Odd numbers take the form , where
is an integer. When
, the last odd number would be 799. So we're adding
By reversing the order of terms, we have
and we can pair up terms in both sums at the same position to write
so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:
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We could also make use of the formulas,
We have
It looks like the differential equation is
Factorize the right side by grouping.
Now we can separate variables as
Integrate both sides.
You could go on to solve for explicitly as a function of
, but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.
Answer:
Step-by-step explanation:
The missing figure is attached.
For this exercise you can divide the given figure into three rectangles.
The formula for calculate the area of a rectangle is:
Where "l" is the lenght and "w" is the width.
Knowing this, you can calculate the area of each rectangle.
Then:
Area of the Rectangle A
You can identify that:
Then, its area is:
Area of the Rectangle B
Observe that:
Then, its area is:
Area of the Rectangle C
You can identify that:
Then, its area is:
Add the area of the rectangles in order to find the total area. This is:
Therefore, you will need of outdoor carpet for that hole.
