# Tagged Questions

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### A question in application of derivatives and vectors

Consider a skier who is sliding without friction on the hill ${y = h(x)}$ in a two dimensional world. The skier is subject to two forces. One is gravity. The other acts perpendicularly to the hill. ...
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### Creating a mathematical formula to price a taxi booking

I've been asked to create a mathematical formula that will be used to price taxi bookings at a local taxi company. Current system used: A table is used as a reference Variables: x is the ...
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### Number sequences in nature.

I'm getting ready to teach the second calculus course in the 4 course sequence at my school. One of the required topics is an introduction to number sequences. I want to motivate this section with ...
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What is the order of the corrector of Adams-Moulton type required in order to apply Milne's method for estimating the error in PECE mode? Find the coefficient of the leading term in the truncation ...
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### A model for the spruce budworm population

A model for the spruce budworm population $u(t)$ is governed by $$\frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\frac{u^2}{1+u^2}$$ where $r,q$ are positive dimensionless parameters. The nonzero stedy ...
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### The intuitive understanding of $\sqrt{x}$ to model “inversely proportional / inverse square”?

Can someone lay out what the concept I am trying to convey below in a more clear manner? Square root functions are sometimes used to model non-linear relationships. The value of a square root is ...
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### SIR Models - interpretation (epidemiology) - help!

I am doing a project on modelling the spread of diseases and am using a SIR (susceptible, infected and recovered) model to do so. I need help interpreting this plot: What does this plot say about ...
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### matrix question - help needed

I am doing revision on matrices and came across this question. The solution (the matrix provided below the question) is there. I am not sure how or why 180 is in the position (1,4) (row and column ...
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### Are there rigorous mathematical definitions for these waves?

My friend linked this .gif to me tonight, and asked me if I knew of any equations that might model these bottom two waves (the blue and green waves). Unfortunately, I am not far enough in my education ...
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### Creating a model

Here's a seemingly simple pondering. If one item is more valuable the higher it is (i.e., $a=5$ is worth more than $a=2$) and another item is more valuable the lower it is (i.e., $b=2$ is worth more ...
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### Cat Dog problem using integration

Consider this equation : $$\sqrt{\left( \frac{dy\cdot u\,dt}{L}\right)^2+(dy)^2}=v\,dt,$$ where $t$ varies from $0$ to $T$ , and $y$ varies from $0$ to $L$. Now how to proceed ? This equation ...
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### Question Based On Mathematical Modeling [Applied Functions]

An example of a calulus book reads: A rectangular storage container with an open top has a volume of $10$ m . The length of its base is twice its width. Material for the base costs $10$ per ...
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### How to change Hermite function to have a same shape with moving extremum point and zeros

If somebody has a experience with polynomials. How to set this Hermite function to have a general minimum where I want on $x$ axis, for example in $0.5$. Is it possible to be in analytic form ...
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### Find The General Solution [closed]

Using separation of variables and partial fractions find the general solution: $$dP/dt = re^{-at}p(1-p)$$
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### How to approach mathematical modeling of the human heart problem?

I have to create a mathematical model of the human heart but it was quite a time ago I finished University and I experience some difficulties with the math behind the subject. What is the necessary ...
### why does $\frac{b\partial a}{a \partial b} = \frac{\partial \log a}{\partial \log b}$?
I am doing some background research on sensitivity and elasticity analysis, and I came across the following definitions of elasticity: e_{ij}=\frac{a_{ij}\partial \lambda}{\lambda \partial ...