Phoebe
2021-02-12
Answered

Manuel has $54 to buy CDs and books. Each CD costs $9, and each book costs $6. He wants to buy exactly 7 items to spend all of his money. Write a system of equations that could be solved to determine the number of CDs and the number of books Manuel buys.

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asked 2022-06-25

When solving systems of equations for first-year physics, I am told that to be able to find the solution for a system of n unknowns (if one exists), I need at least n equations.

In this system, I am looking for $a$. The known quantities are ${\theta}_{0}$ and ${\theta}_{1}$.

${T}_{0}\mathrm{cos}{\theta}_{0}=mg$

${T}_{0}\mathrm{sin}{\theta}_{0}=\frac{m{v}^{2}}{\ell \mathrm{sin}{\theta}_{0}}$

${T}_{1}\mathrm{cos}{\theta}_{1}-mg=ma$

${T}_{1}\mathrm{sin}{\theta}_{1}=\frac{m{v}^{2}}{\ell \mathrm{sin}{\theta}_{1}}$

In this system of equations, I had 5 unknown quantities: ${T}_{0}$, ${T}_{1}$, $m$, $\ell $, $a$. But I was able to successfully solve for $a$ with four equations. Where is the logical error in my understanding?

In this system, I am looking for $a$. The known quantities are ${\theta}_{0}$ and ${\theta}_{1}$.

${T}_{0}\mathrm{cos}{\theta}_{0}=mg$

${T}_{0}\mathrm{sin}{\theta}_{0}=\frac{m{v}^{2}}{\ell \mathrm{sin}{\theta}_{0}}$

${T}_{1}\mathrm{cos}{\theta}_{1}-mg=ma$

${T}_{1}\mathrm{sin}{\theta}_{1}=\frac{m{v}^{2}}{\ell \mathrm{sin}{\theta}_{1}}$

In this system of equations, I had 5 unknown quantities: ${T}_{0}$, ${T}_{1}$, $m$, $\ell $, $a$. But I was able to successfully solve for $a$ with four equations. Where is the logical error in my understanding?

asked 2022-05-23

Is the following equation regarded as a linear equation?

$0{x}_{1}+0{x}_{2}+0{x}_{3}=5$

The original question is as below:

Solve the linear system given by the following augmented matrix:

$\left(\begin{array}{cccc}2& 2& 3& 1\\ 2& 5& 3& 0\\ 0& 0& 0& 5\end{array}\right)$

Note the words linear system in the original question. So, I was asking myself whether $0{x}_{1}+0{x}_{2}+0{x}_{3}=5$ is a linear equation. Can we call all of the equations given by the matrix collectively as a linear system?

$0{x}_{1}+0{x}_{2}+0{x}_{3}=5$

The original question is as below:

Solve the linear system given by the following augmented matrix:

$\left(\begin{array}{cccc}2& 2& 3& 1\\ 2& 5& 3& 0\\ 0& 0& 0& 5\end{array}\right)$

Note the words linear system in the original question. So, I was asking myself whether $0{x}_{1}+0{x}_{2}+0{x}_{3}=5$ is a linear equation. Can we call all of the equations given by the matrix collectively as a linear system?

asked 2021-08-11

Two lines , P and Q , are graphed:

asked 2022-05-29

System of equations with n unknowns

How should explain solving a system of n unknowns we need n equations?

How should explain solving a system of n unknowns we need n equations?

asked 2022-05-07

Solve for the variables y and z in the system of equations:

$\{\begin{array}{l}6y+2z=-5\\ 4y+2z=3\end{array}$

$\{\begin{array}{l}6y+2z=-5\\ 4y+2z=3\end{array}$

asked 2022-06-25

For ${x}^{\prime}=y$, and ${y}^{\prime}=-x-y$, Find all equilibrium points and decide whether they are stable, asymptotically stable, or unstable.

I found that the equilibrium points are $(0,0)$. Then I try to find the eigenvalues. The characteristic equation I found is $\lambda +{\lambda}^{2}+1=0$. I realize that they are complex eigenvalues...The real part of this complex eigenvalues are negative. Does this mean this is stable ? Is this also asymptotically stable? What are the differences between asymptotically stable and stable?

I found that the equilibrium points are $(0,0)$. Then I try to find the eigenvalues. The characteristic equation I found is $\lambda +{\lambda}^{2}+1=0$. I realize that they are complex eigenvalues...The real part of this complex eigenvalues are negative. Does this mean this is stable ? Is this also asymptotically stable? What are the differences between asymptotically stable and stable?

asked 2022-08-03

Solve the following system of equations. If there are no solutions, type "No Solution" for both x and y. If there are infinitely many solutions, type "x" for x, and an expression in terms of x for y.

1 x + 3 y = 8

2 x + 6 y = 16

x =

y =

1 x + 3 y = 8

2 x + 6 y = 16

x =

y =