Recent content by MartynaJ

So I attempted this problem and to satisfy the first condition (for t in the range of [1, 5]), I drew the straight line that has a slope of 5 (i.e. f(x)=5x). I just don't understand how I can have the same function with a different slope (average rate of change) for the interval [1,10] or for [2...

Ya sorry I now understand how you got these values... But how did you know it is an even function?

why ##\frac{\pi}{3}## and not ##\frac{5\pi}{6}+\frac{\pi}{3}##?

Create one equation of a reciprocal trigonometric function that has the following: Domain: ##x\neq \frac{5\pi}{6}+\frac{\pi}{3}n## Range: ##y\le1## or ##y\ge9## I think the solution has to be in the form of ##y=4sec( )+5## OR ##y=4csc( )+5##, but I am not sure on what to include...

For a polynomial inequality, I would just need to multiply them together. I'm not sure how to find make a rational expression. Like how do I know what to put in the numerator and what to put in thre denominator?

Ya x < -4 becomes x+4 < 0 (that was a typo)... and yes the idea in this question is to do it in reverse (i.e. try to find the polynomial)... I am just unsure of how to do that exactly.

Yes exactly my point... for the first part, I didn't really use much of what was given in the problem. And for the second part I am not sure id I am able to explain in words why it's 30. I am also not too sure if ##\frac{200000}{t}## approaches zero as ##t## approaches infinity just because...

My attempt so far: I put all the terms to become smaller than zero: so ##x<-4## becomes ##x-4<0## ##-1\leq x\leq 3## becomes ##-1-x\leq 0## and ##x-3 \leq 0## ##x>6## becomes ##x-6>0## which is the same as ##-x+6<0## (i think)... I am now stuck on making it a rational inequality... anyone...

This is my attempt so far: ##0.05=\frac{30t}{200000+t}## then I solved for t. And I got 333.88 min. I feel like this is way too simple of a solution and I didn't use all of what's given in the problem. For part 2 of the problem it asks, what happens to the concentration over time. I tried to...

Ya we studied polynomials in factors form, but I am not sure how I can solve this.

I am honestly not sure where to start. Please give me a hint on how to solve this problem. Thanks!

It's ##\sigma=\chi\int{\dfrac{dA}{A}}##. Also ##\sigma(R)## is the surface tension and ##\chi## is the stiffness of the spherical bubble (assumed to be constant).

I am trying to integrate ##\sigma=\chi\int\frac{dA}{A}## for a sphere. The answer is supposed to be ##\sigma(R)=\chi(R^2/R_0^2-1)##. The answer I keep getting is ##\sigma(R)=2\chi ln\frac{R}{R_0}##. I also tried doing it in spherical coordinates, and all I get for the integration of...

Before: ##\int_\infty ^\infty {\left| F_i(u) \right|}^2 du=\int_0 ^{40} a^2 du=40 a^2## Therefore: ##a^2= \frac{1}{40}\int_\infty ^\infty {\left| F_i(u) \right|}^2 du## After: ##\int_\infty ^\infty {\left| F_f(u) \right|}^2 du=\int_0 ^{10} a^2 du=10 a^2## Therefore: ##a^2=...