Questions tagged [slope]
For questions on finding or applying slope, a number that describes both the direction and the steepness of a line.
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Solving logistic regression equation for slope
I've calculated a logistic regression model involving two variables $X_1$ and $X_2$ and their interaction $X_1 \times X_2$ and obtained regression coefficients for each.
The equation takes following ...
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Finding missing values with slopes
I am having difficulty with a math homework problem (grade 9).
Given that $(m,18)$ is a point on the line $y=5x+58$, solve for $m$.
I have been searching my notes and I cannot find anything like ...
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Linear clustering when plotting Pisano periods
Recently I saw a video on YouTube where the Fibonacci numbers were studied and around minute 4:20 appears a graph showing the period against the modulus. Something that caught my attention is that ...
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Find equations for the two lines through the point (3, 13) that are tangent to the parabola $y = 6x - x^2. $
Find equations for the two lines through the point (3, 13) that are tangent to the parabola $y = 6x - x^2$
since both lines must be tangent to the parabola their slope must be:
$$y' = 6- 2x$$
so.
$$6-...
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Typo in book or I am wrong?
Find the equation of the tangent to the parabola $y = x^2$,
if the $x$-intercept of the tangent is $2$.
Now
$$y = mx + b$$
$$0 = m(2) + 2$$
$$m = -1$$
so
$$m = \frac{y-0}{x-2}$$
$$m(x-2) = y$$
$$-x-y =...
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Best fit of deltas unequally spaced to reconstruct original curve
I have a collection of measurement deltas $m_1...m_n$ where each measurement consists of two points $(x_{n1},y_{n1})$ and $(x_{n2},y_{n2})$ the $x_{n1}$ and $x_{n2}$ represent where the measurement ...
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A term that describes the scenario when there is at one least trending data set for data sets over same time range
Given that I have 2 separate sets of plotted data points. Both data points run over the same time interval. Assume that at any given time interval, both datasets are either trending or one is trending ...
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In what sense not using a unit vector would "mess up" the directional derivative?
I've read dozens of questions and answers here regarding the usage of unit vectors when calculating directional derivative, and I get that it's only a convention and not mandatory.
But the tendency to ...
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Finding x-axis-intercept of a parametric equation and slope
let $x = t^2$ and $y = t^3-3t$
now the equation for the slope is:
$$\frac{dy}{dx} = \frac{3t^2-3}{2t} = 0$$
now at the point (0,0) is the first intercept with the x-axis with slope $\infty$ what is ...
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Question about limsup and liminf of slope
Consider the function $g:[0,1] \to \mathbb{R}$ defined by $g(x)=1 - \sqrt{0.5-x}$ when $x \leq 0.5$ and $g(x)=1$ otherwise.
What is $\lim_{h \to 0^{+}} \inf \{\frac{g(0.5+t)-g(0.5)}{t} : 0< \lvert ...
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How can I find how far above the ground is point $A$ with gradients?
This is the problem. I feel like there is something missing I can't relate how we use gradients to find the point
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Solutions of a quadratic equation and their range
Find the range of $m$ such that the equation $|x ^ 2 - 3x + 2| = mx$ has $4$ distinct real solutions $\alpha$, $\beta$, $\gamma$, and $\delta$.
Express the value $s(m) = 1/\alpha ^ 2 + 1/\beta ^ 2 + ...
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What is the difference between Expectation and Sum formula for the slope of line in regression?
As book I'm reading now shows, formula for the slope of the line in linear regression is
$\beta_1 = \dfrac{\displaystyle \sum_{i=1}^n(X_i - \bar{X_n})(Y_i - \bar{Y_n})}{\displaystyle \sum_{i=1}^n(X_i -...
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Difference of derivative and slope of secant line
Let $f \colon [x_0,x_1] \to \mathbb{R}$ be smooth and $|f^{\prime \prime}(x)|\leq L$ for some $L \in \mathbb{R}^+$. I want to have an estimation of the form
$$
\left| f^\prime(x) - \frac{f(x_1)-f(x_0)}...
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what will the slope of mean vs std tell us?
I might be asking something very basic here with this question.
I have ND:YAG laser system and I would like to evaluate shot to shot noise from laser. To evaluate this, I take a set of 500 images of a ...
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what is the slope of the board?
