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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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2 votes
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78 views

How to determine the elevation at the edges of a tilted rectangle?

The rectangle is slanted in direction B to C and the elevation at point B (between the edge and the floor) is 1.2 cm. C is the only edge that touches the floor. How to determine the elevation at ...
TheLostInUnknown's user avatar
0 votes
0 answers
29 views

Slope and GCD points

given a slope in the form $y=ax+b$ My question is to know if there are (and if yes how to find them) points $(x,y)$ where : $gcd(x,y)>1$ (to be more precise, the $gcd$ is made between the $x$ and ...
Davinator's user avatar
1 vote
0 answers
33 views

How to find the upper and lower bounds for slope and intercept in linear algebra? [closed]

I'm trying to make an algorithm for linear regressions where it will test every slope and intercept to find the perfect slope and intercept. From what I was taught, that is the standard way of making ...
Henryk's user avatar
  • 21
0 votes
1 answer
30 views

Significance of tangent passing through the origin in graphical interpretation

(This question was asked in CSIR NET June 2019 examination) A monkey climbs a tree to eat fruits. The amount of energy spent climbing on the different branches has a relationship, as shown in the ...
S.S's user avatar
  • 1,239
0 votes
1 answer
49 views

Get all slopes of $x^3 + 2y^2 -2xy = 0$ at $(0,0)$

Consider the curve with the equation $x^3 + 2y^2 -2xy = 0$. If we want to find the slope at $(0,0)$, we can differentiate implicitly and substitute $(0,0)$. This gives $y' = 0$ and all seems well, but ...
Misha Shklyar's user avatar
2 votes
1 answer
60 views

slope of vertical line

I have multiple lines (let's say 8 lines for this example) and I want to cluster these lines by their slopes. Therefore I calculate the slope of every line using the formula: $m=\frac{y2−y1}{x2−x1}$ ...
jonsken's user avatar
  • 23
0 votes
1 answer
26 views

what is the unit of this rate of change?

I'm given a table that shows the percent of Canadian households that used e-mail from year A to year B. Then what is the unit of the average rate of change of the percent of households using e-mails ...
OSCAR's user avatar
  • 573
0 votes
1 answer
35 views

Finding the percentage change in the slope with the correct plus or minus symbol.

I am trying to build a formula with the data that I have below. The formula will be embedded in a Arduino sketch. Column A is the time stamp and Column B is my voltage value. Column C is a threshold ...
Mars Sojourner's user avatar
1 vote
3 answers
79 views

An odd equation that is a straight line: $x(y^2-x^2)=y^3$

I was idly messing around in Desmos the other day and came up with this equation: $$x(y^2-x^2)=y^3$$ The graph looks like this. A perfectly straight line. My first instinct was to differentiate it, ...
lanye74's user avatar
  • 13
3 votes
2 answers
105 views

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 ...
Johannes's user avatar
  • 135
3 votes
0 answers
72 views

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 ...
Amahury Diaz's user avatar
0 votes
1 answer
70 views

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-...
MrJonesBones's user avatar
6 votes
4 answers
639 views

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 =...
MrJonesBones's user avatar
3 votes
0 answers
70 views

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 ...
TJR's user avatar
  • 131
0 votes
0 answers
28 views

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 ...
FawaMop's user avatar
0 votes
0 answers
65 views

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 ...
HeyJude's user avatar
  • 261
1 vote
0 answers
60 views

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 ...
SirMrpirateroberts's user avatar
0 votes
0 answers
27 views

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 ...
Donut's user avatar
  • 155
0 votes
1 answer
73 views

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 + ...
Sahil Desai's user avatar
0 votes
1 answer
55 views

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)}...
JoeGlas's user avatar
  • 55
1 vote
2 answers
86 views

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 ...
Mohamed Khaled's user avatar
2 votes
2 answers
53 views

Is my method correct to check if three point lie on a line in euclidean co-ordinates

Question : Given are three points in euclidean coordinates: $x_1=(2,2)T$ $x_2=(−8,−8)T$ $x_3=(17,17)T$ Do these three points lie on a line? My attempt/thinking : I was given this question. In order to ...
Purple_Ad's user avatar
0 votes
0 answers
62 views

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 ...
GPrathap's user avatar
  • 151
1 vote
1 answer
137 views

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 ...
Esteban's user avatar
  • 45
0 votes
0 answers
117 views

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 ...
gvd's user avatar
  • 119
1 vote
1 answer
554 views

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 ...
KIM CHANGJUN's user avatar
0 votes
1 answer
48 views

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 ...
Ben's user avatar
  • 198
1 vote
1 answer
73 views

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 ...
venkatesh pandian's user avatar
0 votes
0 answers
41 views

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 ...
Ejlal Sumbal's user avatar
1 vote
2 answers
250 views

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 ...
Dont Zont's user avatar
0 votes
1 answer
57 views

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 ...
Jason's user avatar
  • 27
3 votes
3 answers
58 views

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} =...
Murad Petrosyan's user avatar
1 vote
0 answers
90 views

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 ...
There's user avatar
  • 111
-2 votes
1 answer
40 views

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, ...
Divins Mathew's user avatar
0 votes
1 answer
660 views

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 ...
aarbee's user avatar
  • 8,338
3 votes
0 answers
33 views

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 ...
Eugene Zolotuhin's user avatar
0 votes
3 answers
63 views

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 ...
griefter's user avatar
0 votes
1 answer
118 views

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 ...
spiroulis's user avatar
1 vote
3 answers
122 views

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 ...
Mark Cavendish's user avatar
2 votes
3 answers
278 views

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 ...
Math Curious's user avatar
1 vote
2 answers
82 views

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 ...
Kishor Kumar's user avatar
0 votes
1 answer
44 views

How to reshape a nonlinear curve into a linear curve?

I have this data: ...
euraad's user avatar
  • 2,962
3 votes
3 answers
139 views

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}...
ArthD21's user avatar
  • 382
0 votes
1 answer
30 views

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. ...
RexSir9001's user avatar
2 votes
1 answer
85 views

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. ...
sonnet pronnet's user avatar
3 votes
3 answers
321 views

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 ...
insipidintegrator's user avatar
-2 votes
2 answers
146 views

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 ...
Debanjan Biswas's user avatar
0 votes
1 answer
46 views

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 ...
SinonOW's user avatar
  • 343
1 vote
0 answers
85 views

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/...
Mustafa K.'s user avatar
2 votes
0 answers
61 views

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 ...
Midhun Raj's user avatar

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