Yes, I'm getting C also!
Since it's asking for the left-endpoint Riemann Sum, you will only be using the top left point as the height for each of your four boxes, making -1, -2.5, -1.5, and -0.5 your heights. The bases are all the same length of 2. You don't include f(8) because you're not using right-endpoints, and that would also add another 5th box that isn't included in the 0 to 8 range.
Answer:
Pencil: $0.60 Rubber: $0.48
Step-by-step explanation:
Let the cost of a pencil be p and the cost of a rubber be r.
(Equation 1)
(Equation 2)
Divide both sides by 4:
![p=\frac{5}{4} r](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B5%7D%7B4%7D%20r)
Substitute this into Equation 1:
![\frac{5}{4} r+r=1.08](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D%20r%2Br%3D1.08)
Multiply both sides by 4:
![\frac{5}{4}r* \:4+r* \:4=1.08*4](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7Dr%2A%20%5C%3A4%2Br%2A%20%5C%3A4%3D1.08%2A4)
![5r+4r=4.32](https://tex.z-dn.net/?f=5r%2B4r%3D4.32)
![9r=4.32](https://tex.z-dn.net/?f=9r%3D4.32)
Divide both sides by 9:
![\frac{9r}{9}=\frac{4.32}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B9r%7D%7B9%7D%3D%5Cfrac%7B4.32%7D%7B9%7D)
![r=0.48](https://tex.z-dn.net/?f=r%3D0.48)
Since r + p = 1.08,
![p=1.08=0.48=0.60](https://tex.z-dn.net/?f=p%3D1.08%3D0.48%3D0.60)
You move the decimal point two times to the right
1.5 is 150%
![\rm 5=e^{3b}](https://tex.z-dn.net/?f=%5Crm%205%3De%5E%7B3b%7D)
The unknown b is stuck in the exponent position.
We can can fix that by using logarithms.
Log is the inverse operation of the exponential.
We'll take log of each side.
Log of what base tho?
Well, the base of our exponential is e,
so we'll take log base e of each side.
![\rm log_e(5)=log_e(e^{3b})](https://tex.z-dn.net/?f=%5Crm%20log_e%285%29%3Dlog_e%28e%5E%7B3b%7D%29)
We'll apply one of our log rules next:
![\rm \log(x^y)=y\cdot\log(x)](https://tex.z-dn.net/?f=%5Crm%20%5Clog%28x%5Ey%29%3Dy%5Ccdot%5Clog%28x%29)
This allows us to take the exponent out of the log,
![\rm log_e(5)=(3b)log_e(e)](https://tex.z-dn.net/?f=%5Crm%20log_e%285%29%3D%283b%29log_e%28e%29)
Another thing to remember about logs:
When the base of the log matches the inside of the log,
then the whole thing is simply 1,
![\rm log_{10}(10)=1](https://tex.z-dn.net/?f=%5Crm%20log_%7B10%7D%2810%29%3D1)
![\rm log_5(5)=1](https://tex.z-dn.net/?f=%5Crm%20log_5%285%29%3D1)
![\rm log_e(e)=1](https://tex.z-dn.net/?f=%5Crm%20log_e%28e%29%3D1)
So our equation simplifies to this,
![\rm log_e(5)=(3b)\cdot1](https://tex.z-dn.net/?f=%5Crm%20log_e%285%29%3D%283b%29%5Ccdot1)
As a final step, divide both sides by 3,
![\rm \frac13log_e(5)=b](https://tex.z-dn.net/?f=%5Crm%20%5Cfrac13log_e%285%29%3Db)
k, hope that helps!
It will take Eli 2.4 minutes to complete 6 laps
Step-by-step explanation:
Given
Speed = s = 1000 meters per minute
Length of one lap = 400 meters
We have to compute time for 6 laps,, so we have to find the length of 6 laps combined
![Length\ of\ laps = Length\ of\ one\ lap * 6\\= 400 * 6\\= 2400\ meters](https://tex.z-dn.net/?f=Length%5C%20of%5C%20laps%20%3D%20Length%5C%20of%5C%20one%5C%20lap%20%2A%206%5C%5C%3D%20400%20%2A%206%5C%5C%3D%202400%5C%20meters)
So our total distance will be: 2400 meters
using the formula for speed
![s = \frac{d}{t}\\1000 = \frac{2400}{t}\\t = \frac{2400}{1000}\\t = 2.4](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D%5C%5C1000%20%3D%20%5Cfrac%7B2400%7D%7Bt%7D%5C%5Ct%20%3D%20%5Cfrac%7B2400%7D%7B1000%7D%5C%5Ct%20%3D%202.4)
So
It will take Eli 2.4 minutes to complete 6 laps
Keywords: Speed, distance
Learn more about distance at:
#LearnwithBrainly