You will lay the yardsrick down flat & see how many inches the rug is, if needed , do it multiple times and add inches together.
Answer
Step-by-step explanation:
- The number of cyclists the group needs to raise at least $57,000 must be at least 1000 cyclists
- Let x represent the number of cyclists.
- Since, the activists receive $60 per cyclist entry and $15,000 in donations, hence:
- Revenue = 60x + 15000
- Also, the cost of the race is $18 per entry, hence:
- Cost = 18x
- They need to raise at least $57,000, hence:
- Profit ≥ 57000
- Revenue - Cost ≥ 57000
- (60x + 15000) - 18x ≥ 57000
- 42x ≥ 42000
- x ≥ 1000
- Therefore the number of cyclists the group needs to raise at least $57,000 must be at least 1000 cyclists
Method 1:By graphing, we can find the graph of y = 5log(x + 3) and y = 5 to see where they intersect.
Method 2:Alternatively, by subtracting 5 from both sides, we can find where the graph 5log(x + 3) - 5 hits the x-axis. In essence, we are finding when y hits 0 and thus, finding where it hits the x-axis.
Method 3:We can also just solve this algebraically. When we don't have any superscripts, we take the assumption that we're working in base 10.
Divide both sides by 5:
![log(x + 3) = 1](https://tex.z-dn.net/?f=log%28x%20%2B%203%29%20%3D%201)
Take the inverse of log(x + 3) to both sides:
![10^{log_{10}(x + 3)} = 10^{1}](https://tex.z-dn.net/?f=10%5E%7Blog_%7B10%7D%28x%20%2B%203%29%7D%20%3D%2010%5E%7B1%7D)
![x + 3 = 10](https://tex.z-dn.net/?f=x%20%2B%203%20%3D%2010)
![x = 7](https://tex.z-dn.net/?f=x%20%3D%207)
Hence, we know that at x = 7, 5log(7 + 3) = 5.
The graphs of Method 1 is pictured first, and the graph of Method 2 is pictured on the right.