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3 years ago

Find the values of the variables

Mathematics

1 answer:

Umnica [9.8K]3 years ago

7 0

Looks like you're given an equality between two matrices,

$\begin{bmatrix}-12&-w^2\\2f&3\end{bmatrix}=\begin{bmatrix}2k&-81\\-14&3\end{bmatrix}$

Two matrices are equal if the entries in the same positions (row and column) are equal. This means

$\begin{cases}-12=2k\\-w^2=-81\\2f=-14\\3=3\end{cases}$

We can ignore the last one, since it's clearly true. For the remaining, we get

$-12=2k\implies k=-\dfrac{12}2=-6$

$-w^2=-81\implies w^2=81\implies w=\pm9$

$2f=-14\implies f=-\dfrac{14}2=-7$

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Read 2 more answers

What is 11 1/2 + 10 11/16=

ahrayia [7]

Hey!

To solve this equation, we must first convert the mixed numbers into improper fractions. To do that we'll multiply the denominator by the whole number and add the total to the numerator.

Original Equation :

$11\frac{1}{2} + 10\frac{11}{16} = ?$

New Equation {Converted Mixed Numbers Into Improper Fractions} :

$\frac{23}{2} + \frac{171}{16} = ?$

Now that we've successfully changed our equation, we'll move onto the next step. Next we'll have change the fractions one more time so that the denominators are the same. To do that we'll multiply two by eight to get sixteen. We'll also be multiplying the top portion of the fraction by eight, because whatever you do to the bottom must also be done to the top; And vise versa.

Fraction Conversion :

$\frac{23*8}{2*8} = \frac{184}{16}$

So, now that we have our new fraction we can go ahead and plug that into our equation so we can start adding. Remember, we don't add the denominators, just the numerators.

Old Equation :

$\frac{23}{2} + \frac{171}{16} = ?$

New Equation {Input New Fraction With Common Denominator} :

$\frac{184}{16} +\frac{171}{16} = ?$

Solution {New Equation Solved} :

$\frac{355}{16}$

Now I'm not exactly sure how your instructor will accept your answer, but most prefer the final answer to be in the simplest form. In other words, they don't want it in the form of an improper fraction. They'd most likely rather have it as a mixed number.

New Solution {Converted to a Mixed Number} :

$22\frac{3}{16}$