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Why gradient of scalar field is vector?
The Law of Numbers?There are two kinds of numbers scalars and vectors. The law of multiplication of Numbers says, the product of a scalar and a vector is a vector.In 4D derivative is X = [d/dr, GRAD] = [d/dr, Id/dx + Jd/dy + kd/dz]GRAD is a vector.The 4D derivative of a number [b,B], where b is the scalar and B is the vector, is;X[b, B] = [d/dr, GRAD] [b.B] = [db/dr - GRAD.B, dB/dr + GRAD b + GRADxB]The general rules of numbers are:1.Scalar by scalar products are scalars e.g. db/dr2. Scalar by vectors and vector by scalars are vectors, e,g, dB/dr and GRAD b3. Vector Dot (.) Products are scalars ,e.g. GRAD.B4. Vector Cross (x) Products are vectors, e.g. GRADxB.
What cases where friction is disadvantageous?
I'll give you two examples of each: a1) In a car engine, the parts rub against each other - pistons rub in the cylinders, the crankshaft rubs against its bearings, etc, etc. Sme thing in the transmission. The friction between those parts means that you have to apply some force to get the engine and transmission to turn. That means that some of the power of the engine is used to overcome friction instead of actually moving the car - so you use more fuel, which costs you money and releases more pollutants and global warming gases into the atmosphere. It also creates wear on the parts, which will eventually break. In the case of your pistons in the cylinders, wear will result in a bad seal, which means loss of power, and even more wasted fuel. b1) But at the tires, friction is a good thing! The engine turns the wheels, but the thing that gets the car moving forward is the force on the ground applied by the tires. The force that can be applied is related to the friction between the tires and the ground. If you've ever stomped on the gas on a rainy day, you might have noticed that your tires started spinning without actually moving the car, because the layer of water reduces the friction between the tire and the road. The same goes for breaking - the brakes stop the wheels from spinning (as a matter of fact, they use friction to do that, too!), and friction between the tires and the road stops the car. If you try to stop on ice, there might not be enough friction, and you can lose control of your car. a2) If you've ever hung around runners, especially long distance runners, you might have heard them talk about putting band aids over their nipples. That's because as they run, their shirts move across the skin of their chest, and there's friction between the cloth and the skin. Sensitive areas can be abraded and irritated by this constant motion, so runners use the band aids to create a barrier - the cloth rubs against the band aid, but the band aid doesn't move against the skin. b2) Have you ever used a nail to hold two pieces of wood together? Why doesn't the nail fall out of the hole you made when you hammer it in? That's right - friction between the nail and the wood! When you hammer in a nail, it displaces the wood, which wants to go back to where it was originally. This presses inward on the surface of the nail (providing a force perpendicular, or "normal" to the surface), and the coefficient of friction between the nail and the wood determines how much force it will take to pull the nail free. b3) I'll give you another one, just for fun. Ever been a boy scout? Did they teach you to start a fire by rubbing sticks together? What happens when you do that is, the energy you put into rubbing the sticks together (overcoming the friction between them) is converted into heat. If you get a high enough temperature, you can light your fire! So, how can friction be reduced? Well, putting a layer of a lubricant between the surfaces is a good place to start - you put oil in your engine, you don't slam on the gas or the brakes when it's wet or icy out. Another way to reduce friction is to polish the surfaces so they're smooth - try rubbing two pieces of sandpaper together, and then turn them over so they're smooth side in! I hope that helps you out!
How do you use the worksheet function to fill the selected cell with Y if cell B4 is greater than cell B3 and N if cell B4 is less than cell B3?
Note that your question does not specify what happens if B4 is equal to B3, so the following assumes it is left blank: =IF(B4>B3,"Y",IF(B4<B3,"N","")) If Y is for greater or equal to: =IF(B4>=B3,"Y","N") If it is N for equal to and Y is only for greater than: =IF(B4>B3,"Y","N")
A3 plus b3 equals?
A3+b3
What is the correct formula to calculate the total cell of B3 and B4?
The proper and best way to do it is: =B3+B4 You could also do it in any of the following ways: =SUM(B3:B4) =SUM(B3,B4) =SUM(B3+B4)
How do you calculate 90 percent of a total in Excel?
You can use the percentage sign in a formula or use the value as a decimal. If you have a value in B3 and want to get 90 percent of it, you could use any of the following formulas in another cell:=B3*90%=B3*0.9=B3-(B3*10%)=B3/10*9
What is the formula for multiplying a3 b3?
a3*b3 = a3b3
What does the test B3 D7 ask?
b3 is not equal to d7
Scientific name for vitamin b3?
Vitamin B3 is Niacin
What is the formula of a3 plus b3?
(a+b)3=a3+b3+3ab(a+b) a3+b3=(a+b)3-3ab(a+b) a3+b3=(a+b)(a2-ab+b2)
How do you prove a3-b3?
0
What is binary equivalent of B3?
The binary equivalent of Hexidecimal B3 = 1011 0011
What is another term of vitamin B3?
Vitamin B3 is also known as niacin.
Which formula correctly adds the contents of two cells and then multiplies the result by 5 percent Excel?
To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05To multiply a number in B2 by a number in B3 and then get 5% of the total, the formula would be as follows:=B2*B3*5%If you want to increase that total by 5% of itself, then the formula would be:=B2*B3*1.05
