Ezequiel Olson

2022-04-24

Simultaneous Equations Finding the Intersection of a Cubic and a Quadratic

My functions are

$y=-0.65{(x-8.165)}^{2}+1.5(x-8.165)+6.872$

$y=0.08{(x-11)}^{3}-2.2(x-11)+5.9$

By using simultaneous equations and equating the functions to one another I've simplified it to the point where:

$0.08{x}^{3}-1.99{x}^{2}+14.7255x-27.608=0$

This had me stuck for a while but when I looked it up online I found I could use the Newton - Raphson Method to solve it.

I got the intercepts:$x=2.85281,x=10.98682,x=11.03536$

And although this helped me greatly, for the assignment I'm doing I won't be marked on using that method as we haven't been taught it and it's not on the criteria.

I'm just wondering if there is another method I can use that would get the same results.

My functions are

By using simultaneous equations and equating the functions to one another I've simplified it to the point where:

This had me stuck for a while but when I looked it up online I found I could use the Newton - Raphson Method to solve it.

I got the intercepts:

And although this helped me greatly, for the assignment I'm doing I won't be marked on using that method as we haven't been taught it and it's not on the criteria.

I'm just wondering if there is another method I can use that would get the same results.

Waylon Padilla

Beginner2022-04-25Added 19 answers

You know that you have three real roots.

Using whole numbers, your cubic equation write

$\frac{2}{25}{x}^{3}-\frac{199}{100}{x}^{2}+\frac{29451}{2000}x-\frac{22136643}{800000}=0$

${x}_{k}=\frac{199}{24}+\frac{19}{12}\sqrt{\frac{59}{5}}\mathrm{cos}(\frac{2k\pi}{3}-\frac{1}{3}{\mathrm{cos}}^{-1}(-\frac{69497939}{4046810\sqrt{295}}))$

with$k=0,1,2$ .

Using whole numbers, your cubic equation write

with

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V=??

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a) $f(x)=-3x+4$

b) $f\left(x\right)=-3{x}^{2}+7$

c) $f(x)=\frac{x+1}{x+2}$

?

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B)Parallelogram;

C)Kite;

D)none of theseWhat is the order of the numbers from least to greatest.

$A=1.5\times {10}^{3}$,

$B=1.4\times {10}^{-1}$,

$C=2\times {10}^{3}$,

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B)4;

C)6;

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