Recent content by tysonk

Using a scalar projections how do you show that the distance from a point P(x1,y1) to line ax + by + c = 0 is \frac{|ax1 +b y1 + c|}{\sqrt{a^2 +b^2}} I do not know how to approach this, please provide some guidance.

All real numbers except for 0.

1) No, it wouldn't. 2) well x can't be negative, but since we have zero in the numerator I think x can also include negative reals in this case.

Because we have (0/0)^0.5

I have a question about domain. Let's say we have a function in the form of y=(C/X)^0.5 Let's say for a particular case C = 0. Is the domain of the function x cannot equal 0? Or is it all real?

I learned that one can plug in things like y=x, y=2x to help determine whether a limit can exist. If a different value is obtained then a limit may not exist. Is it still possible to plug in y=x^3 Because when we plug in y=x and y=x^3 we get different values. Thanks.

How do I approach such question, 0/0 case in two variables, I can't find a simplification. Thanks for the help.

Intuitively, -false -false -true

Can someone verify these for me and explain? True/False No square matrix with real entries can obey A^2 = -I The only 2X2 matrix that obeys A^2 = 0 is A=0 The only 2X2 matrices that obey A^2=A are A=0 and A=I Much appreciated.

Makes sense, Thanks! Edit: yes, the ordering should be the other way.

The question actually is: Solve for X. If you need to invert a matrix explain why that matrix is invertible. A,B,X, are nbyn matrices. A,X, A-AX are invertible. (A-AX)^-1 = X^-1 B So I got X = BA(I + BA) ^-1 I'm just not sure why (I + BA) is invertible. Thanks for the help

What about

Hi, I have a question about invertible matrix. If A is invertible does adding the identity matrix to it still make it invertible. In other words, A +I = B , it B still invertible? Why? Thanks.

Consider a spool of inner radius r and outer radius R. A string is wrapped around the inner cylinder. The spool is motionless on a table. The string is pulled so that it feeds off the bottom side of the spool. If the angle feta=0 so that the string is pulled horizontally, it is possible to...

For einstein solid, 1/T = dS/dE Where E is internal energy and S is entropy. I can find relevant equations for E and S. But how do I calculate dS and dE? Still not sure how to find their temp when in contact at equilibrium.