How do you write an equation in point-slope form for the given (-2,-7) and (3,1)?

hiposopj
2022-09-13
Answered

How do you write an equation in point-slope form for the given (-2,-7) and (3,1)?

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asked 2021-06-01

Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2021-09-12

Do the equations
5y−2x=18

and

6x=−4y−10

form a system of linear equations? Explain.

and

6x=−4y−10

form a system of linear equations? Explain.

asked 2022-05-19

While studying linear algebra I encountered the following result regarding the solutions of a non homogeneous system of linear equations: if $Sol(A,b\phantom{\rule{1px}{0ex}}b)\ne \mathrm{\varnothing}$

$Sol(A,b\phantom{\rule{1px}{0ex}}b)=x\phantom{\rule{1px}{0ex}}x+Sol(A,0\phantom{\rule{1px}{0ex}}0)$

Where x is a particular solution.

Then, while studying differential equations, I found that the solutions for

${y}^{\prime}=a(x)y+b(x)$

are all of the form

$y={y}_{p}+C{e}^{A(x)}$

Where the last term refers to the solutions of the associate homogeneous equation and ${y}_{p}$ is a particular solution.

These two concepts seem related to me, but I've not been able to find/think about a satisfying reason, so I'd like to know whether there is actually a relation or not.

I should specify that I've not been able to study properly systems of differential equations of the first order or equations of the n-th order yet, I suspect that the answer is there but I can't be sure. However I'd like to get the complete answer, so if it involves the latter topics it's not a problem.

$Sol(A,b\phantom{\rule{1px}{0ex}}b)=x\phantom{\rule{1px}{0ex}}x+Sol(A,0\phantom{\rule{1px}{0ex}}0)$

Where x is a particular solution.

Then, while studying differential equations, I found that the solutions for

${y}^{\prime}=a(x)y+b(x)$

are all of the form

$y={y}_{p}+C{e}^{A(x)}$

Where the last term refers to the solutions of the associate homogeneous equation and ${y}_{p}$ is a particular solution.

These two concepts seem related to me, but I've not been able to find/think about a satisfying reason, so I'd like to know whether there is actually a relation or not.

I should specify that I've not been able to study properly systems of differential equations of the first order or equations of the n-th order yet, I suspect that the answer is there but I can't be sure. However I'd like to get the complete answer, so if it involves the latter topics it's not a problem.

asked 2022-06-09

Question: Given a system of linear equations

$a{x}_{1}+a{x}_{2}+a{x}_{3}=2\phantom{\rule{0ex}{0ex}}{x}_{1}+a{x}_{2}+a{x}_{3}=0\phantom{\rule{0ex}{0ex}}2{x}_{1}+3{x}_{2}+a{x}_{3}=1$

For what 2 values of $a$ will the system's augmented matrix have less than 3 pivots?

I'm not looking for an answer to the question, but I'm currently using trial and error to try and form a row 0000, and was wondering if there's some conceptual understating I'm missing that would point to a more logical strategy for finding $a$?

$a{x}_{1}+a{x}_{2}+a{x}_{3}=2\phantom{\rule{0ex}{0ex}}{x}_{1}+a{x}_{2}+a{x}_{3}=0\phantom{\rule{0ex}{0ex}}2{x}_{1}+3{x}_{2}+a{x}_{3}=1$

For what 2 values of $a$ will the system's augmented matrix have less than 3 pivots?

I'm not looking for an answer to the question, but I'm currently using trial and error to try and form a row 0000, and was wondering if there's some conceptual understating I'm missing that would point to a more logical strategy for finding $a$?

asked 2022-09-04

61 is the difference between Carlos's age and 23. How do you write this as an equation?

asked 2022-02-15

My book says the general form of a linear differential equation is:

${y}^{\prime}+P\left(x\right)y=Q\left(x\right)$

But my teacher said that a linear differential equation has the general form:

$y{}^{\u2033}+P\left(x\right){y}^{\prime}+Q\left(x\right)y=f\left(x\right)$

Which is the correct form or they are both correct?

But my teacher said that a linear differential equation has the general form:

Which is the correct form or they are both correct?

asked 2022-07-07

I would like to find the closed form of the sequence given by

${a}_{n+2}=2{a}_{n+1}-{a}_{n}+{2}^{n}+2,\text{}\text{}\text{}\text{}n0\text{}\text{}\text{}\text{}and\text{}\text{}\text{}{a}_{1}=1,\text{}\text{}\text{}\text{}{a}_{2}=4$

This task is in the topic of differential and difference equation. I don't know how to start solving this problem and what are we looking for? (${a}_{n},{a}_{n+2}$)

I do know how to solve the following form

${a}_{n+2}=2{a}_{n+1}-{a}_{n}$

using linear algebra as well. The actual problem I encountered the obstructionist term ${{2}^{n}+2}$

Are there some kind of variational constant method for recursive linear sequences,?

I only now this method for linear ODE with constant coefficient.

But I believe that such method could be doable here as well. Can any one provide me with a helpful hint or answer?.

${a}_{n+2}=2{a}_{n+1}-{a}_{n}+{2}^{n}+2,\text{}\text{}\text{}\text{}n0\text{}\text{}\text{}\text{}and\text{}\text{}\text{}{a}_{1}=1,\text{}\text{}\text{}\text{}{a}_{2}=4$

This task is in the topic of differential and difference equation. I don't know how to start solving this problem and what are we looking for? (${a}_{n},{a}_{n+2}$)

I do know how to solve the following form

${a}_{n+2}=2{a}_{n+1}-{a}_{n}$

using linear algebra as well. The actual problem I encountered the obstructionist term ${{2}^{n}+2}$

Are there some kind of variational constant method for recursive linear sequences,?

I only now this method for linear ODE with constant coefficient.

But I believe that such method could be doable here as well. Can any one provide me with a helpful hint or answer?.