A 5-foot-long board is leaning against a wall so
that it meets the wall at a point $4$ feet above the
floor. What is the slope of the board?
the solution is $\frac{4}{3}$ or $\frac {-4}{3}$ if the ...
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What is the difference between slope and gradient? [duplicate]
I've seen several answers but non of them do not answer what I am looking for, therefore I am asking here again,
According to my understanding,
Slope, $\frac{\partial f}{\partial x}$, is generally ...
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Condition of two orthogonal lines in homogeneous coordinates
Let $l_1$ and $l_2$ be the representations in homogeneous coordinates of two lines in the plane. How could you express the fact that these two lines are orthogonal?
Deduce that, in general, the image ...
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How to generate an wave with some slope?
I want to generate this wave with an slope
I believe that is a kind of amplitude modulation with some slope: $y(t) = [A_c + A_m \sin(ω_m \ t)] \sin(ω_c \ t)$. After plot the AM equation I get the ...
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tangent slope of cardioid graph
Hi i am student working on calculus and i have got question that i came up with wrong answer.
So we get $r=2(1+\cos\theta)$ cardioid function and the question is to looking for Θ angle where tangent ...
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What is the meaning of normalization (in this specific context)? [closed]
Though I want to address a specific aspect which is about normalization I also would like to see short answers/reasons about the purpose of normalization.
Maybe this will answer the next:
I got ...
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Differentitation and Integeration
I am trying to solve a differentiation/integration. I know the following relationship that indicates the rate of change of $x$ with time.
$\dfrac{dx}{dt} = H\dfrac{dy}{dt} - kx$, where $H$ and $k$ are ...
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Finding gradient of perpendicular lines
What will be the gradient of a vertical line and a horizontal line? Both are perpendicular to each other, and I know the product of their gradients must be $-1$, but that is for slanted lines. What if ...
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is the slope of a point on a straight line the same as the overall slope of that straight line
I am wondering if the slope of a point on a straight line is equal to the overall slope of that straight line,
Because I've just started with calculus, and we took an intro to differentials and ...
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Consider the two-variable function: $F(x; y) = \sqrt x+2\sqrt{\frac y3}$ s.t $3x+y=b$. Determine the optimal solution
Determine the optimal solution to the following constrained maximization. Then consider the level curve of F passing through the optimal solution poin and show that its slope at the point is equal to ...
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Find slope of the tangent line of $4\sqrt x + 2e^\frac {3x-12}{x+2}$ at $ x_0$ [closed]
Find the slope and the equation of the tangent line to the
graph $y = f(x)$ at $x_0=4$, $$4\sqrt x + 2e^\frac {3x-12}{x+2} $$
$$\lim_{h\to 0}\tfrac{4\sqrt {4+h} + 2e^\frac {12+3h-12}{4+h+2} - 10}{h} =...
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Calculate slope for 5 data points with no specific X value
I'd like to easily find out if the five points are getting better, worse, or staying flat. This is in regard to performance of a machine learning classifier when the classifier is provided fractions ...
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Give coordinates of line A, find the coordinates of another line meeting line A at an angle. [closed]
In the diagram, if x1, y1, x2, y2, ...
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Finding number of values of slope of line L
The following question is taken from JEE practice set.
In a plane rectangular coordinate system, there are three points $A(0,\frac43), B(-1,0)$ and $C(1,0)$. The distance from point P to line BC is ...
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Derived function slope to the given function [closed]
Preface:
I'm just a musician, trying to understand some math. Don't blame me, please ;)
Synopsis:
Given next 5 images, calculate slope of the proportion function. Make so the highest proportion is ...
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Finding a downward sloping function given a tangent point on a linear curve
I have a linear function $10-5x$. I am trying to create a downward sloping curve at a point where the tangency point is $(1.5, 2.5)$.
I tried using a function of $3.75/x$, but instead of making it a ...
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How does dividing rise/sum result in the slope of a line?
I can't get my head around how dividing the differences of two points gives us the inclination of a line. I do understand that the slope will show how much or little a change in $X$ will affect the ...
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Are these two graphs touching or intersecting?
Do the curves $x^2 - 1$ and $2^x$ touch or intersect at $x=3$? Both have same values ($=8$) but values of their derivatives at $x=3$ are different. If two curves touch shouldn't their tangents have ...
