Jo has baked 40 cakes for her husband's 40th birthday, one for each of his years, weighing 1, 2, 3 ... 40kg. She forgets which c
ake is which and has to check the weight of each cake using a large pair of balancing scales. Each cake is placed individually on the left-hand pan of the scales and balanced againt one or more scale-weights which can be put on either or both scale pans as necessary. She has four scale-weights available, each a different whole number of kg. Find their values in kg and make a list showing the particular combination of the scale-weights for identifying each cake
1 answer:
Since the weight can be put on either pan, any given weight can contribute 3 values +w, 0, -w. The weights need to be chosen to be a factor of 3 of each other:
.. 1 kg, 3 kg, 9 kg, 27 kg.
The base-3 version of the numbers 1 to 40 tell you where to put the weights.
If we use the code - = weight not used, o = weight opposite the cake, w = weight with the cake, then we can make a table, as in the attachment. Left-to-right the corresponding weights are 27 kg, 9 kg, 3 kg, 1 kg.
.. 1 kg, 3 kg, 9 kg, 27 kg.
The base-3 version of the numbers 1 to 40 tell you where to put the weights.
If we use the code - = weight not used, o = weight opposite the cake, w = weight with the cake, then we can make a table, as in the attachment. Left-to-right the corresponding weights are 27 kg, 9 kg, 3 kg, 1 kg.
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Answer:
16Km due east of school P
Step-by-step explanation:
Given
A school P is 16km due west of a school Q
Thus, we can say that distance PQ = 16 km.
________________________________
now we have to find the bearing of Q from P
As distance is same
distance PQ = distance QP
Thus,
Distance will remain same of 16 km.
For direction,
If Q is west of P, then P will be east of Q
as shown in figure P is west of Q,
now from point P , Q is west P.
Thus,
Bearing of School Q from P is 16Km due east of school P