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Tju [1.3M]
3 years ago
14

The area of a rectangle increased by seven is the same as for less than twice the area of the rectangle. Right and solve an equa

tion to determine the area of the rectangle
Mathematics
1 answer:
never [62]3 years ago
7 0

Answer:

11 Square Units

Step-by-step explanation:

Let A be the area of the Rectangle

First statement: The area of the rectangle is increased by seven, we have :

A+7

Second Statement: Four less than twice the area of the rectangle

Twice the Area=2A

Four less = 2A-4

Therefore:

2A-4=A+7

Collecting like terms

2A-A =7+4

A=11

The area of the rectangle is 11 Square Units.

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Answer:

The matrix form of given linear system is

\begin{bmatrix}x'\\ y'\\ z'\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}

Step-by-step explanation:

Let as assume that

X=\begin{bmatrix}x\\ y\\ z\end{bmatrix}

Given differential equations are

\frac{dx}{dt}=-8x+7y-9z

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\frac{dz}{dt}=10x+7y+8z

We need to find the matrix form of given linear system.

Write the elements of left side in a column matrix.

Write all the coefficients in one matrix first which is called a coefficient matrix.  Multiply coefficient matrix with the variables matrix and equate left and right side.

\begin{bmatrix}\frac{dx}{dt}\\ \frac{dy}{dt}\\ \frac{dz}{dt}\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}

It can be written as

\begin{bmatrix}x'\\ y'\\ z'\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}

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