✧・゚: *✧・゚:* *:・゚✧*:・゚✧
Hello!
✧・゚: *✧・゚:* *:・゚✧*:・゚✧
❖ Mean = 4.8 Median = 4.5
The mean is the average. To find the mean add up all the numbers and divide by the number of numbers:
3 + 3 + 4 + 5 + 5 + 9 = 29
29 ÷ 6 = 4.8
To find the mean, keep crossing out numbers until you are left with one number (for an odd amount of numbers). When you have an even amount of numbers, keep crossing out until you are left with 2 numbers. Add those 2 numbers and then divide:
4 + 5 = 9
9 ÷ 2 = 4.5
~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡
~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ
Answer:
3200 ft-lb
Step-by-step explanation:
To answer this question, we need to find the force applied by the rope on the bucket at time ![t](https://tex.z-dn.net/?f=t)
At ![t=0, the weight of the bucket is 6+36=42 \mathrm{lb}](https://tex.z-dn.net/?f=t%3D0%2C%20the%20weight%20of%20the%20bucket%20is%206%2B36%3D42%20%5Cmathrm%7Blb%7D)
After
seconds, the weight of the bucket is ![42-0.15 t \mathrm{lb}](https://tex.z-dn.net/?f=42-0.15%20t%20%5Cmathrm%7Blb%7D)
Since the acceleration of the bucket is the force on the bucket by the rope is equal to the weight of the bucket.
If the upward direction is positive, the displacement after
seconds is ![x=1.5 t](https://tex.z-dn.net/?f=x%3D1.5%20t)
Since the well is 80 ft deep, the time to pull out the bucket is ![\frac{80}{2}=40 \mathrm{~s}](https://tex.z-dn.net/?f=%5Cfrac%7B80%7D%7B2%7D%3D40%20%5Cmathrm%7B~s%7D)
We are now ready to calculate the work done by the rope on the bucket.
Since the displacement and the force are in the same direction, we can write
![W=\int_{t=0}^{t=36} F d x](https://tex.z-dn.net/?f=W%3D%5Cint_%7Bt%3D0%7D%5E%7Bt%3D36%7D%20F%20d%20x)
Use
and ![F=42-0.15 t](https://tex.z-dn.net/?f=F%3D42-0.15%20t)
![W=\int_{0}^{36}(42-0.15 t)(1.5 d t)](https://tex.z-dn.net/?f=W%3D%5Cint_%7B0%7D%5E%7B36%7D%2842-0.15%20t%29%281.5%20d%20t%29)
![=\int_{0}^{36} 63-0.225 t d t](https://tex.z-dn.net/?f=%3D%5Cint_%7B0%7D%5E%7B36%7D%2063-0.225%20t%20d%20t)
![=63 \cdot 36-0.2 \cdot 36^{2}-0=3200 \mathrm{ft} \cdot \mathrm{lb}](https://tex.z-dn.net/?f=%3D63%20%5Ccdot%2036-0.2%20%5Ccdot%2036%5E%7B2%7D-0%3D3200%20%5Cmathrm%7Bft%7D%20%5Ccdot%20%5Cmathrm%7Blb%7D)
![=\left[63 t-0.2 t^{2}\right]_{0}^{36}](https://tex.z-dn.net/?f=%3D%5Cleft%5B63%20t-0.2%20t%5E%7B2%7D%5Cright%5D_%7B0%7D%5E%7B36%7D)
![W=3200 \mathrm{ft} \cdot \mathrm{lb}](https://tex.z-dn.net/?f=W%3D3200%20%5Cmathrm%7Bft%7D%20%5Ccdot%20%5Cmathrm%7Blb%7D)
The remainder is 8
Step-by-step explanation:
Given expression is
![x^2+4](https://tex.z-dn.net/?f=x%5E2%2B4)
Which has to be divided by:
![x-2](https://tex.z-dn.net/?f=x-2)
We have used the long division method for the given problem
The process is completed in two steps (Picture Attached)
Hence,
The remainder is 8
Keywords: Division, long division
Learn more about long division at:
#LearnwithBrainly