Answer:
21.835 kilograms
Step-by-step explanation:
(4,367x5)/1000
So, the best way to do this is translate it to clockwise. 90 degrees counterclockwise is equal to 270 degrees clockwise. So, basically, to rotate, you would follow the following format for each point-
(X,Y) -> (-Y,X)
Now, you do it for each of the points.
A= (-5,5), so A' would be (-5,-5)
B= (-1,5), so B' would be (-5,-1)
C= (-5,4), so C' would be (-4,-5)
D= (-1,4) so D' would be (-4,-1)
Notice, how all the points end up in the square below it. Each quadrant has a specific number. The top right is quadrant 1, the top left is quadrant 2, the bottom left is quadrant 3, and the bottom right is quadrant 4. If you are rotating 270 degrees clockwise, you move to the right, like a clock. That puts the new rectangle in quadrant 3. That is a way to check your work.
Now, just so you know for future reference, the following are also different formats for different problems--
A 90 degree Clockwise rotation about the origin will be (X,Y) -> (Y, -X) *Note, -x just stands for the opposite. Say your original x is a negative number. Then the prime (new) x will be positive.
A 180 degree Clockwise rotation about the origin would be (X,Y) -> (-X,-Y) *Note, -y also stands for the opposite.
A 270 degree clockwise rotation about the origin would be (X,Y) -> (-Y,X).
For translating---
90 degrees Clockwise = 270 degrees Counter
270 degrees Clockwise = 90 degrees Counter
Hope this helped!
On three does it tells you the data
Answer:
1584
Step-by-step explanation:
The sum of this sequence can be found a number of ways. One way is to recast it as the series whose terms are groups of three terms of the given series.
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<h3>series of partial sums</h3>
The partial sums, taken 3 terms at a time, are
1+2-3 = 0
4+5-6 = 3
7+8-9 = 6
...
97+98-99 = 96
So the original series is equivalent to ...
0 +3 +6 +... +96 = 3×1 +3×2 +... +3×32 = 3×(1 +2 +... +32)
That is, the sum is 3 times the sum of the consecutive integers 1..32.
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<h3>consecutive integers</h3>
The sum of integers 1..n is given by the equation ...
s(n) = n(n+1)/2
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<h3>series sum</h3>
Using this to find the sum of our series, we find it to be ...
series sum = 3 × (32)(33)/2 = 1584
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<em>Alternate solution</em>
The given series is the sum of integers 1-99, with 6 times the sum of integers 1-33 subtracted. That is, ...
1 + 2 - 3 + 4 + 5 - 6 = 1+2+3+4+5+6 -2(3 +6) = 1+2+3+4+5+6 -6(1+2)
Continuing on to ...97 +98 -99 gives the result s(99) -6s(33).
Computed that way, we find the sum to be ...
(99)(100)/2 -6(33)(34)/2 = 4950 -3366 = 1584
