Galena is solving the following system. 3x+2y+3z =5 7x+y +7z=-1 4x-4y-z=-3
2 answers:
Answer:
She did not multiply equation 3 in step 2 by the correct value.
Step-by-step explanation:
Given:
In order to solve this, we need to eliminate any one variable and then form a simultaneous equation with the remaining two variables. Then, we nee to solve the simultaneous equation.
Here, Galena is trying to eliminate the variable first.
Step 1: She multiplies equation (3) by 3 and adds it to equation (1)
Let us multiply equation (3) by 3
Now, adding this to equation 1 will cancel out z terms.
Now, she need to make one more equation in .
Step 2: She multiplies equation (3) by -7 and adds it to equation (2)
Multiplying equation (3) by -7 will give,
Now, adding this to equation 2 will not cancel out z terms.
So, she makes mistake in step 2 as the terms are not being cancelled.
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Answer:
Step-by-step explanation:
Here's a pattern to consider:
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.