Multiply and simplify: (1 - 7i)(5 + 3i). Write the answer in the form a + bi, wh
ID: 3031327 • Letter: M
Question
Multiply and simplify: (1 - 7i)(5 + 3i). Write the answer in the form a + bi, where a and b are real numbers. Solve, and write the answer in interval notation: x - 1/x - 6 greaterthanorequalto 0. Water initially at 200 degree F. is left in a room of temperature 60 degree F to cool. After t minutes, the temperature T of the water is given by T(t) = 60 + 140 e^-0.096 t Find the temperature of the water 20 minutes after it is left to cool. (Round to the nearest tenth of a degree.) Find the value of the logarithm: log_5 (1/125).Explanation / Answer
13. We have (1-7i)/( 5+3i) = (1-7i) (5-3i)/( 5+3i)(5 -3i) = ( 5 -3i -35i+21i2)/( 25 -9i2) = ( -16- 38i)/34 = -(8+19i)/17 [ as (a+b)(a-b) = a2 – b2 and i2 = -1 ].
14. We have (x-1)/(x-6) 0 . If x = 6, the fraction (x-1)/(x-6) is indeterminate as then the denominator is 0 and division by 0 is not defined. However, if x 6, then (x-1)/(x-6) 0 implies that (x -1) 0 ( on multiplying both the sides by (x -6)). Now, if (x -1) 0 then x 1 i.e. x [ 1, ). However, since x 6, hence x [ 1, 6)U(6, ).
15. The temperature of water after t minutes is given by T(t) = 60+ 140e-0.096t. Hence, 20 minutes after water in the room is left to cool, its temperature is 60 + 140e-0.096*20 = 60 +140e-1.92 = 60+140*0.14660696213 = 60 + 20.52 = 80.520 F or 810 F ( on being rounded off to the nearest whole number).
16. We have log5( 1/125)= log5 (5-3) = -3
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