What is Cubic: Definition and 427 Discussions

CUBIC (abbreviation for “clear, unobstructed brain/body imaging cocktails and computational analysis) is a histology method that allows tissues to be transparent (process called “tissue clearing”). As a result it makes investigation of large biological samples with microscopy easier and faster.
The method was published in 2014 by Etsuo A. Susaki and Hiroki R. Ueda, primarily for use in neurobiology research of brains from model organisms like rodents or small primates. But in upcoming years there were other works published, using CUBIC method on other tissues like lymph nodes or mammary glands. CUBIC can be also combined with CLARITY-based tissue clearing methods.

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  1. Y

    Coloumbs law with inverse cubic

    1. Homework Statement A permanent electric dipole consisting of charges +q and -q separated by the fixed distance s. Charge +Q is distance r from the center of the dipole. We'll assume s << r. a) Use the binomial approximation (1+x)-n ~= 1-nx if x << 1 to show that the net force exerted...
  2. B

    Solving for a Cubic Function with Given Points

    Homework Statement Find an expression for a cubic function f if f(1)=6 and f(-1)=f(0)=f(2)=0 Homework Equations I figured it out but I am not sure why we use the equation f(x) = a[x-(-1)](x-0)(x-2) The Attempt at a Solution Im assuming its because if u times that equation that is a...
  3. T

    What is the Inverse of a Cubic Function?

    Homework Statement Find the inverse of f(x)=ln(x^3-3x^2+3x-1) Homework Equations n/a The Attempt at a Solution y=ln(x^3-3x^2+3x-1) x=ln(y^3-y^2+3y-1) e^x=(y^3-y^2+3y-1) i looked around for inverse of cubic functions and i found a monster of a formula...
  4. O

    How can I solve a cubic equation in terms of a variable?

    Can anyone help solve S3+101S2+(10K+100)S+100K to find the roots of S in terms of K
  5. D

    MHB Expressing a number in scientific notation and factoring a cubic

    Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 5) Express .00024 in Sci Notation My answer: 2.4 x 10^-4 6) Factor the following completely: 3x^3 - 18x^2 + 24x My Answer: (3x)(x - 4)(x - 2)
  6. H

    How to factor a Cubic Polynomial?

    Homework Statement Factorise: f(x)=x^3-10x^2+17x+28
  7. alyafey22

    MHB Prove Cubic Log Integral: -π^4/15

    Prove the following \int^1_0 \frac{\log^3(1-x)}{x}\, dx=-\frac{\pi^4}{15}
  8. anemone

    MHB Finding the Sum of Real Numbers Satisfying Cubic Equations

    The real numbers x and y satisfy x^3-3x^2+5x-17=0 and y^3-3y^2+5y+11=0. Determine the value of x+y.
  9. anemone

    MHB Can You Match Constants to This Cubic Polynomial?

    Find the constants a,\;b, \;c,\; d such that 4x^3-3x+\frac{\sqrt{3}}{2}=a(x-b)(x-c)(x-d).
  10. J

    Cubic Function Help Homework Statement

    Homework Statement A table is given: x | -2 | -1 | 0 | 1 | 2 | 3 h(x) | 0 | 9 | y | 3 | 0 | 6 Well actually the h(x) line was based on a graph that we had to look at, it should be right. I discovered y = 8 (the graph increments by 3 on y-axis and 1 on x axis, so I couldn't tell...
  11. K

    Separate Variables Differential Eq. of Cubic Power

    Homework Statement When possible express the general solution in explicit form. Solve dy/dx =x^2 /(1+y^2) Homework Equations This is a first order non-linear ordinary differential equation. The Attempt at a Solution dy(1+y^2) = x^2 dx Integration both sides returns: y+ (y^3 )/3=...
  12. G

    How do I Expand a Cubic Problem?

    Homework Statement Hey I have a question that I have to do that involves expanding a cubic. It is given in the form y = , once it is found I have to square it and then substitute it into a formula to find the area. All I need help with is the expansion than after that it's quite easy.Homework...
  13. S

    Cubic and Linear Thermal Expansion.

    Homework Statement 1. a 100m long copper wire of diameter 4mm is heater from 20C to 80C. What is the change in the length of the wire? 2. a 0.2m diameter aluminium sphere is cooled from 250C to 0C. What is the change in the volume of the sphere? The coefficients of linear and cubic expansion...
  14. S

    How do i factor cubic trinomials?

    Homework Statement x3-13x+12=0 The book shows the following solutions, i should add that i have very little practice with factoring cubic TRINOMIALS, you see i factor trinomials through an intuitive understanding, i tried staring at the problem a few hours yesterday, tried youtube/google for...
  15. r-soy

    MHB What are the steps to find the roots of a cubic equation?

