Step-by-step explanation:
= √2x × √8x³
= √(2.8x^4)
= √16x^4
= 4x²
Answer:
The value is ![W= 2640 \ ft \cdot lb](https://tex.z-dn.net/?f=W%3D%202640%20%5C%20%20ft%20%5Ccdot%20lb)
Step-by-step explanation:
From the question we are told that
The weight of the bucket is ![F = 5 lb](https://tex.z-dn.net/?f=F%20%3D%20%205%20lb)
The depth of the well is ![x_1 = 60 \ ft](https://tex.z-dn.net/?f=x_1%20%3D%20%2060%20%5C%20ft)
The weight of the water is ![W_w = 42 lb](https://tex.z-dn.net/?f=W_w%20%20%3D%20%2042%20lb)
The rate at which the bucket with water is pulled is ![v = 1.5 \ ft/s](https://tex.z-dn.net/?f=v%20%20%3D%201.5%20%5C%20%20ft%2Fs)
The rate of the leak is ![r = 0.15 lb/s](https://tex.z-dn.net/?f=r%20%3D%200.15%20lb%2Fs)
Generally the workdone is mathematically represented as
]
Here G(x) is a function defining the weight of the system (water and bucket ) and it is mathematically represented as
![G(x) = F + (W_w- Ix)](https://tex.z-dn.net/?f=G%28x%29%20%3D%20%20F%20%20%2B%20%20%28W_w-%20Ix%29)
Here I is the rate of water loss in lb/ft mathematically represented as
![I = \frac{r}{v}](https://tex.z-dn.net/?f=I%20%20%3D%20%5Cfrac%7Br%7D%7Bv%7D%20)
=> ![I = \frac{0.15 }{1.5 }](https://tex.z-dn.net/?f=I%20%20%3D%20%5Cfrac%7B0.15%20%7D%7B1.5%20%7D)
=>
So
![G(x) = 5 + (42- 0.1x)](https://tex.z-dn.net/?f=G%28x%29%20%3D%20%205%20%20%2B%20%20%2842-%200.1x%29)
=> ![G(x) = 47- 0.1x)](https://tex.z-dn.net/?f=G%28x%29%20%3D%20%2047-%200.1x%29)
So
]
=> ![W = [47x - \frac{0.1x^2}{2} ]|\left 60} \atop {0}} \right.](https://tex.z-dn.net/?f=W%20%3D%20%20%5B47x%20-%20%5Cfrac%7B0.1x%5E2%7D%7B2%7D%20%5D%7C%5Cleft%2060%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
=> ![W= [47(60) - 0.05(60)^2]](https://tex.z-dn.net/?f=W%3D%20%5B47%2860%29%20-%200.05%2860%29%5E2%5D)
=> ![W= 2640 \ ft \cdot lb](https://tex.z-dn.net/?f=W%3D%202640%20%5C%20%20ft%20%5Ccdot%20lb)
Answer: x=5
Step-by-step explanation:
![\frac{2}{14} =\frac{x}{35}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B14%7D%20%3D%5Cfrac%7Bx%7D%7B35%7D)
![\frac{x}{35}=\frac{2}{14}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B35%7D%3D%5Cfrac%7B2%7D%7B14%7D)
simplify
![\frac{x}{35}=\frac{1}{7}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B35%7D%3D%5Cfrac%7B1%7D%7B7%7D)
multiply 35 on both sides
![\frac{35x}{35}=\frac{1\cdot \:35}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B35x%7D%7B35%7D%3D%5Cfrac%7B1%5Ccdot%20%5C%3A35%7D%7B7%7D)
![\frac{1}{7} \cdot 35=5](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B7%7D%20%20%5Ccdot%2035%3D5)
x=5
Answer:
Hello There!!
Step-by-step explanation:
I believe the answer is 4,9,0-0.7,1.31,4,9 and 9.The probability of an event if from 0 to 1.
hope this helps,have a great day!!
~Pinky~
Answer:
the answer is 40 dollars
Step-by-step explanation:
all you have to do is multiply 15x2 and then add 10