Melody

Can it solve modular equatiions ? like: 17 mod x = 2. here, answer is: x = 5

I have just been mucking around with the calculator.

It can certainly find the solution for 17 mod 5 but maybe it cannot do what you want.

I am not sure though.

of course, 5 is not the only answer. 15 is another answer.

2). What is the instantaneous rate of change of f(x) = ln(csc2 x) at π/4

(a) 0 (b) 2 (c) - 2 (d) 1 (e) − ∞

\(\boxed{y=ln(g(x))\\\frac{dy}{dx}=\frac{g'(x)}{g(x)}}\\ g(x)=cosec^2x\\ g(x)=(sinx)^{-2}\\ g'(x)=-2(sinx)^{-3}cosx\\ ....\\ f(x)=ln(cosec^2x)\\ f'(x)=\frac{-2(sinx)^{-3}cosx}{cosec^2x}\\ f'(x)=\frac{-2cosx*sin^2x}{(sinx)^{3}}\\ f'(x)=\frac{-2cosx}{sinx}\\ f'(x)=-2cotx\\ f'(\pi/4)=-2cot(\pi/4)\\ f'(\pi/4)=-2\)

3)Rewrite (3logx+1/2log(x-2))-log(x+4) as a single logarithm.

\((3logx+1/2log(x-2))-log(x+4) \\ =3logx+0.5log(x-2)-log(x+4) \\ =logx^3+log(x-2)^{0.5}-log(x+4) \\ =log \left(\frac{x^3(x-2)^{0.5}}{x+4}\right) \\ =log \left(\frac{x^3 \sqrt{x-2}}{x+4}\right) \\\)

1)If f(x) = x3+x+1 find d/dx (f-1(x))

there as 4 choices, A 3x2+1 B 1/X3+X+1 C 1/ 3X2+1 D 1/3y2+1 E NOTA

I'm going for    1/(3y^2+1)  

I will show you how i did it but I think I might get my hand slapped by a better mathematician.  LOL

Even if my answer is right i will probably be told that my method suxs :)

That is ok, I want to be corrected if it is not correct or not presented properly :)

original function

y=x^3+x+1

y'=3x^2+1

No stationary points

gradient is always positive.

This means that the function is a 1 to 1 mapping and therefore the inverse function is too.

So the domain for the function and the inverse function are both  all real x

and the range for the function and the inverse function are both  all real y

here is the graphs             https://www.desmos.com/calculator/m457r8jips

\(function\\ y=x^3+x+1\\ \frac{dy}{dx}=3x^2+1\\ inverse\; function\\ x=y^3+y+1\\ \frac{dx}{dy}=3y^2+1\\ \frac{dy}{dx}=\frac{1}{3y^2+1}\\ \)

How many did he give to his other sister?

I thought our guest posted a different question - maybe they posted a number of questions?

Anyway, if this is the case maybe our guest deleted the contents. (2 edits are logged)

I thought that if you deleted you still had to leave something behind but maybe with the new forum you do not have to anymore?

what is 3.5i mean

It could just mean 3.5*i where i is an ordinary variable 

OR

it could mean  3.5*i where i is the basic unit of the complex number system.

\(i=\sqrt{-1}\)

i    is an imaginary number

so

\(3.5i=3.5*\sqrt{-1}\)

yes, I think everyone agrees :)

how do i find degrees of inside a triangle if i only know measurements

That is what trigonometry is for :)

Maybe you will find this interesting  :/      

What is the direct variation equation if y=8 and x=4?

y=kx

8=k*4

so k =2

y=2x

If you want me to explain better than ask me too :)