Answer:
k = 10
Step-by-step explanation:
The sum of k terms of a geometric sequence with first term a1 and common ratio r is given by ...
... Sk = a1·(1 -r^k)/(1 -r)
For the given numbers, this is ...
... 118096 = 78732·(1 -(1/3)^k)/(1 -1/3)
Manipulating this to get the term containing k, we have
... 1 -(2/3)(118096/78732) = (1/3)^k
... 1/59049 = (1/3)^k
Taking logarithms, we get
... -log(59049) = -k·log(3)
... log(59049)/log(3) = k = 10
Answer:
2x+15=33
Step-by-step explanation:
Let n be the number of days he has been doing sit ups, not counting the first day. Since he does 2 more sit-ups for each day, then the number of additional sit-ups is 2n.
Since he started doing 15 sit-ups on the first day, the total number of sit-ups
after x days would be 2n+15.
Since he did a total of 33 sit ups today, then 2n+15=33
Answer:
John is 21 and bill is 15
Step-by-step explanation:
Answer:
d) one solution; (4, 1)
Step-by-step explanation:
It often works well to follow problem directions. A graph is attached, showing the one solution to be (4, 1).
_____
You know there will be one solution because the lines have different slopes. Each is in the form ...
y = mx + b
where m is the slope and b is the y-intercept.
The first line has slope -1 and y-intercept +5; the second line has slope 1 and y-intercept -3. The slope is the number of units of "rise" for each unit of "run", so it can be convenient to graph these by starting at the y-intercept and plotting points with those rise and run from the point you know.
Answer:
The correct answer for the second one is,
