The volume of each cube is given. Estimate the side length of the cube to the nearest integer. Use the formula V=s(cubed). The v
1 answer:
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1. Let 
be the number of seats in the 
-th row. The number seats in the -th row relative to the number of seats in the 
-th row is given by the recursive rule
Since
, we have
So the explicit rule for the sequence is
In the 15th row, the number of seats is
2. Let
be the amount of profit in the -th year. If the profits increase by 6% each year, we would have
with
.
The second part of the question is somewhat vague - are we supposed to find the profits in the 20th year alone? the total profits in the first 20 years? I'll assume the first case, in which we would have a profit of
3. Now let denote the number of pushups done in the -th week. Since 
, 
, and 
, it looks like we can expect the number of pushups to quadruple per week. So,
starting with
.
We can apply the same reason as in (2) to find the explicit rule for the sequence, which you'd find to be
Since
So the explicit rule for the sequence
In the 15th row, the number of seats is
2. Let
with
The second part of the question is somewhat vague - are we supposed to find the profits in the 20th year alone? the total profits in the first 20 years? I'll assume the first case, in which we would have a profit of
3. Now let
starting with
We can apply the same reason as in (2) to find the explicit rule for the sequence, which you'd find to be
Answer:
11 music lessons.
Step-by-step explanation:
We know that membership costs $165 and members pay $25 per music lesson.
So, we can write the following expression:
The 165 represents the one-time membership fee and the 25m represents the cost for m music lessons.
We know that non-members pay no membership fee but their cost per lesson is $40. So:
Represents the cost for non-members for m music lessons.
We want to find how many music lessons would have to be taken for the cost to be the same for both members and non-members. So, we can set the expressions equal to each other:
And solve for m. Let's subtract 25m from both sides:
Now, divide both sides by 15:
So, at the 11th music lesson, members and non-members will pay the same.
Further Notes:
This means that if a person would only like to take 10 or less lessons, the non-membership is best because there is no initial fee.
However, if a person would like to take 12 or more lessons, than the membership is best because the membership has a lower cost per lesson than the non-membership.
And we're done!