    Hi, If we have this equation: m^3 - m^2 - 8m + 12 = 0 how we can get the roots m_1,\,m_2,\,m_3? can someone please help... ?
  16. A

    Cubic polynomial unable to be factored nicely

    Found this on a test for an integrated algebra 2 high school math class! Factor completely. 6x3 - 3x2 + 12 The Attempt at a Solution 3( 2x3 - x2 + 4) eq.1 At this point I checked for rational roots using the rational roots theorem and synthetically dividing. I got nothing...
  17. MarkFL

    MHB Kkittiee's question at Yahoo Answers involving factoring a cubic polynomial

    Here is the question: Here is a link to the question: Math help: factoring? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  18. C

    MHB Using Trigonometry for solving a Cubic equation

    Dear Everyone, I need some help for this general cubic equation. \[ax^3+bx^2+cx+d=0\]. First divide the equation by a \[x^3+b/ax^2+c/ax+d/a=0\] Let x=y-b/(3a) ... $$y^3+py+q=0$$ where $$p=c/a-(b/a)^2)/3;q=d/a-(b/a*c/a)/3+(b/a)^3/27$$ $$y=cos \theta$$ then i need to use the identity for...
  19. phosgene

    Finding a cubic polynomial that attains a max/min value over an open interval

    Homework Statement Give an example of a cubic polynomial, defined on the open interval (-1,4), which reaches both its maximum and minimum values. Homework Equations - The Attempt at a Solution I can see that I would need a function such that there is some f(a) and f(b) in...
  20. S

    Weighted Moving Average of Cubic

    1. Show that applying a second-order weighted moving average to a cubic polynomial will not change anything. X_t = a_0 + a_1t + a_2t^2 + a_3t^3 is our polynomial Second-order weighted moving average: \sum_{i=-L}^{i=L} B_iX_{t+i} where B_i=(1-i^2I_2/I_4)/(2L+1-I_2^{2}/I_4) where...
  21. MarkFL

    MHB Covert's question at Yahoo Answers regarding a line tangent to a cubic and finding parameters

    Here is the question: Here is a link to the question: Curve Tangent Question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  22. V

    How Does Symmetry Solve a Cubic Resistor Network?

    Dear all, I'm trying to understand the second figure of the following webpage. The webpage simply solve it by 'symmetry', but I could not figure out its reasoning. Could someone explain how does it work? Thanks in advance...
  23. K

    What is the Cubic Function that Passes Through Given Points?

    Homework Statement I have a line of a cubic function that passes through (-10,4), (-2,3), (-1,2), (0,1), (7,0). I must find the function of this line. Homework Equations The Attempt at a Solution I know you can't see this but the line has a "S" curve to it. Making me assume that...
  24. A

    Cubic non-linear inequality (HELP)

    I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.
  25. C

    Degeneracy for different energy states in Infinite cubic well

    Alright, I'm back with yet another question... So the prof was explaining that the energy in an infinite cubical well is E((h2∏2)/2ma2))(nx2+ny2+nz2) Which is all well and good, and he gave us the example of: ψ1,2,1 = E = 6((h2∏2)/2ma2)) And with little explanation mixed it up once...
  26. L

    Theory of cubic equation question

    Homework Statement Find the equation who roots are the squares of the roots of the equation x^3-4x^2+x- is the answer x^3-16y^2+y+1?
  27. V

    Understanding Potential Difference in a Cubic Circuit

    Homework Statement A potential electrostatic difference is stablished between points M and Q in the cubic circuit of identical capacitors shown in the image. What is the potential difference between points N and P? Homework Equations The Attempt at a Solution I tried opening up...
  28. S

    Why solids aren't organized in simple cubic (SC) and Simple Hexagonal(SH) ?

    My book mentioned that SC and SH are both "Theoretical arrangement" for crystal lattices, and later posed the question "Why it doesn't happen?", however it never provided an answer. Well, I can 'sort of' (very non-scientifically, mind you) imagine why, three stacked layers of spheres(atoms)...
  29. E

    Weight of water from molecular mass to grams per cubic centimeter

    I’ve been scratching my head (and working in ms excel) about the following for about 6 hours and would greatly appreciate it if somebody could help me. Basically, I am trying to figure out WHY the density of water is approximately one gram per cubic centimeter (at 1 atm pressure and 4 degrees...
  30. E

    Estimating f(2) using Cubic Interpolation

    If a cubic function satisfies f(0) = -32, f(1) = 0, f(3) = 10 and f(4) = 0, use cubic interpolation to estimate f(2) I'm not sure how to approach this since I have only ever done quadratic interpolation and linear interpolation, is it just an extension of the lagrange interpolating...
  31. E

    Find the cubic polynomial satisfying f(0) = -5, f(1) = 0, f(2) = 15, f(3) = 52.?

    Here is the correct answer: 2x^3 - x^2 + 4x - 5 My attempt only gives me one cubed term and the other terms are also marginally off, any help on who can show me how to get the correct answer will be hugely appreciated
  32. T

    Can you draw a cubic function with one real root without using calculus?

