1
vote
1answer
42 views

Find the linear-to-linear function whose graph passes through the given three points

Find the linear-to-linear function whose graph passes through the points $(1, 1)$, $(4, 2)$ and $(30, 3)$. So by using the $$f(x)=\frac{ax +b}{x+d}$$ I got my final answer to be ...
1
vote
1answer
39 views

re-arranging polynomial (newton interpolation)

How does: $$ f(x_2)= f(x_0)+\frac{f(x_1)-f(x_0)}{x_1-x_0}(x_2-x_0)+a_2(x_2-x_0)(x_2-x_1)\tag1 $$ rearrange to: $$ a_2 = \frac{\frac{f(x_2)-f(x_1)}{x_2-x_1}-\frac{f(x_1)-f(x_0)}{x_1-x_0}}{x_2-x_0} ...
0
votes
2answers
50 views

How can I find the gradient of this function? $f(r,t)=r^3\cos(t).$

$$f(r,t)=r^3\cos(t).$$ Is it not like this: $<3r^2,-\sin(t)>$
0
votes
2answers
32 views

Find a formula that describes the given day-price relation

Given data: Days Prices 0 0 1 1000 2 1000 3 1000 4 1600 5 2200 6 2800 7 3400 8 4000 9 4600 10 5200 Price is function of day. I had my formula but always put negative ...
2
votes
2answers
56 views

Converting data to a specified range

I am trying to convert data to a particular range of 0-10. Actual Data may vary from - 50000 - 26214400. I have broken this down in to 4 parts as follows - ...
3
votes
1answer
205 views

Curve through four points — simple algebra??

The motivation for this is Bezier curves. But, if you don't know what these are, you can skip down to the last paragraph, where the problem is described in purely algebraic terms. Suppose I want to ...
1
vote
0answers
75 views

What are the constants in the relationship between point density and median point distance?

Given $\rho$ particles uniformly distributed on a plane within a unit square ($\rho > 1$), each particle has another particle that is closest to it; the median of those nearest distances is called ...
2
votes
1answer
123 views

A Question About Linear Interpolation

So lets say I have two points $A=(x_1, y_1, z_1)$ and $B=(x_2, y_2, z_2)$. $A$ and $B$ are each associated with some scalar value $K_1$ and $K_2$. $K_1$ is negative and $K_2$ is positive and all the ...
1
vote
3answers
1k views

Smooth transition between two lines (2d)

I have function that is defined as $$ Y = \frac{1}{15} x \longrightarrow {\rm if}\qquad 0 \leq x \leq 30 $$ $$ Y = \frac{1}{70} x + \frac{11}{7} \longrightarrow {\rm if}\qquad x > 30 $$ The ...