cone is equal to one-half the product of the circumference of the base and the slant height. Lateral area of a pyramid The lateral surface of a right pyramid is equal to one-half the product of the perimeter of the base and the slant height. Lateral area of a cylinder The lateral area of a cylinder is equal to the circumference of the base times the height.

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