<p>13.If n is a positive integer and 2^n + 2^n+1 = k what is 2^n+2 in terms of k?</p>
<p>I got the right answer by plugging in numbers but whats the algebraic way?</p>
<ol>
<li>ON a square gameboard that is divided into n rows of n squares each, k of these squares lie along the boundary of the gameboard. which of the following is a possible value for k?
a.10
b.25
c.34
d.42
e.52</li>
</ol>
<h1>of squares on boundary = 4 * side length - 4 (4 corners overlap)</h1>
<p>4n-4
Since n is an integer, only one of those numbers work.
I believe it is 52.</p>
<p>for the first question,
2^n(1+2)=k
then 2^n=k/3
multiply by 4 on both sides
2^n+2=4k/3</p>
<p>gertrude… i don’t quite get what you did there… its right though.</p>
<p>uh…first you factor out 2^n…by exponent laws, the inside would be (2^0-2^1) which is 3. you then divide by 3 on both sides…then multiply by 4, which is 2^2.</p>
<p>still don’t get quite get it… any other attempts at explaining it to me?!</p>
<p>Waitttt…
2^n + 2^n+1</p>
<p>Is it 2^n + 2^(n+1) or actually what you posted?</p>
<p>he meant 2^(n+1) probably…and uh…its just factoring out a number…</p>
<p>why do you multiply by 4?</p>