First we need to differentiate y



Now let it be 0




Put it in y


Well, if you disregard the signs for a second, you can work this like a normal equation:
-6 - 12v = 90
-12v = 96
v = 8
Now just reincorporate the less than sign:
v < 8
I'll do problem 13 to get you started.
The expression
is the same as 
Then we can do a bit of algebra like so to change that n into n-1

This is so we can get the expression in a(r)^(n-1) form
- a = 8/7 is the first term of the geometric sequence
- r = 2/7 is the common ratio
Note that -1 < 2/7 < 1, which satisfies the condition that -1 < r < 1. This means the infinite sum converges to some single finite value (rather than diverge to positive or negative infinity).
We'll plug those a and r values into the infinite geometric sum formula below
S = a/(1-r)
S = (8/7)/(1 - 2/7)
S = (8/7)/(5/7)
S = (8/7)*(7/5)
S = 8/5
S = 1.6
------------------------
Answer in fraction form = 8/5
Answer in decimal form = 1.6
Answer:
Nicole needs 550 meters of ribbon for making 1,000 bows
Step-by-step explanation:
1,000 * 0.55
or
0.55 + 0.55 + 0.55 + 0.55 + etc...
5.45787878 = 545787878/100000000
divide both numerator and denominator by 2 or any other number
545787878 ÷ 2 = 272893939
100000000 ÷ 2 = 50000000
272893939/50000000 is your answer