A Laplace expansion along the first row gives

$\begin{vmatrix}1&4&4\\5&2&1\\1&5&5\end{vmatrix}=1\begin{vmatrix}2&1\\5&5\end{vmatrix}-4\begin{vmatrix}5&1\\1&5\end{vmatrix}+4\begin{vmatrix}5&2\\1&5\end{vmatrix}$
$=1(10-5)-4(25-1)+4(25-2)$
$=1$

7 0

3 years ago

A student has a 2% salt water solution and a 7% salt water solution. To best imitate salt water at a local beach, he needs 1 lit

FromTheMoon [43]

Let

x-------> the amount of $2\%$ solution

y--------> the amount of $7\%$ solution

we know that

$2\%=0.02\\7\%=0.07\\3.5\%=0.035$

$x+y=1$

$y=1-x$ -------> equation A

$0.02x+0.07y=0.035$ -------> equation B

substitute equation A in equation B

$0.02x+0.07(1-x)=0.035$

$0.02x+0.07-0.07x=0.035$

$0.05x=0.035$

$x=0.7\ liters$

find the value of y

$y=1-x$

$y=1-0.7=0.3\ liters$

therefore

The student need $0.7\ liters$ of $2\%$ solution and $0.3\ liters$ of $7\%$ solution

<u>the answer is</u>

A) The percent values were written incorrectly in the equation

B) The amount of 7% solution should be written as 1 – x, not x – 1.

8 0

2 years ago

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