Answer:
Step-by-step explanation:y – y1 = m(x – x1) * substitute (-0.5, 4.1) for x1 and y1
y - (4.1) = (0.8)(x - (-0.5))
y - 4.1 = 0.8(x + 0.5) * distribute the 0.8
y - 4.1 = 0.8x + 0.4 * add 4.1 to both sides
y = 0.8x + 4.5
this is the example hope this helped!
Answer:
20 feet
Step-by-step explanation:
The value of y is zero where x=2 and x=22. The distance between those points is 22 -2 = 20 feet.
The ball lands 20 feet from where it leaves the ground.
Answer: 
; 5
Step-by-step explanation:
Given series : ![[\dfrac{5}{1\cdot2}]+[\dfrac{5}{2\cdot3}]+[\dfrac{5}{3\cdot4}]+....+[\dfrac{5}{n\cdot(n+1)}]](https://tex.z-dn.net/?f=%5B%5Cdfrac%7B5%7D%7B1%5Ccdot2%7D%5D%2B%5B%5Cdfrac%7B5%7D%7B2%5Ccdot3%7D%5D%2B%5B%5Cdfrac%7B5%7D%7B3%5Ccdot4%7D%5D%2B....%2B%5B%5Cdfrac%7B5%7D%7Bn%5Ccdot%28n%2B1%29%7D%5D)
Sum of series = ![S_n=\sum^{\infty}_{1}\ [\dfrac{5}{n\cdot(n+1)}]=5[\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}]](https://tex.z-dn.net/?f=S_n%3D%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5C%20%5B%5Cdfrac%7B5%7D%7Bn%5Ccdot%28n%2B1%29%7D%5D%3D5%5B%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5Cdfrac%7B1%7D%7Bn%5Ccdot%28n%2B1%29%7D%5D)
Consider 
⇒ ![S_n=5\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}=5\sum^{\infty}_{1}[\dfrac{1}{n}-\dfrac{1}{n+1}]](https://tex.z-dn.net/?f=S_n%3D5%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5Cdfrac%7B1%7D%7Bn%5Ccdot%28n%2B1%29%7D%3D5%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5B%5Cdfrac%7B1%7D%7Bn%7D-%5Cdfrac%7B1%7D%7Bn%2B1%7D%5D)
Put values of n= 1,2,3,4,5,.....n
⇒ 
All terms get cancel but First and last terms left behind.
⇒
Formula for the nth partial sum of the series :
Also, 
In the question, it is already mentioned that the water tank holds = 24,000 gallons
In the given question it is also mentioned that the need is to find the time required to use 2/3 of the total water that the tank holds.
So the need is to find the amount of water that equals 2/3 of the total water in the tank.
Then
Quantity of water that needed to be used = [24000 * (2/3)] gallons
= 16000 gallons
In the problem it is also mentioned that the average rate of consumption per day is 650 gallons.
So
650 gallons of water used in = 24 hours
16000 gallons of water will be used in = [(24/650) *16000] hours
= 590.77 hours
So the time required to consume 2/3 of the total water in the tank is 590.77 hours.
