Which statements describe a parallelogram that must be a rectangle? Select each correct answer. parallelogram with opposite side
1 answer:
You might be interested in
There's a slight problem with your question, but we'll get to that...
Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the <em>n</em>-th term of the sequence, <em>a</em> (<em>n</em>), is given recursively by
• <em>a</em> (1) = 1
• <em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 21 … … … for <em>n</em> > 1
We can find the explicit rule for the sequence by iterative substitution:
<em>a</em> (2) = <em>a</em> (1) + 21
<em>a</em> (3) = <em>a</em> (2) + 21 = (<em>a</em> (1) + 21) + 21 = <em>a</em> (1) + 2×21
<em>a</em> (4) = <em>a</em> (3) + 21 = (<em>a</em> (1) + 2×21) + 21 = <em>a</em> (1) + 3×21
and so on, with the general pattern
<em>a</em> (<em>n</em>) = <em>a</em> (1) + 21 (<em>n</em> - 1) = 21<em>n</em> - 20
Now, we're told that the sum of some number <em>N</em> of terms in this sequence is 2332. In other words, the <em>N</em>-th partial sum of the sequence is
<em>a</em> (1) + <em>a</em> (2) + <em>a</em> (3) + … + <em>a</em> (<em>N</em> - 1) + <em>a</em> (<em>N</em>) = 2332
or more compactly,
It's important to note that <em>N</em> must be some positive integer.
Replace <em>a</em> (<em>n</em>) by the explicit rule:
Expand the sum on the left as
and recall the formulas,
So the sum of the first <em>N</em> terms of <em>a</em> (<em>n</em>) is such that
21 × <em>N</em> (<em>N</em> + 1)/2 - 20<em>N</em> = 2332
Solve for <em>N</em> :
21 (<em>N</em> ² + <em>N</em>) - 40<em>N</em> = 4664
21 <em>N</em> ² - 19 <em>N</em> - 4664 = 0
Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead
<em>N</em> = (19 ± √392,137)/42 ≈ -14.45 or 15.36
so there is no positive integer <em>N</em> for which the first <em>N</em> terms of the sum add up to 2332.
Check the picture below.
neverminding for a few seconds the volume of the cylinder, the percentage in the height used by the water will be the same as the percentage of its volume. We know the total amount or 100% of the height is 14, so what is 11 in percentage?