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Intuitive Way to Find Maximum Gradient of a Bezier Curve
I'm trying to find if any point on a bezier curve has a slope that is lesser than some predetermined angle, let's say $45^\text{o}$.
For certain cases I can see that the answer is obvious. Like ...
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How to bring $\log(y) = \log(a) + \log(e^{bx})$ to $y=mx+c$ format?
I was solving a problem regarding equation of the straight line. The question is to find the best value of $a$ and $b$ if
$$ y = ae^{bx}. $$
What I tried?
I multiplied LHS and RHS with $\log$ in order ...
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3
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A Pseudo-Derivative for $f(x)=|x|$
I was wondering what the significance of a function that gives the slope of $y=|x|$ at any $x$ is. If$$f(x)=|x|$$then we could do, as the derivative:$$\frac{d f}{d x}=\frac{x}{|x|}$$or$$\frac{d f}{d x}...
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What is the 'slope' of a function that has x, instead of y as the subject, called?
We are all familiar with y = mx + b, the slope-intercept form with y as the subject:
m is the gradient - how much y changes by an increase in x of 1.
b is the y-intercept - the value of y at x = 0.
...
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A Transylvanian Hungarian MC Problem.
question
Show that there exist infinitely many non similar triangles such that the side-lengths are positive integers and the areas of squares constructed on their sides are in arithmetic progression.
...
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Differentiability of a piecewise defined discontinuous function
Let
$ f(x) = \begin{cases}
x-4 & \text{if } x \lt 1; \\
x+1 & \text{if } x > 1; \\
0 & \text{if } x = 1.
\end{cases}$
Why isn’t this function differentiable at 1? Why isn’t its ...
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Why is $\frac {d}{dx} (x^2) = 2x$ not $x$?
I am new at calculus and so I am studying derivatives now. We know that, $$\frac {d}{dx} (x^2) = 2x$$
I know the proof of it by the first rule derivatives. But still, my question is why. It is simply ...
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Rigorous proof of intersection of straight line and two graphs in a translation relationship
The question is :
$f(x) = \log_3 x, g(x) = \log_3{(x+3)+4}$
There are two intersections $\mathrm A$ and $\mathrm B$ made by $y=-{4\over 3}x+4$
$\overline {\mathrm {AB}} = ?$
It was obvious by the ...
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Slope of Tangent line of Polar Curve at Point
Question
We had an examination today in college and the question was this:
Find the slope of the tangent line of polar curve $r = 3(1-\cos\theta)$ at point $B(\pi/3, 3/2 )$.
Answers are: $2\pi$, $\pi/...
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Doubt regarding finding the gradient of of a scalar field
I am new to vector calculus.
I watched few you tube videos and came to the conclusion that directional derivative is something like slope with direction and its ...
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Find the Point/s on the Curve $y-x^3=0$ where the normal line have a slope of $\frac{-1}{3}$.
I am bit clueless on how to start the problem. The only idea I have is to use derivatives, yet I can't continue on. I have tried researching different problems connected to it as well, but the results ...
user1058997
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negative slope of a triangle given only the sides
So my teacher gave me this graph and I needed to calculate the slope of the hypothenuse or f'(0.25).
So 62/121 is positive and I can see that the slope is negative....
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How to prove this hypothesis regarding slopes and ellipses?
Let $a, b\in \mathbf{R}^+, \lambda >1$. $\Omega: \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, Point $M(\dfrac a{\lambda}, 0), A(-a,0),B(a, 0)$. Let line $l$ pass through $M$ and intersect with $\Omega$ at ...
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A question regarding the point-slope formula : does the formula really hold for any point of the straight line?
I can see only one way to derive the point slope formula, but this derivation also seems to bring a question.
Let $D$ be the straight line of slope $m$ passing through point $P=(a,b)$.
Let $Q=(x,y)$ ...
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"Slope" in mathematics and " slope" in economics.
Note : I mainly consider the case in which demand curves are linear , to keep things simple.
I'm having trouble in applying mathematics to (micro)economics due to the fact that in this discipline , ...
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Find the equation of a line that is tangent to both parabolas simultaneously [closed]
Consider the parabolas $y=x^2$ and $y=x^2-2x+2$. How to find the equation of a line that is tangent to both of them at the same time? Please, walk me through the most intuitive solution.
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