Questions tagged [slope]
For questions on finding or applying slope, a number that describes both the direction and the steepness of a line.
0
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2answers
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Finding the slope of the line normal to the graph at a given point
My Problem: What is the slope of the line normal to the graph of $f(x) = e^x-x^e-e$ at the point where the graph crosses the $x$-axis?
a. $-0.288$
b. $-0.110$
c. $3.471$
d. $9.106$
I ...
0
votes
3answers
31 views
Given only the slope, find the shortest distance from a line to a point on the x-axis
I have the following amusing question.
Suppose that the red dot is the point $x = -1$
The blue line is the line crossing the origin with slope $-1/k, k > 0$
I wish to find the length of the ...
3
votes
1answer
50 views
Quadratics: Intuitive relation between discriminant and derivative at roots
While working with quadratics that have real roots, I realized an interesting fact:
The slope of a quadratic at its roots is equal to $\pm \sqrt{D}$ where $D=b^2-4ac$
Proof:
$$f(x) = ax^2 + bx +c$$...
1
vote
2answers
16 views
slope of a linear function in semi-log plot
I have a decreasing linear function. So,the slope of this function df/dt <0. Now, if we plot this function in a semi-log plot with log(t) in horizontal axis and y in vertical axis, can we say that ...
0
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2answers
88 views
How can I find the slope of a line tangent to a small circle on a sphere? [closed]
I draw a circle on the earth, so that it passes through the north pole. I then begin walking around the circle, keeping track of my latitude. How do I tell what direction that I'm facing by knowing ...
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1answer
25 views
how to find slope of discrete point?
I am wondering if it is possible to find the slope at each point in the following dataset,
...
1
vote
0answers
35 views
Sketch the slope field
I need to sketch the slope field for this ODE $ y'=\frac{y+x-6xe^{\frac{y}{x}-2}}{x} $.
The first step is $f(x,y)=\frac{y+x-6xe^{\frac{y}{x}-2}}{x}=c $, where $c=const$. Now I have to draw the curves ...
-1
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1answer
37 views
How to shorten a line but maintain its angle? [closed]
I have a line that looks like this:
to draw this line i have the following:
point A: (x,y)
point B: (x,y)
so for example, i will be given this path:
(90,20),(400,300)
and then i can draw a line ...
0
votes
2answers
45 views
What is the unit of this “Rate of Change”?
This is the plot of the function $f(x) = 0.9x$.
So, the rate of change of $y$ with respect to $x$ is $0.9$.
My question is, what is the unit of this Rate of Change?
$0.9$ per $x$?
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votes
1answer
17 views
calculate angle of line with negative slope
I want to use the formula
$$
tan(\alpha)=m
$$
for negative slopes but always get negative degrees. For instance, say the slope of a line $g$ is $-1$. Using the formula above (arctan$(-1)=\alpha$), I ...
2
votes
1answer
31 views
Does an endpoint of a function have a slope?
Say I have the following function which is defined for $0 \leq x \leq 1$:
If you would derive this function and substitute $y = 0$, you would get $x = 0.5$ and $x = 0.75$ for the respective as the ...
0
votes
0answers
86 views
Find the value of Δx for which the value of Δy/Δx is within 0.1 units of slope.
Here is the link for the problem that I am trying to solve:
https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/...
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votes
0answers
26 views
When the slope of the angle bisector is 1, is the product of the slopes of the 2 lines forming the angle equal to 1
When the slope of the angle bisector is 1, I have been told that the product of the slopes of the 2 lines forming the original angle is 1. Is this true?
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1answer
23 views
Slope of a triangle where the sum of the height at each integer equals 1.
I have a problem where I'm trying to determine a proof to get the slope of a triangle $m$ in terms of $n$ where $\sum_{i=1}^n h_i = 1$.
I think I stumbled apon the answer being $m = \frac{2}{n(n+1)}$ ...
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0answers
21 views
Slope Intercept Form of a line - Derivation
Question: 1
I have 2 coordinates i.e. $(0,c)$ and $(x,y)$
Assumption y is less than c.
Find slope $(c-y) / (0-x) = m $
Simplify to get $y = mx + c$.
But the slope of the line connecting $(0, ...
0
votes
1answer
15 views
Determine the slope of a plane whose rise in z is zero, but whose change in x and y are not.
Determine the slope of a plane whose rise in z is zero, but whose change in x and y are not. Explain what this plane looks like.
Would it be a plane in the xy plane? Not sure how to start this ...
0
votes
2answers
18 views
How can I prove if l1 is as twice as steep as l2?
How do I find the slope of each line using SohCahToa? I plan on using the unit circle but I am having difficulty calculating slope.
0
votes
1answer
30 views
Would parallel lines in 2 parallel planes have the same slope?
