These two things are equivalent quantities.

Once again, these are vector quantities

They use large quantities chloroprene and benzene.

Japan used to trade silk in large quantities.

So ratios are just expressions that compare quantities.

Foreign products arrived on the market in large quantities.

Smart materials are hard to obtain in small quantities.

High quantities of phosphorous protein and all that crap.

And the way that we differentiate between vector and scalar quantities ... ... is that we put little arrows on top of vector quantities.

We grow the cells outside the body in large quantities.

And we are going to combine these quantities together as follows.

We're just adding or subtracting the same quantities on both sides.

These are just scalar quantities, and we saw that the dot product is associative with respect to scalar quantities, so we can just change the order here.

So, you might price the product if you buy in quantities of 1 10 it's 1000, but if you buy in quantities of 10 100 it's 900.

This is a very well known feature in which we perceive quantities in relative ways quantities like the intensity of light or the loudness of a sound.

In the city, large quantities of garbage are being produced every day.

With this new equation we can just plug in the known quantities.

If i wanted to write an analogous thing for the scalar quantities ... ...

Or, I guess order these quantities however you want to do it

I'm just These are all just expressions that are comparing two quantities.

These regular quantities are just written non bolded, while the vectors are bolded.

Coal exists in vast quantities, and generates almost half of the planet's electricity.

This is when you care about directions ... ... so you're dealing with vector quantities.

And now I can solve this by saying, look, I have two quantities.

Those are correlations between two quantities. One of which does not depend on distance.

Liquid means it's very easy to buy and sell those securities in large quantities.

And these strands of magnetic field inside the superconductor, they come in discrete quantities.

But even more surprising is if you look at socio economic quantities, quantities that have no analog in biology, that have evolved when we started forming communities eight to 10,000 years ago.

Like most thermodynamical quantities, it can be expressed as a function of these two variables.

The right hand side must be always negative, because both density pressure are positive quantities.

And when the sun shines, you get copious quantities of these things, called neutrinos, pouring out.

Yeah, every single cell in us can produce minute quantities of hydrogen sulfide in great crises.

Perhaps, we can somehow uncover these three different quantities using only three recursive calls rather than four.

We integrate the equations, producing observable quantities, such as distances, and then we compare that to the observations.

We can't just do it into two of these now because now my ratio has three actual quantities.

For quantities of 20 or more, we can allow you a special discount of 10 on the prices quoted.

They were reasonable portions of protein served with copious quantities of vegetables and small amounts of starch, usually rice.

For four quantities whose average value is less than 10 percent, you have people guessing three, four times that level.

Penicillin was discovered in 1928, but even by 1940, no commercially and medically useful quantities of it were being produced.

So we care about AD and BC as quantities individually, only in as much as we care about their sum.

You know, breathing high concentrations here of sulfur dioxide, carbon dioxide and methane gas, in unequal quantities 19 years of this.

However, both farms made up for some of the shortfall by purchasing equal quantities of apples from farms in neighboring states.

The energy that it takes to power civilization is flooding through the Solar System in quantities we can scarcely imagine unused.

So essentially my operating profit divided by my initial investment, depending on the different prices I might charge and the different quantities.

Now, they say both farms made up for some of the shortfall by purchasing equal quantities of apples from farms in neighboring states.