Here is a 2019 applied maths question for pharmacists I was asked to help with as I was told it was particularly difficult. Comments are welcome. A 1 year old child weighing 10kg is prescribed ceftriaxone at 80mg/kg for a complicated unrinary tract infection. This is given as an intravenous infusion over 30 minutes. You have 1g powder for solution for injection vials. For intravenous infusion the vials are reconstituted to provide a 100 mg/ml solution. After reconstitution the entire vial... Medical infusion rate ..read more

Given α≠0 (α constant) $u_{tt}−u_{xx}=0$ , $x,t>0$ $u(x,0)=f(x)$ , $x≥0$ $u_t(x,0)=g(x)$ , $x≥0$ $u_x(0,t)+αu(0,t)=0$ ,$t≥0$ How do I solve this Robin problem? Follow-up Q: After I have the solution: What are the conditions on f and g for which the solution is real? And - is the solution to this problem singular? I started by solving like I would do with any wave equation but couldn't understand how to incorporate the Robin IC. Thanks in advance ..read more

Can someone please explain me how to find convergence rate here? I’ve found somewhere that the rate of Jacobi convergence is equal to the rate of convergence of a geometric progression with a denominator q = \(\displaystyle \parallel G_2\parallel\). Second norm of matrix G here is equal to \(\displaystyle \sqrt{18}\). Is it correct and how to use it then ..read more

Jorge knows that every new hour a faucet fills up with twice the volume of the previous hour. He also knows that this tap fills an empty tank in 10 hours. He is in a hurry and decides to turn on two of these taps on the empty tank. In how many hours will the tank fill up ..read more

Hi everyone I'm struggling with a problem because the service time is different depending on the number of tickets purchased. Following is the case: "The owner wants to reduce the waiting and serving time for customers to buy tickets knowing that this has a negative effect on the time available to them to consume at the food concessions. He knows that the configuration of the store must take into account the needs of the customers. The manager has compiled data from his other branches and... Queuing models - Solving problem with different service time 1 ..read more

The following problem came up in a previous post Find the probability of \(\displaystyle b^2-4ac \geq 0\) where \(\displaystyle 0<a,b,c<1\) Triple integrals were set up and a complete solution was given together with the answer \(\displaystyle \frac{5}{36}+\frac{1}{6}\ln 2\approx 0.2544\) How would we set up a triple integral or triple integrals to solve the related problem Find the probability of \(\displaystyle b^2-4a c <0\) where \(\displaystyle 0<a,b,c<1\) Of course, we know the answer must be... Probability using triple integrals ..read more

Question: In Example 3.17 would the answer change if the interval (0,100) is used instead of (0,1)? Explain Example 3.17 is given below alongwith solution: My answer:$$\displaystyle\int_0^{\frac{1}{400}}\displaystyle\int_0^{100}\displaystyle\int_{2\sqrt{a}\sqrt{c}}^{100} 1 db dc da + \displaystyle\int_{\frac{1}{400}}^{100}\displaystyle\int_0^{\frac{1}{4a}}\displaystyle\int_{2\sqrt{a}\sqrt{c}}^{100} 1 db dc da =... Probability of quadratic equation being solved with at least one real solution ..read more

I don't know how to do a search for information on a specific equation. It's \(\displaystyle f(n + 1) = 2 - \dfrac{d(n)}{f(n)}\), where d(n) is more or less arbitrary. It came up in some work I've been doing and I can't seem to get anywhere with it. Being non-linear it may not even have a closed form solution. There are two other ways to look at it. It's a non-linear difference equation: \(\displaystyle f \Delta f + f(f - 2) = d\) and it can also be considered as a continued fraction. (I'm... Looking for a specific recursion relation ..read more

Write a computer program (in the language of your choice) that verifies the results in Example 3.18 for the case n = 3 and n = 4 by taking large numbers of samples. I don't have any idea to generate real random number from (0,1) in any language e.g. R, Octave, C, C++,Java, Javascript, PHP etc ..read more

From the numbers used I guess this might be an oldie. Which is greater: $50$ or $(1+1/2)\times (1+1/3) \times... \times(1+1/2018 ..read more