If I am given 2 points in Plane A and 2 points in Plane B and I connected those points, would the lines have the same slopes? How can I show that algebraically?
0
votes
1answer
25 views
Kink versus jump
Suppose I have a function defined as follows
$n(r) = \begin{cases} n_h \quad \text{if} \quad r< \hat{r} \\ n_l \quad \text{if} \quad r \ge \hat{r}\end{cases}$. Where $n_h > n_l$ and $r \in [0,\...
1
vote
0answers
24 views
Given a plane with mx = 1 and my = 2, find the slope in the direction when x both increases by 2 and y increases by 3. [closed]
Slope =rise/run would it be as simple as 6/2=3?
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0answers
18 views
Formula for finding the slope of a regression line
I want to calculate the gradient of a regression line and have been looking at various websites and books to find the formula for it. My school textbook writes that this is:
$$m={S_{xy}\over(S_x)^2}$$...
0
votes
1answer
36 views
Why is the slope of a linear equation of the form $ Ax + By + C = 0 $, $ - \frac {A}{B} $?
The slope of a linear equation of the form $ Ax + By + C = 0 $ (general form) is given by $- \frac {A}{B} $. Could someone intuitively explain why we use this formula?
I've read that this is ...
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0answers
18 views
vertically −a/b units for every 1 unit of movement horizontally as it is to say that linear equations move vertically −a units…
So I have previously asked a question and the user was very much helpful. But I am still having difficulty with the problem. This is what I have done so far. Can someone please guide me in the right ...
0
votes
3answers
61 views
Explain why the slope of the equation is defined only for nonzero values of $b$. What happens when $b$ is zero?
Consider the equation $ax+by=c$ in 2-space and the slope for that equation where $a$ and $b$ are real numbers.
Explain why the slope of the equation is defined only for nonzero values of $b$. ...
0
votes
2answers
34 views
Consider the equation $ax + by = c$ in 2-space and the slope for that equation where $a$ and $b$ are real numbers.
Consider the equation $ax + by = c$ in 2-space and the slope for that equation where a and b
are real numbers.
Explain using multiple representations why it is equivalent to say that a linear ...
0
votes
2answers
40 views
Finding value(s) for x where the tangent line of f(x) has a slope of 4.
I have this equation $\frac{3}{4}x^4 - 4x^3 + \frac{1}{2}x^2 + 7$
I am trying to find the value(s) for $x$ where the tangent line of $f(x)$ has a slope of 4.
So I take my first derivative which I ...
0
votes
2answers
17 views
How do significant figures work in a cross unit division?
In one of my problems, I needed to find a slope on a graph with different units in physics.
309 cm² - 0.0 cm² / 100 cm - 0.0 cm
The answer is A = 3.09 r² with A being area and r² being radius ...
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0answers
10 views
Decrease Beta bewteen to variables
I have two time series of return data. One is global equity and one is a seperate stock. I would like to know if there is a theoretical way of decreasing the EQ Beta of the stock?
To be more clear: ...
0
votes
0answers
17 views
Slope and Expected Value of Percentile Ranks
Looking for help with this problem:
Assume a child's expected income percentile is a linear function of their parents' income percentile. It turns out the intercept is enough to deduce the slope. If ...
0
votes
1answer
39 views
A line in the xy-plane contains the points (5, 4) and (2, –1)
Question:
"A line in the $xy$-plane contains the points $(5, 4)$ and $(2, –1)$. Which is bigger: a) the slope of the line or b) $0$."
Result: They draw out the figure and say "you can see that the ...
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votes
0answers
19 views
How to measure the rate of decrease or increase of a particular stock in a specific time period
I need to measure the drop or increase of the value of a stock within a specific time frame. For example given a company XYZ, I need a formula to calculate the percentage change in value for stock XYZ ...
9
votes
1answer
117 views
If $\sigma: \mathbb{R}\to \mathbb{R}^2$ is a function that spirals,goes to infinity and repeats itself, then is $\sigma$ non-injetive?
Let $\sigma:\mathbb{R}\to \mathbb{R}^2$ be a smooth function such that $$\frac{\text{d}\sigma}{\text{d}t}(s) \neq 0, \quad \forall s \in \mathbb{R},$$ and
$$\sigma(t+n) = \sigma(n) +\sigma(t),\ \...
0
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0answers
138 views
find root-mean-square (RMS) of sawtooth waveform
bipolar sawtooth
I just want to make sure that I am right or not. I have to find Vrms of bipolar sawtooth waveform. The equation of RMS is
RMS equation
Slope I =
Y1 = 0
X1 = 0
Y2 = 3
X2 = 0.25
X(t)...
1
vote
2answers
102 views
How to find point in Descartes Folium with slope of -1/3?
