Step 1:
Start by setting it up with the divisor 8 on the left side and the dividend 27 on the right side like this:
8 ⟌ 2 7
Step 2:
The divisor (8) goes into the first digit of the dividend (2), 0 time(s). Therefore, put 0 on top:
0
8 ⟌ 2 7
Step 3:
Multiply the divisor by the result in the previous step (8 x 0 = 0) and write that answer below the dividend.
0
8 ⟌ 2 7
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (2 - 0 = 2) and write the answer below.
0
8 ⟌ 2 7
- 0
2
Step 5:
Move down the 2nd digit of the dividend (7) like this:
0
8 ⟌ 2 7
- 0
2 7
Step 6:
The divisor (8) goes into the bottom number (27), 3 time(s). Therefore, put 3 on top:
0 3
8 ⟌ 2 7
- 0
2 7
Step 7:
Multiply the divisor by the result in the previous step (8 x 3 = 24) and write that answer at the bottom:
0 3
8 ⟌ 2 7
- 0
2 7
2 4
Step 8:
Subtract the result in the previous step from the number written above it. (27 - 24 = 3) and write the answer at the bottom.
0 3
8 ⟌ 2 7
- 0
2 7
- 2 4
3
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 27 divided by 8 calculated using Long Division is:
3
Answer: 1. sadly yes, some people are treated unfairly for crimes people yet have commited. 2. no 3. yes
Explanation:
i did this last year
Answer:
<em>The maximum efficiency the plant will ever achieve is 75%</em>
<em>Explanation:</em>
From the question given, we recall the following:
<em>Th flames in the boiler reaches a temperature of = 1200K</em>
<em>the cooling water is = 300K</em>
<em>The maximum efficiency the plant will achieve is defined as:</em>
Let nmax = 1 - Tmin /Tmax
Where,
Tmin = Minimum Temperature in plants
Tmax = Maximum Temperature in plants
The temperature of the cooling water = Tmin = 300K
The temperature of the flames in boiler = Tmax = 1200k=K
The maximum efficiency becomes:
nmax = 1 - Tmin /Tmax
nmax = 1 - 300 /1200
nmax = 1-1/4 =0.75
nmax = 75%
Answer:
Proof is as follows
Proof:
Given that , 
<u>for any function f with period T, RMS is given by</u>
<u />
<u />
In our case, function is 
![RMS = \sqrt{\frac{1}{T}\int\limits^T_0 {[V_{ac} + V_{dc}]^{2} } \, dt }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7BT%7D%5Cint%5Climits%5ET_0%20%7B%5BV_%7Bac%7D%20%2B%20V_%7Bdc%7D%5D%5E%7B2%7D%20%7D%20%5C%2C%20dt%20%20%7D)
Now open the square term as follows
![RMS = \sqrt{\frac{1}{T}\int\limits^T_0 {[V_{ac}^{2} + V_{dc}^{2} + 2V_{dc}V_{ac}] } \, dt }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7BT%7D%5Cint%5Climits%5ET_0%20%7B%5BV_%7Bac%7D%5E%7B2%7D%20%2B%20V_%7Bdc%7D%5E%7B2%7D%20%2B%202V_%7Bdc%7DV_%7Bac%7D%5D%20%7D%20%5C%2C%20dt%20%20%7D)
Rearranging terms

You can see that
- second term is square of RMS value of Vac
- Third terms is average of VdcVac and given is that average of

so
![RMS = \sqrt{\frac{1}{T}TV_{dc}^{2} + [RMS~~ of~~ V_{ac}]^2 }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7BT%7DTV_%7Bdc%7D%5E%7B2%7D%20%20%20%2B%20%5BRMS~~%20of~~%20V_%7Bac%7D%5D%5E2%20%7D)
![RMS = \sqrt{V_{dc}^{2} + [RMS~~ of~~ V_{ac}]^2 }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7BV_%7Bdc%7D%5E%7B2%7D%20%20%20%2B%20%5BRMS~~%20of~~%20V_%7Bac%7D%5D%5E2%20%7D)
So it has been proved that given expression for root mean square (RMS) is valid