All Questions
30
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Estimate root scale of a cubic equation
Consider the following cubic dispersion equation of $\omega(k)$ $$\omega^2-\omega_a^2(k)-\frac{\alpha^2k^4}{\omega-\omega_b(k)}=0.$$
$\omega_a=vk,\omega_b=b-v'k$ are two unhybridized dispersions that ...
- 784
-1
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2
answers
334
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finding the equation of a cubic function with 2 points [closed]
A cubic function is in the form $y=kx^3+c$. Find the equation if it passes through $(0,5)$ and $(2,-3)$.
I’m not sure how i would work this out algebraically or if i even can without graphing.
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1
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How to get the coefficients in a parametric cubic function
Let's say I have 4 points with x and y coordinates. And I want to determine the parametric cubic function:
$x(t) = a_x t^3 + b_x t^2 + c_x t^3 + d_x$ and $y(t) = a_y t^3 + b_y t^2 + c_y t^3 + d_y$
So, ...
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4
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$f(x)$ and $g(x)$ are monic cubic polynomials, with $f(x)-g(x)=r$. If $f$ has roots $r+1$ and $r+7$, and $g$ has roots $r+3$ and $r+9$, then find $r$.
Let $f(x)$ and $g(x)$ be two monic cubic polynomials, and let $r$ be a real number. Two of the roots of $f(x)$ are $r+1$ and $r+7$. Two of the roots of $g(x)$ are $r + 3$ and $r + 9,$ and$$f(x) - g(x) ...
- 800
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0
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60
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How would I mathematically model this curve from Sonic the Hedgehog?
Hey guys!
I'm looking at the S-Curve from the first Sonic the Hedgehog game. Out of interest, I would like to know how to mathematically model this? I'm not sure, but I suspect that it may some sort ...
- 41
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1
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Functions from numerical solutions
Here is the context, I have numerically solved a cubic equation which is an irreducible case.
Here is the polynomial I have solved:
$P(x)=x^{3}+(1.45-2i\omega)x^{2}+(0.64 \lambda-w^{2}-1.9i\omega+1.06)...
4
votes
3
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157
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Cubic equation problem $\frac{x^3}{3}-x=k$
The cubic function $\frac{{{x^3}}}{3} - x = k$ has three different roots $\alpha,\beta,\gamma$ about the real number k. Let's call the minimum value of $|\alpha|+|\beta|+|\gamma|$ as $m$. FInd the ...
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7
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What does$ f(f(x))=0$ mean?
I came across a question: If $f(x)=x^3-x+1$ then find the number of real distinct values of $f(f(x))=0$.
Here is what I interpreted the $f(f(x))$ as:
I assumed $a, b$ and $c$ to be the roots of $f(x)$,...
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1
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181
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How do I find g(x) given the stationary points (2,9)?
question image
given the info I form the equation g(x) = AX³+BX²+AX+C and did g'(x) = 0 to find B = -13A/4 (when x = 2). So using B and putting it into g(x) = 9, I get AX³-13A/4X²+AX+C = 9 and I am ...
0
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2
answers
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Find a Cubic Function given an inflection point, critical point, and function value.
Find a cubic function f(x) = ax^3 + bx^2 + cx + d
Given:
Inflection point (0,18)
Critical point x = 2
F(2) = 2
I know how to solve for the general forms of the derivatives, and to set the values of ...
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-2
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2
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142
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solving cubic eq without using derivatives [closed]
enter image description here
Hi, I had this question, but I'm unable to solve it without using derivatives, though I have the answer (which is $15.7$ approx). I would appreciate it if you could help ...
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1
vote
1
answer
397
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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 ...
0
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0
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78
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Two distinct tangents drawn from an external point to a cubic
In this question
Phillip mentions is his answer
The equation $y=x^3+cx$ can have two distinct tangents drawn from an external point only if $c>0$
I tried to prove this:
Let the external point ...
- 2,205
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1
answer
48
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Solving for a variable in a polynomial with arbitrary x
The graphs of the functions $f(x)=x^3+(a+b)x^2+3x−4$ and $g(x)=(x−3)^3+1$ touch. Express a in terms of b.
The solution in the textbook is $a=−\frac{(27+11b)}{11}$
I've tried looking for a worked ...
0
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2
answers
143
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Solving for the constants of a cubic function where its graph is tangent to the x-axis at x=3
$$x^3-4x^2+ax+b$$
I am unsure of my understanding of theory yet, but from what I do understand I assume that y=0 when x=3 because the graph is tangent to the x-axis at that point. With that amount ...
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