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lara [203]
3 years ago
7

Mitchell deposited $651.37 in a savings account that earns 3.9% simple interest what is Mitchell's account balance after 15 year

s
Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
4 0
The formula to find the account balance is
A=p (1+rt)
A account balance?
P amount deposited 651.37
R interest rate 0.039
T time 15 years
A=651.37×(1+0.039×15)
A=1,032.42

Hope it helps!
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We have f(x)=\dfrac{x+5}{3x-1}.

To find inverse function f^{-1}(x) we substitute x with f^{-1}(x) and vice-versa to get

x=\dfrac{f^{-1}(x)+5}{3f^{-1}(x)-1}

Now solve for f^{-1}(x). Note that I will use j instead.

x=\dfrac{j+5}{3j-1} \\x(3j-1)=j+5 \\3jx-x=j+5 \\3jx-x-j-5=0 \\3jx-j=x+5 \\j(3x-1)=x+5 \\j=\dfrac{x+5}{3x-1}

So we find that f(x)=f^{-1}.

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Solve the system of equations by row-reduction. At each step, show clearly the symbol of the linear combinations that allow you
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Answer:

1) The solution of the system is

\left\begin{array}{ccc}x_1&=&5\\x_2&=&8\\x_3&=&-13\end{array}\right

2) The solution of the system is

\left\begin{array}{ccc}x_1&=&2\\x_2&=&-7\\x_3&=&-1\end{array}\right

Step-by-step explanation:

1) To solve the system of equations

\left\begin{array}{ccccccc}&3x_2&-5x_3&=&89\\6x_1&&+x_3&=&17\\x_1&-x_2&+8x_3&=&-107\end{array}\right

using the row reduction method you must:

Step 1: Write the augmented matrix of the system

\left[ \begin{array}{ccc|c} 0 & 3 & -5 & 89 \\\\ 6 & 0 & 1 & 17 \\\\ 1 & -1 & 8 & -107 \end{array} \right]

Step 2: Swap rows 1 and 2

\left[ \begin{array}{ccc|c} 6 & 0 & 1 & 17 \\\\ 0 & 3 & -5 & 89 \\\\ 1 & -1 & 8 & -107 \end{array} \right]

Step 3:  \left(R_1=\frac{R_1}{6}\right)

\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 3 & -5 & 89 \\\\ 1 & -1 & 8 & -107 \end{array} \right]

Step 4: \left(R_3=R_3-R_1\right)

\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 3 & -5 & 89 \\\\ 0 & -1 & \frac{47}{6} & - \frac{659}{6} \end{array} \right]

Step 5: \left(R_2=\frac{R_2}{3}\right)

\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & -1 & \frac{47}{6} & - \frac{659}{6} \end{array} \right]

Step 6: \left(R_3=R_3+R_2\right)

\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & 0 & \frac{37}{6} & - \frac{481}{6} \end{array} \right]

Step 7: \left(R_3=\left(\frac{6}{37}\right)R_3\right)

\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & 0 & 1 & -13 \end{array} \right]

Step 8: \left(R_1=R_1-\left(\frac{1}{6}\right)R_3\right)

\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 5 \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & 0 & 1 & -13 \end{array} \right]

Step 9: \left(R_2=R_2+\left(\frac{5}{3}\right)R_3\right)

\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 5 \\\\ 0 & 1 & 0 & 8 \\\\ 0 & 0 & 1 & -13 \end{array} \right]

Step 10: Rewrite the system using the row reduced matrix:

\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 5 \\\\ 0 & 1 & 0 & 8 \\\\ 0 & 0 & 1 & -13 \end{array} \right] \rightarrow \left\begin{array}{ccc}x_1&=&5\\x_2&=&8\\x_3&=&-13\end{array}\right

2) To solve the system of equations

\left\begin{array}{ccccccc}4x_1&-x_2&+3x_3&=&12\\2x_1&&+9x_3&=&-5\\x_1&+4x_2&+6x_3&=&-32\end{array}\right

using the row reduction method you must:

Step 1:

\left[ \begin{array}{ccc|c} 4 & -1 & 3 & 12 \\\\ 2 & 0 & 9 & -5 \\\\ 1 & 4 & 6 & -32 \end{array} \right]

Step 2: \left(R_1=\frac{R_1}{4}\right)

\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 2 & 0 & 9 & -5 \\\\ 1 & 4 & 6 & -32 \end{array} \right]

Step 3: \left(R_2=R_2-\left(2\right)R_1\right)

\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 0 & \frac{1}{2} & \frac{15}{2} & -11 \\\\ 1 & 4 & 6 & -32 \end{array} \right]

Step 4: \left(R_3=R_3-R_1\right)

\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 0 & \frac{1}{2} & \frac{15}{2} & -11 \\\\ 0 & \frac{17}{4} & \frac{21}{4} & -35 \end{array} \right]

Step 5: \left(R_2=\left(2\right)R_2\right)

\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 0 & 1 & 15 & -22 \\\\ 0 & \frac{17}{4} & \frac{21}{4} & -35 \end{array} \right]

Step 6: \left(R_1=R_1+\left(\frac{1}{4}\right)R_2\right)

\left[ \begin{array}{cccc} 1 & 0 & \frac{9}{2} & - \frac{5}{2} \\\\ 0 & 1 & 15 & -22 \\\\ 0 & \frac{17}{4} & \frac{21}{4} & -35 \end{array} \right]

Step 7: \left(R_3=R_3-\left(\frac{17}{4}\right)R_2\right)

\left[ \begin{array}{ccc|c} 1 & 0 & \frac{9}{2} & - \frac{5}{2} \\\\ 0 & 1 & 15 & -22 \\\\ 0 & 0 & - \frac{117}{2} & \frac{117}{2} \end{array} \right]

Step 8: \left(R_3=\left(- \frac{2}{117}\right)R_3\right)

\left[ \begin{array}{cccc} 1 & 0 & \frac{9}{2} & - \frac{5}{2} \\\\ 0 & 1 & 15 & -22 \\\\ 0 & 0 & 1 & -1 \end{array} \right]

Step 9: \left(R_1=R_1-\left(\frac{9}{2}\right)R_3\right)

\left[ \begin{array}{cccc} 1 & 0 & 0 & 2 \\\\ 0 & 1 & 15 & -22 \\\\ 0 & 0 & 1 & -1 \end{array} \right]

Step 10: \left(R_2=R_2-\left(15\right)R_3\right)

\left[ \begin{array}{cccc} 1 & 0 & 0 & 2 \\\\ 0 & 1 & 0 & -7 \\\\ 0 & 0 & 1 & -1 \end{array} \right]

Step 11:

\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 2 \\\\ 0 & 1 & 0 & -7 \\\\ 0 & 0 & 1 & -1 \end{array} \right]\rightarrow \left\begin{array}{ccc}x_1&=&2\\x_2&=&-7\\x_3&=&-1\end{array}\right

8 0
3 years ago
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