Hi everyone!
1. Is a linear equation the same as a polynomial of first(or 0th) degree?
2. The book 'Mathematics for physicists and engineers' by springer(publisher) states that an example of a linear (DE) equation is 5.dy(x)/dx = x.y(x). Yet I read somewhere else that f(x,y)=a.x.y+b is not...
Hi everyone,
There are 2 things I do not understand in the derivation of kinetic energy from work:
https://www.physicsforums.com/showthread.php?t=111162
(1) W = \int\vec{F}(t).d\vec{r}(t)=
(2) m.\int\frac{d\vec{v}(t)}{dt}.d\vec{r}(t)=
(3) m.\intd\vec{v}(t).\frac{d\vec{r}(t)}{dt}=
(4)...
Hey Tiny-tim : ),
You are just saying that if the implication is true, than the contrapositive must be true. I know, but my question is just if the negation of the converse must also be true if the implication is true.
Using the example:
(1) Implication: "I am human" implies that "I am an...
Dear jedishrfu,
Nope. I know that when the contrapositive is true, the implication must be true as well. But this is not what I am asking. Thnx for the response though.
Hi everyone,
I was thinking about logic and proofs and I concluded that "proving the negation of the converse of an implication to be true" proves "the implication to be true". But strangely I can't find any information about this proof method, so I doubt if I am correct.
Just to be clear...
Hi Spinnor,
In the solution, the velocity of the product is denoted with vr. So they are saying that the velocity is a real quantity (consists of a real number) as opposed to an infinitesimal quantity (like dv, a hyperreal number).
Ok, I think I understand this now.
Questions:
1. How can one tell that at time t+dt the velocity of the rocket is an infinitesimal quantity and the velocity of the ejected product a real quantity?
2. Why is for the mass of the rocket not simply written m-dm and why for the mass of the ejected product not written (+)dm?
In this solution the t in the y-coordinate equation is substituted using the x-coordinate equation and ultimately leads to the answer.
My questions:
1. Why don't I get the same answer when I substitute the v or v and t instead?
2. How am I supposed to know to substitute t in this example and...
True but without consistency in notation and semantics accuracy is lost eventually. Than we need to use new symbols or existing symbols that are infrequently used in that context.