What is the height of a room which is 8m long, 6m wide and contains 144 meters cube of air?
1 answer:
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The first thing we must do for this case is find the factors of each of the numbers.
We have then:
60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Therefore the GCF is given by:
So, by rewriting the sum we have:
The error is not having written the GCF multiplying.
Answer:
Xiao did not write the sum as the product of GCF and the sum of two numbers.
The correct expression is:
The series is -10-2+6+14+...+110
We see that the common ratio is 8, so it is of the form T0+8n
We also see that T0=-10 (i.e. when the pattern starts.
So we have
Tn=-10+8n
and the summation would be
∑ (-10+8n)
Next to determine the limits.
We know that the first term is -10, which fits T0=-10+8(0).
The last term is 110, which gives the equation Tn=110=-10+8(n)
Solving for n gives
n=(110+10)/8=15
Therefore the limits of summation are 0, 15
hence the summation formula is
I will leave the other problem you posted for your own exercise.
We see that the common ratio is 8, so it is of the form T0+8n
We also see that T0=-10 (i.e. when the pattern starts.
So we have
Tn=-10+8n
and the summation would be
∑ (-10+8n)
Next to determine the limits.
We know that the first term is -10, which fits T0=-10+8(0).
The last term is 110, which gives the equation Tn=110=-10+8(n)
Solving for n gives
n=(110+10)/8=15
Therefore the limits of summation are 0, 15
hence the summation formula is
I will leave the other problem you posted for your own exercise.