Simplifying nested/complex fractions with variables
I have the equation $$x = \frac{y+y}{\frac{y}{70} + \frac{y}{90}} $$ and I need to solve for x. My calculator has already shown me that it's not nece...
19 Apr 2026 1 READS
Archive: General
Trouble integrating $\sec x$
I have to evaluate the integral of the $\sec x$ function and I do it as follows $$\int\sec xdx=\int\frac{dx}{\cos x}=\int\frac{\cos^2 x+\sin^2 x}{\cos x}d...
19 Apr 2026 1 READS
What does the graph of $\sin^2 x$ look like?
When solving trig equations, sometimes it comes out as a hidden quadratic, like this: $2\sin^2x-5\sin x+2=0$ Obviously it is possible to factorise and sol...
19 Apr 2026 1 READS
![Are definitions axioms? [duplicate]](https://edu.smbbmcl.edu.pk/uploads/are-definitions-axioms-duplicate_720.jpg)
Are definitions axioms? [duplicate]
I just want to ask a very elementary question. When we introduce a "definition" in a first order logical system. For example when we say Define: $Empty(x)...
19 Apr 2026 1 READS
What is the difference between Riemann and Riemann-Stieltjes integrals?
I'm quite confused, what is the difference between these two integrals (R and RS)? It seems that RS is closer to Lebesgue in its treatment of discont...
19 Apr 2026 1 READS
A Sample of Tritium-3 Decayed to 94.5% of its Original Amount After a Year. (a) What is the half-life of tritium-3?
Please use the following notation when explaining the solution. The formula I am aware of is $P(t)=P_oe^{kt}$ $P_o=\ initial\ amount$ t = time k = growth ...
19 Apr 2026 1 READS
How to find the smallest side of a triangle when the interior angles are unknown?
I am confused on how to find the answer for this problem. So far what I believe would apply is the triangle inequality but I'm not sure on how to use...
19 Apr 2026 1 READS
Find the number of values of k?
Find the number of values of k for which the expression $$y= (x^2 - x(k-2) + k^2)(x^2 + kx + (2k-1))$$ is a perfect square . I tried by assuming the produ...
19 Apr 2026 1 READS
Determine polar form of complex number without a calculator
Determine the polar form of $\mathcal z_1 = 2 + \mathcal i \sqrt 3$. This is how far I have gotten: $\mathcal r = \sqrt{2^2 + (\sqrt{3^2})}= \sqrt7$ There...
19 Apr 2026 1 READS
Find the not-a-knot cubic spline over each subinterval in standard form
Looking over some cubic spline interpolation problems and unsure which method to use. Given the values: x= [-2,-1,0,1,2,3], y = [18,12,6,4,5,18] respectiv...
19 Apr 2026 1 READS
