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Answer:
Step-by-step explanation:
We have been given a graph of a rectangle. The area of the shaded section is 63 square units. We are asked to find the value of x.
We can see from our given graph that shaded section forms a trapezoid, so we will use area of trapezoid formula to find the value of x.
, where, a and b represents the parallel sides of trapezoid and h represents height of trapezoid.
Upon substituting our given values in above formula we will get,
Upon dividing both sides of our equation by 3.5 we will get,
Let us subtract 7 from both sides of our equation.
Therefore, the value of x is 11 units.
We have a sequence that meets the given criteria, and with that information, we want to get the sum of all the terms in the sequence.
We will see that the sum tends to infinity.
So we have 5 terms;
A, B, C, D, E.
We know that the sum of each term and its neighboring terms is 15 or 25.
then:
- A + B + C = 15 or 25
- B + C + D = 15 or 25
- C + D + E = 15 or 25
Now, we want to find the sum of all the terms in the sequence (not only the 5 given).
Then let's assume we write the sum of infinite terms as:
Now we group that sum in pairs of 3 consecutive terms, so we get:
So we will have a sum of infinite of these, and each one of these is equal to 15 or 25 (both positive numbers). So when we sum that infinite times (even if we always have the smaller number, 15) the sum will tend to be infinite.
Then we have:
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