Mathematics for Collegiate Students of Agriculture and General Science |
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Page 8
... third , fourth , and fifth powers should be memorized . EXERCISES Use the laws of exponents to combine and simplify the following expressions . 1. 8-1 / 2.82 / 3.8-1 / 5.8283 / 4.81 / 12 . 3. ( 32.31 / 2.55 / 2 ) 2 ÷ ( 73 2. 32 / 5.42 ...
... third , fourth , and fifth powers should be memorized . EXERCISES Use the laws of exponents to combine and simplify the following expressions . 1. 8-1 / 2.82 / 3.8-1 / 5.8283 / 4.81 / 12 . 3. ( 32.31 / 2.55 / 2 ) 2 ÷ ( 73 2. 32 / 5.42 ...
Page 54
... third point . Then the point P is said to divide the segment P1P2 in the ratio ( 2 ) P1P PIP2 =入. This ratio is called the ratio of division or the division ratio . FIG . 14 If we choose an origin 0 on the given line then the abscissas ...
... third point . Then the point P is said to divide the segment P1P2 in the ratio ( 2 ) P1P PIP2 =入. This ratio is called the ratio of division or the division ratio . FIG . 14 If we choose an origin 0 on the given line then the abscissas ...
Page 57
... P ( x , y ) is any point satisfying the given condition and is therefore on the curve . SECOND STEP . Write down the given condition . THIRD STEP . Express the given condition in coördinates , III , § 50 ] 57 GRAPHIC REPRESENTATION.
... P ( x , y ) is any point satisfying the given condition and is therefore on the curve . SECOND STEP . Write down the given condition . THIRD STEP . Express the given condition in coördinates , III , § 50 ] 57 GRAPHIC REPRESENTATION.
Page 58
... Third step . We now make use of the formula for the distance between two points . This gives PA = PB = √ ( x + 3 ) 2 + y2 , √ ( x − 2 ) 2 + ( y + 8 ) 2 . Substituting in the equation PA √ ( x + 3 ) 2 + y2 = = PB , we find √ ( x - 2 ) ...
... Third step . We now make use of the formula for the distance between two points . This gives PA = PB = √ ( x + 3 ) 2 + y2 , √ ( x − 2 ) 2 + ( y + 8 ) 2 . Substituting in the equation PA √ ( x + 3 ) 2 + y2 = = PB , we find √ ( x - 2 ) ...
Page 59
... for the other variable . THIRD STEP . Plot the points corresponding to the values so determined . FOURTH STEP . Draw a smooth curve through the points . EXAMPLE . Plot the locus of the equation x2 - III , §51 ] 59 GRAPHIC REPRESENTATION.
... for the other variable . THIRD STEP . Plot the points corresponding to the values so determined . FOURTH STEP . Draw a smooth curve through the points . EXAMPLE . Plot the locus of the equation x2 - III , §51 ] 59 GRAPHIC REPRESENTATION.
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Mathematics for Collegiate Students of Agriculture and General Science Alfred Monroe Kenyon,William Vernon Lovitt No preview available - 2016 |
Common terms and phrases
abscissas algebraic amount annuity arithmetic mean average ax² axes axis binomial binomial coefficients binomial theorem called cent circle coefficient common logarithm completing the square computed coördinates correlation cos² cosine COTANGENT curve decimal denoted determine distance ears ellipse equal error EXAMPLE EXERCISES exponent feet Find the equation forces formula frequency geometric given equation graph Hence hyperbola inches intersection law of sines law of tangents length locus Log10 Value Log10 logarithm magnitude mantissa measured multiplying negative parabola parallel perpendicular plane Plot positive quadratic quadratic equation RADIANS radius ratio real number represents respect resultant side sin² sine slope solution solve square root standard deviation straight line Substituting tabular difference tangent temperature term tion trigonometric functions Value Log10 Value varies vertex vertical weight whence x-axis y-axis zero
Popular passages
Page 59 - Find the equation of the locus of a point which moves so that the sum of the squares of its distances from the x and the j/-axis equals 4.
Page 122 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Page 277 - The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.
Page 124 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 199 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 167 - moment of a force" with respect to a point is the product of the force and the perpendicular distance from the given point to the line of action of the force.
Page 223 - The weight of an object above the surface of the earth varies inversely as the square of its distance from the center of the earth.
Page 207 - Find and classify the equation of the locus of a point which moves so that...
Page 204 - PF'/PH'= e, by the definition of the curve. Furthermore :J (b) \PF—PF'\=2a. In fact, the hyperbola is often defined as the locus of a point which moves so that the difference of its distances from two fixed points is constant.
Page 74 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.