Im just confused. Can you multiply the 3 on each side or is it not allowed. I just thought you could only multiply the denominator but i dont really know anymore
I haven't learned how to simplify and solve a rational equation that has a rational equation in its numerator and the denominator.
My math knowledge is lacking in this section of solving equations like this.
Here an example of what I am trying to say and solve: https://imgur.com/a/kDpoODW
Any help or youtube video on how to do these would be very helpful :)
https://preview.redd.it/f6yznwvbbky71.png?width=1417&format=png&auto=webp&s=b026bbcc012d72a14521eef2ddceec2a85b016bd
I am trying to make up some m x n matrix A, some ? x ? vector x and some 1 x n vector b for which their combination works out but I can't find any. Can someone help me? My teacher says that the total number of parameters we'd need to work out would be mn+n but i don't get why.
Just a reminder to anyone shopping that land purchase price is only a piece of the puzzle.
For instance, an acre of raw land may be between $1,000-$100,000+. Generally, there’s a reason. An area where you can consistently find $1,000 acres is likely going to be one or more of the following things:
- hard to get water
- expensive to heat
- expensive to cool
- far from essential services you’re unlikely to find on a homestead like education and hospitals
- very cold with a short growing season, have to be able to consistently remove snow
- shortage of skilled labor in the area (plumbers, carpenters, electricians)
- far from a market where a self sustaining person might needs to sell goods
Every one of these things can be mitigated. But it’s likely that a $10,000 acre will be far less expensive in the long run than a $1,000 one when you factor in the opportunity cost (time and money).
Here’s the decision tree I’ve seen many people looking to homestead fall into: look for all cheap land, buy something that’s affordable without considering all the costs, realize their mistake after already investing to the point where it’s hard to pivot.
Here is what I suggest you do instead: determine the type of climate you want to live in, narrow it down by state and create a short list, do research on possible areas that meet your cost requirements as well as taking all the other cost factors I’ve listed and any additional you might consider important to you, visit those places, then make your decision.
The first is a whole lot easier. The second will get you a lot further. Thanks for coming to my Ted Talk.
I'm struggling to understand this and none of my own drawn out class examples provide much detail. I need an example so I can figure out how to solve this. Thank you so much!
Edit for title: product solubility constant.
Excel help https://imgur.com/gallery/YTICSlS In the link I have a picture of my graph that is in Excel that contains all my values. I just need to add another y value then match it up with the corresponding x value using lines. The other image is an example my professor gave to base our graph on.
I'm a maths-teacher-to-be and I'm trying to design a modelling task that teaches students how to solve quadratic trig equations, but I can't find any use or application of them anywhere. Can anyone help?
My paper can be read here on imgur Enjoy! I hope JM takes a look too.
I am current reading *History of Functional Analysis* by Jean Dieudonne. The author states in chapter 1 section 2,
>Now it was well known experimentally that $\phi(x)$ could be quite different from an analytic function, for instance it could have no derivative at some points...
where [; u(x,t=0) = \phi(x) ;] is the initial profile of a one dimensional string in the wave equation.
My question is then, what were these (or any) known initial conditions with non-differentiable points?
My trouble understanding this is that any example I can come up with seems like the non-differentiable point was introduced as a simplification to a differentiable function with a possibly large second derivative. For example, "plucking the string" could be modeled via a piecewise linear function.
[; \phi(x) = ;]
[;\begin{cases} x & 0 \le x \le 1/2\\ 1-x & 1/2 \le x \le 1 \end{cases} ;]
On the other hand, the initial condition could be modeled as the length minimizing curve pinned at [; x=0 ;] and [; x=1;] which must be above some shape (e.g. a sphere representing the contact point of a finger or pick).
All modelling requires some amount of simplification, but if the initial condition contradicted the understanding of the mathematics of the time, what forced the hand of mathematicians to accept these initial conditions with non-differentiable points rather than stating that a different, more realistic initial condition was needed?
Holding a sledge hammer closer to your person is easier than holding it with your arm extended (at the same height). What is this called? Thank you
Here are examples where angular energy is conserved but r × F =/= 0.
|r| = (1 - t)
w = 1/(1 - t)
theta = ln(1 - t)
r(t) = ((1 - t)cos(ln(1 - t)), (1 -t)sin(ln(1 - t)), 0)
r(t) × r''(t) is non-zero.
|r| = (1-t^2 )
w = 1/(1 - t^2)
Theta = (ln(|t + 1|) + ln(|t - 1|)) / 2
r(t) = ((1 - t^2) cos(Theta), (1 - t^2) sin(theta),0)
Again there's a non-zero torque.
Here is an example where r x F = 0 but angular energy changes:
r(t) =( (1 - t)cos(t/(1 - t)), (1 - t)sin(t/(1 - t)), 0)
So why is it that I can find examples where the rules of angular momentum are being followed but not those of angular energy?
Shouldn't we be able to find the position equation of a ball on a string? And if we can't then dosen't that imply that it's impossible for the ball to move that way under newton's laws? u/mandlbaur
