We will use demonstration of recurrences<span>1) for n=1, 10= 5*1(1+1)=5*2=10, it is just
2) assume that the equation </span>10 + 30 + 60 + ... + 10n = 5n(n + 1) is true, <span>for all positive integers n>=1
</span>3) let's show that the equation<span> is also true for n+1, n>=1
</span><span>10 + 30 + 60 + ... + 10(n+1) = 5(n+1)(n + 2)
</span>let be N=n+1, N is integer because of n+1, so we have
<span>10 + 30 + 60 + ... + 10N = 5N(N+1), it is true according 2)
</span>so the equation<span> is also true for n+1,
</span>finally, 10 + 30 + 60 + ... + 10n = 5n(n + 1) is always true for all positive integers n.
<span>
</span>
Graham: -50x + 14,040
Max: 20x + 12,500
Graham = Max
-50x + 14,040 = 20x + 12,500
<u>+50x </u> <u>+50x </u>
14,040 = 70x + 12,500
<u> -12,500 </u> <u> -12.500 </u>
1,540 = 70x
220 = x
Answer: 220 minutes <em>(3 hours 40 minutes)</em>
6 is only the double of 3
3×2=6
Any number that's multiplied by 6 will be the double of any number multiplied by 3, or vice versa, any number multiplied by 3 will be half of any number multiplied by 6. This is because 6 is a multiple of 3.
Take for example:
850×6=5100 ⇔ 850×(3×2)=5100
The answer is 14137.17 because to find the volume of the sphere, the equation is 4/3 times pi times the radius cubed.
