A crystal growth furnace is used in research to determine how best to manufacture crystals used in electric components for the space shuttle. For proper growth of the crystal, the temperature must be controlled accurately by adjusting the input power. Suppose the relationship is given by the following equation, where T is the temperature in degrees Celsius and w is the power input in watts.
T(w) = 0.1w^2 + 2.156w + 20
(a) How much power is needed to maintain the temperature at 204°C? (Give your answer correct to 2 decimal places.)
(b) If the temperature is allowed to vary from 204°C by up to ±1°C, what range of wattage is allowed for the input power? (Give your answer correct to 2 decimal places.)
smaller value=?
larger value=?
2007-09-27 04:15:53 · 2 answers · asked by lady_divine@sbcglobal.net 1 in Science & Mathematics ➔ Mathematics
T(w) = 0.1w^2 + 2.156w + 20 is the function for temperature (T) in terms of power (w). If you want 204 C, then
204 = 0.1w^2 + 2.156w + 20 and solve for w (If you don't know how to solve a simple quadratic, then you is in -far- deeper trouble than anything that can be fixed here)
Now go back and do the same thing for T = 203 and T = 205.
Doug
2007-09-27 04:25:15 · answer #1 · answered by doug_donaghue 7 · 0⤊ 0⤋
(a) set the equation equal to 204 and solve for w:
204=0.1w^2 + 2.156w+20
184=0.1w^2 + 2.156w
0.1w^2 + 2.156w -184 = 0 now use the quadratic formula to get w. Remember that w has to be positive.
(b) to get the smaller value, do the same as in part (a) using 203 instead of 204. for the larger value, use 205.
2007-09-27 11:33:46 · answer #2 · answered by Nilly 3 · 0⤊ 0⤋