wile catching fireflies, you and your friend decide to have a competition. after m minutes, you have (3m +13) fireflies and your friend has (4m+6) fireflies.
a. how many fireflies are caught per minute?
b. ow many fireflies caught before the competition?
for a. we tried (3m+13 +4m + 6)/m
that is (7m+19)/m that was rejected as wrong answer ... I have no clue then..
you didnt answer B... mind telling me???
10.) While catching fireflies, you and a friend decide to have a competition. After m minutes, you
have (4m + 11) fireflies and your friend has (5m + 6) fireflies.,
a.) Write an expression in simplest form that represents the number of fireflies you and your
friend caught together.
(3+4)m = 7m
when m=0, there were 13+6=19
The 7m/m part was correct. The 19 was how many flies there were at the start of the competition. After that, there were 7 caught each minute.
To find the number of fireflies caught per minute in the competition, you need to find the rate at which the number of fireflies is increasing. In other words, you need to determine the slope of the line represented by the number of fireflies.
The number of fireflies you have after m minutes is given by 3m + 13, and the number of fireflies your friend has is given by 4m + 6.
So, to find the rate of increase, you can take the difference between the two expressions and divide it by the number of minutes, m:
Rate of increase = (4m + 6) - (3m + 13) / m
Simplifying this expression, you get:
Rate of increase = (4m - 3m + 6 - 13) / m
= (m - 7) / m
Therefore, the number of fireflies caught per minute is (m - 7)/m.
For part b, to find the total number of fireflies caught before the competition, you need to calculate the sum of the number of fireflies at each minute from 0 to m.
The number of fireflies after 0 minutes is given by 3(0) + 13 = 13. So, you have 13 fireflies at the start.
To find the total number of fireflies caught before the competition, you can sum up the number of fireflies at each minute from 0 to m:
Total fireflies caught = (3(0) + 13) + (3(1) + 13) + (3(2) + 13) + ... + (3(m) + 13)
To simplify this expression, you can factor out the 3 from each term:
Total fireflies caught = 3(0 + 1 + 2 + ... + m) + (m + 1)(13)
Now, let's consider the sum of the numbers from 0 to m, which is a well-known formula:
Sum of numbers from 0 to m = (m)(m + 1) / 2
Replacing this in the expression:
Total fireflies caught = 3(m(m + 1) / 2) + (m + 1)(13)
Simplifying further:
Total fireflies caught = (3m(m + 1) + 2(m + 1)(13)) / 2
= (3m^2 + 3m + 26m + 26) / 2
= (3m^2 + 29m + 26) / 2
Therefore, the total number of fireflies caught before the competition is (3m^2 + 29m + 26) / 2.