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
Answer:
Hand tools based on job requirement and its importance and the classification of hand tools according to its function and its importance are discussed below in details.
Explanation:
Hand tools based on work requirement is essential because Every tool is specifically invented for a particular purpose, so picking the accurate tool will also reduce the amount of energy needed to get work done right without causing injury or harm to either the tools or the exterior being worked on.
classifying of hand tools: wrenches, screwdrivers, cutters, striking tools, hammer tool or struck, pliers, vise, clamps, snips, saws, drills, and knives.
Answer:
Option A
Explanation:
Alloys are metal compounds with two or more metals or non metals to create new compounds that exhibit superior structural properties. Alloys have high level of hardness that resists deformation thereby making it less ductile compared to polymers. This is due to the varying difference in the chemical and physical characteristics of the constituent metals in the alloy.
Answer:
buy a new one
Explanation:
go on newegg and you will most likely find one there