You can make a start by putting together an expression for the sum of the even integers between 1 and k inclusive.
Let S be the sum of the even integers between 1 and k inclusive.
Then:
<span><span>S=2+4+6+⋯+(k−2)+k</span></span>
As k is even, you can say r = 2k and so:
<span><span>S=2(1+2+3+⋯+(r−1)+r)</span></span>
<span>Now the sum of the first </span><span>r</span><span> numbers is well-known, it's the </span><span>r</span>th triangle number and we have:
<span><span>1+2+3+⋯+(r−1)+r=<span><span>r(r+1)/</span>2</span></span></span>
<span>Now we can keep it simple and say </span><span><span>2k=4r </span></span><span>and so:</span>
<span><span>S=2(1+2+3+⋯+(r−1)+r)=4r=2<span><span>r(r+1)</span>2</span>=r(r+1)</span></span>
<span>So you can build a quadratic in </span><span>r</span><span> and so get </span><span>k.</span>
Answer:
5 stick lengths
Step-by-step explanation:
The question is not structured well. However, the following can be deduced
Required
How many of the stick length can be gotten from the wire length
To do this, we simply divide the length of the wire by the length of the stick.
So, we have:
Using a calculator, we have:
4 quarts = 1 gallon
8 quarts = 2 gallons
12 quarts = 3 gallons
16 quarts = 4 gallons
20 quarts = 5 gallons
24 quarts = 6 gallons
28 quarts = 7 gallons
32 quarts = 8 gallons
Answer:
10,400 or 9360
Step-by-step explanation:
I'm currently doing permutations and combinations, actually I'm finishing it. I'm doing my test rn so I'm finishing geometry today for the whole grade. So I hope I got this right:
26*4*10*10 = 10,400
26 = 26 letters possible as to be the Capital letter
4 = 4 possible special characters
10 = 10 digits are possible, unless you can't repeat numbers, then it's:
26*4*10*9 = 9360