I stumbled upon a problem in my calculus book that asked to find the point in $x^3 + y^3 = 3xy$ that had a slope perpendicualr to $y = 3x + 1$ and also was in the first quadrant.
I began by getting ...
1
vote
0answers
55 views
Find angle and slope of plane passing through 3 points. [closed]
I have a mesh of non-planar points that create triangular faces. I'm trying to find an equation to determine the angle and slope of a line that will create a sloped plane connecting all three points ...
1
vote
1answer
41 views
Find the slope of the line using least squares method
This question is taken from GATE 2005 ICE subject paper.
Using the given data points given below, a straight line passing through the origin is fitted using least squares method.
$$(x, y)$$
...
1
vote
2answers
126 views
Derivative of $\arcsin(\cos(x))$ at $x=0$.
We have to differentiate this function at $x=0$
$$\left. \dfrac{d \arcsin (\cos (x))}{dx} \right|_{x=0}$$
Using the identity $\cos x=\sin \Big(\dfrac{\pi}{2}-x\Big)$ we get
$$\left. \dfrac{d \arcsin (\...
1
vote
3answers
179 views
Graphing Inequality: 5x+10y >0 Saw the graph answer but I can't understand it.
The answer is a diagonal line that cuts through 0,0
Like in this website: https://www.symbolab.com/solver/step-by-step/5x%2B10y%3E0
My attempt:
5x + 10y(0) >0
5x>0
x>0
5x(0)+10y>0
10y>0
y>0
...
-2
votes
2answers
46 views
Rough estimation of the slope of the curve [closed]
I am very much confused on finding the slope the curve at a specific point on a graph. I know the process, draw a tangent at the point and then estimate $y$ units per $x$ units. I am doing that but it ...
1
vote
0answers
78 views
Justifying a Fundamental Theorm of Calculus Video
In this video, speed, defined as the distance traveled in one unit of time, is represented by rectangles on the distance-time (distance as a function of time) graph. At first, the examples stick to a ...
0
votes
0answers
39 views
How to see intuitively that for large values of $x$, the tangent from 1st quad. to 3rd quad. on cubic curve makes $270^\circ$.
This is in continuation to my earlier post at : Tangent to Cubic curve has positive slope.
It is discussed in earlier post (& before that) that given a cubic curve $y = x^3$, if tangents are ...
1
vote
1answer
123 views
Tangent to Cubic curve has positive slope.
This is in continuation to my earlier post at : How many times tangent to a cubic curve $y = x^3$ from a point on it, meets again at another point.
A brief summary of the previous post :
If take a ...
0
votes
1answer
45 views
Find the equation of tangent.
Original Question: Find the equation of the tangent at point P of parabola $x^2=4y$, which is at the minimum distance to center of a circle $x^2+y^2+6x+8=0$.
What i did:
Found coordinates of center ...
1
vote
0answers
87 views
Averaging the slope of multiple lines
I have 25 different trend lines. I'm interested in rate of change, which will be given by the slope of these lines.
While searching on the internet, i came across this interesting post, What good can ...
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votes
2answers
35 views
how to compare slope of two lines and find the angles in 3d
I have three points $A(x_1,y_1,z_1)$ ,$ B(x_2,y_2,z_2)$ and $C(x_3,y_3,z_3)$ and I want to compare the slopes of AB and BC and check the angles between them.
What should I do ?
Thanks in advance .
0
votes
4answers
146 views
Finding the equation of the line that is orthogonal to a tangent line to a Parabola y = x²
There is a parabola $y = x^2$. The question ask for the "a" of the equation $y = ax +$$3 \over 2$, which is the equation for the line that goes through the point $(0,$$3 \over 2$$)$ and is orthogonal ...
0
votes
1answer
86 views
While working with negative slopes, how to decide which slope is greater?
For an example, we take two lines L1 and L2. L1 makes 130 degrees with +ve X axis and has slope m1=tan(130 degrees)= -1.17. Similarly, L2 makes 150 degrees with +ve X axis and has slope m2= -0.577.
...
2
votes
1answer
20 views
Why can a slope field include points outside the domain of the original function?
I'm looking specifically at the slope field for $y'=\frac{2x}{y}$, which is the derivative of the function $2x^2-y^2=1$ (one of the solutions). But for no "family of functions" is a point, say $(0,1)$ ...
1
vote
3answers
97 views
What is intuition behind direction of derivative of a function?
I can't quite grasp the concept of the why gradient of a function points in the direction of steepest ascent. Thinking about it lead me to the basic notions of derivative, but here example first:
$$f(...
0
votes
2answers
48 views
Why slope of line defined as height to length? [closed]
I want to understand: why slope defined as ΔY/ΔX but not ΔX/ΔY ?
