For each of the following sequences, state rule and write down the next two terms
1 answer:
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For the circular cover we have:
A) The area is 379.94 ft²
B) The length of the rope must be 68.2 ft
<h3>How to get the area of the cover?</h3>Remember that the area of a circle of radius R is given by the formula:
Where pi = 3.14
In this case, the diameter of the pool is 20ft, then the radius is:
R = 20ft/2 = 10ft
And it must extend 12 inches beyond, then the radius of the cover must be:
R = 10ft + 12in
Now, we know that 1ft = 12 in, then we can rewrite the radius as:
R = 10ft +1ft = 11ft
Then the area of the cover is:
B) now we want to get the length of the rope, we know that the rope runs along the cover, then the length of the rope must be equal to the circumference of the cover.
Remember that the circumference of a circle of radius R is:
Then the length of the rope will be:
If you want to learn more about circles:
#SPJ1
The sequence
1, 3, 7, 13, 21, ...
has first-order differences
2, 4, 6, 8, ...
Let denote the original sequence, and
the sequence of first-order differences. It's quite clear that
for . By definition of first-order differences, we have
for , or
By substitution, we have
and so on, down to
You should know that
and we're given , so
or
Alternatively, since we already know the sequence is supposed to be quadratic, we can look for coefficients such that
We have
and we can solve this system for the 3 unknowns to find .