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Good Portland local, Betty finished regarding Franklin Senior school and you may worked for two years before signing up at Reed

Good Portland local, Betty finished regarding Franklin Senior school and you may worked for two years before signing up at Reed

She obtained good BA inside the business economics, graduating Phi Beta Kappa, and you can had written a thesis that have Prof. Blair Stewart [1925–49] on the You.S. rules about glucose. She plus did secretarial work with then-President Dexter Keezer [1934–42], and you can assisted Prof. Frank Munk [governmental science 1939–65] into the entering out-of 1st publication shortly after his arrival into the the brand new U.S. Pursuing the graduation, Betty has worked just like the a keen economist for U.S. State department from inside the Arizona, D.C. From inside the 1946, she partnered other business economics major Robert W. Macaulay’43, and you will did as the a receptionist as he acquired an enthusiastic MBA out of Harvard. The couple relocated to the brand new San francisco, in which it remained having 60 years. Betty are an excellent statistician getting Pacific Telephone, although she elevated a child and son, she is actually a volunteer inside schools, for the Girl Scouts, new Group of women Voters, and Presbyterian church. Continue reading Good Portland local, Betty finished regarding Franklin Senior school and you may worked for two years before signing up at Reed

6.5 Indirect Research and Inequalities in a single Triangle

6.5 Indirect Research and Inequalities in a single Triangle

six.3 Medians and you will Altitudes from Triangles

Share with if the orthocenter of one’s triangle to your given vertices try into the, into the, or beyond your triangle. Following select the coordinates of orthocenter.

Explanation: The slope of the line HJ = \(\frac < 1> < 3>\) = \(\frac < 5> < 2>\) The slope of the perpendicular line = \(\frac < -2> < 5>\) The perpendicular line is (y – 6) = \(\frac < -2> < 5>\)(x – 1) 5(y – 6) = -2(x – 1) 5y – 30 = -2x + 2 2x + 5y – 32 = 0 – (i) The slope of GJ = \(\frac < 1> < 3>\) = \(\frac < -5> < 2>\) The slope of the perpendicular line = \(\frac < 2> < 5>\) The equation of perpendicular line (y – 6) = \(\frac < 2> < 5>\)(x – 5) 5(y – 6) = 2(x – 5) 5y – 30 = 2x – 10 2x – 5y + 20 = 0 – (ii) Equate both equations 2x + 5y – 32 = 2x – 5y + 20 10y = 52 y = 5.2 Substitute y = 5.2 in (i) 2x + 5(5.2) – 32 = 0 2x + 26 – 32 = 0 2x = 6 x = 3 The orthocenter is (3, 5.2) The orthocenter lies inside the triangle.

Explanation: The slope of LM = \(\frac < 5> < 0>\) = \(\frac < 1> < 3>\) The slope of the perpendicular line = -3 The perpendicular line is (y – 5) = -3(x + 8) y – 5 = -3x – 24 3x + y + 19 = 0 — (ii) The slope of KL = \(\frac < 3> < -6>\) = -1 The slope of the perpendicular line = \(\frac < 1> < 2>\) The equation of perpendicular line https://datingranking.net/tr/alt-inceleme/ (y – 5) = \(\frac < 1> < 2>\)(x – 0) 2y – 10 = x — (ii) Substitute (ii) in (i) 3(2y – 10) + y + 19 = 0 6y – 30 + y + 19 = 0 7y – 11 = 0 y = \(\frac < 11> < 7>\) x = -6 The othrocenter is (-6, -1) The orthocenter lies outside of the triangle

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