    Such as f(x)=(x^2+1)(x+1)?
  33. C

    Flight of Bird, Cubic Function

    Homework Statement A bird dove under water and re-emerged with a fish. Following is the table which shows the bird's estimated flight: Time(s),Height(m) 0, 7 2, 10 4, 5 6, 0 7, 0 8, 3 Find a cubic equation to model the data. 2. The...
  34. vrmuth

    Is there formula for zeres of a cubic polynomial

    is there any general formula to find out zeros of a cubic polynomial that will give you all the zeros ? if not please tell me what are the different methods to find out the zeros , guessing and trial and error , numerical etc. i want to see where are each methods useful and is there...
  35. karush

    MHB *find coefficients of cubic f(x) given min max & inflexion pt

    find a, b, c, and d, such the cubic $f(x)=ax^3+bx^2+cx+d$ satisfies the given conditions Relative maximum (3,3) Relative minimum (5,1) Inflection point (4,2) I approached this by using the f'(x)= a(3)(x^2)+b(2)(x)+c with the min and max and f''(x)=6x+2b for inflection pt to get $27a +6b + c...
  36. J

    Cubic asymptotes in rational functions?

    I just got this assignment for math and the question was is it possible to have a cubic asymptote in a rational function. If so explain how and where.
  37. C

    Best ways in solving cubic equations without information on roots

    Homework Statement Learning to solve cubic equations without the knowledge of any roots, and the easiest way I found out so far is still time-consuming Homework Equations The equation and attempt is shown in the image below, tell me if its unclear :shy: The Attempt at a Solution...
  38. Y

    Is the Cubic Function Inversely Symmetric about its Point of Inflection?

    As we know, a quadratic function can be expressed in a form of complete square by a method of completing the square. This form enables us to prove that a quadratic equation is symmetric about its stationary point. But for the cubic function, is there a similar way to prove that the cubic curve...
  39. B

    Solve cubic with no rational zeros

    Homework Statement x^3-8x+10=0 Homework Equations The Attempt at a Solution By dividing by x-1 (1 is a factor of the solution), I got (x-1)(x2+x-7)+3+10=0 which equals x^3-8x+20=0 I think the solution would be imaginary but I used a graphing calculator and there is one...
  40. M

    Solving Cubic equation to graph

    Homework Statement Graph this equation: P=-0.2t^3+2t^2+8t+2 t belongs to [0,13] Homework Equations The Attempt at a Solution Can't seem to get factored to find x-int. and the rest of the graph.
  41. L

    How many cubic meters in a cylinder?

    Homework Statement Given a cylinder of radius = 5m, and height = 10m, how many cubic meters is that? If I just compute those values in the formula for a cylinder, I get 785.4. But 785.4 what? Is it785.4m^3? Homework Equations The Attempt at a Solution
  42. S

    Inverse function of a quadratic and a cubic function?

    Homework Statement Homework Equations The Attempt at a Solution for 24. which is a quadratic function, i understand that you have to exchange the positions of x and y and solve from there...but my question is the inverse function of that quadratic for 24 is a negative number...
  43. K

    Calculating approx. Values in km3, m3, cubic miles, and gallons

    Homework Statement Earth’s radius is 6370 km and approximately 70% of its surface is covered with water, to an average depth of 12,000 feet. Calculate the approximate volume, in km 3 , m 3 , cubic miles and gallons of Earth’s oceans. Homework Equations The Attempt at a...
  44. C

    How can I factor a cubic function with a given x-intercept?

    Alright, so I need a little brush up on my pre calc apparently! I need to determine the x-intercepts of the following function. y=x^3 + 2 I know I need to factor it... I'm just not completely sure how! Thanks!
  45. M

    Partial fractions for a cubic root in the denominator of integrand

    Homework Statement \int\frac{1}{x\sqrt[3]{x+1}}dx (That's a cubic root in the denominator, by the way. Not an x cubed.) The Attempt at a Solution I thought possibly partial fractions, but I've never seen it done with a root in the denominator. Integration by parts was...
  46. T

    Higgs Boson and the Missing Cubic Term in the Standard Model

    Why does the standard model have a higgs boson quadratic and a cuartic term but it does not have a cubic term? is there any problem if it happens to have a cubic term? Thanks!
  47. M

    Confirming Conjugate Factor of Cubic Equation

    Homework Statement If a cubic equation, f(x) has a factor of (3+√2), then the conjugate of the factor, (3-√2) is also a factor for f(x). Homework Equations The Attempt at a Solution Just to confirm is that statement correct? I read it else where but i not sure is it correct or...
  48. W

    Non-linear function - Cubic and Quadratic functions

    1. i am stuck 2. The profit function is given by P=-2x^2 + 60x - 250, where x units is the quantity and P the total profit. Find the maximum profit and the number of units where maximum profit occurs. Sketch the curve of the profit function. 3. i can't do anything, my brain just jammed...
  49. V

    Force and Electric field within a cubic lattice

    Homework Statement There are Cl+ ions at the corners of a cube of side a = .4nm and a Cs- ion at the center. a) What is the net force on the Cs- ion? b) What is the electric field at the center of the cube cause by all of the Cl ions? c) What is the electric potential at that point...
  50. Z

    Finding Roots of a Cubic Function: Tips and Tricks

    Homework Statement Actually, part of a question on modeling/control systems. I need to find the poles (or, roots) of the cubic function. Homework Equations x^3 - 13x + 12 = 0 The Attempt at a Solution The rule of thumb for the course is that if you get a cubic function then there...
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