What is the sum of the geometric series: 3∑5(-2/3)^ii=0
1 answer:
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Answer:
(12,10)
Step-by-step explanation:
Let the midpoint of the side opposite this vertex have coordinates B(a,b)
We have the centroid at C(8,7) and the vertex of the triangle at A(0,1).
The centroid divides AB internally in the ratio 2:1
We use the formula:
where m:n=2:1 is the ratio of internal division.
We substitute the coordinates of A and B and the ratio to get:
This should simplify and give us the centroid.
This implies that:
We solve for a and b
Therefore the midpoint of the side opposite this vertex is (12,10)
<h2>Answer:</h2>
A prism is a solid object having two identical bases, hence the same cross section along the length. This is a rectangular prism its base is a rectangle. multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:
Therefore, Associative Property can be used to mentally find the volume of the prisms shown by selecting the easier way of the multiplication. For instance, we can say that:
In whose case:
To operate this mentally is not an easy way, but<em> what if we rotate this shape? </em>so we say that:
Then, the volume can be found as:
There are two forms of finding the result. First, multiplying 18 by 20 and then the result by 5, but as in the previous case this is a tricky way to do mentally:
Hence, here we can use Associative Property multiplying 20 by 5 and then the result by 18:
This last arrangement is easier because 20 x 5 is easy to remember given that the result is 100. Then, by multiplying this result by 18 then we get 1800.