another 2 math question

shun in

2008-10-27 4:05 pm

1. x + y + z = 0
x - y + z = 0
x + z = 0

2. Temperature and Heart Rate
When the temperature , T ( in degree Celius) of a cat is reduced, the cat's heart rate r (in beats per minute) decreases. Under laboratory conditions a cat at a temperature of 36 had a heart rate of 206 and at a temperature of 30 the heart rate was 122. If r is linearly related to T where T is between 26 and 38
a) determine an equation for r in terms of T
b) determine the cat's heart rate at temperature of 27 degree celius

Thanks a lot

回答 (1)

用戶10012

2008-10-27 4:17 pm

✔ 最佳答案

1. Equation 1 plus equation 2 gives the result 2x + 2z = 0, or x + z = 0 which is the same as equation 3. So there is no solution since the equations are not independent to each other.
2.Since r is linearly related to T, we can let the equation be r = mT + C.
When T = 36, r = 206.
So 206 = 36m + C................(1)
When T = 30, r = 122.
So 122 = 30m + C................(2)
(1) - (2) we get
84 = 6m
m = 14.
Sub. into (2), we get 122 = 420 + C
So C = -298.
So r = 14T - 298.
Now T = 27, so r = 14(27) - 298 = 378 - 298 = 80 degree.

2008-10-27 08:38:58 補充：
For Q1. The only solution is x = y = z = 0.

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