Ask question

Ask question

All categories

2 years ago

5

What is the value of this expression

" align="absmiddle" class="latex-formula">?

2 answers:

Oksi-84 [34.3K]2 years ago

7 0

$-8^3=-8\cdot8\cdot8=-512$

BARSIC [14]2 years ago

6 0

-8^3 = (-8)(-8)(-8) = -512

You might be interested in

Solve for XX. Assume XX is a 2×22×2 matrix and II denotes the 2×22×2 identity matrix. Do not use decimal numbers in your answer.

sveticcg [70]

The question is incomplete. The complete question is as follows:

Solve for X. Assume X is a 2x2 matrix and I denotes the 2x2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated.

$\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ · X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ =<em>I</em>.

First, we have to identify the matrix <em>I. </em>As it was said, the matrix is the identiy matrix, which means

<em>I</em> = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

So, $\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ · X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Isolating the X, we have

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ - $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Resolving:

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}2-1&8-0\\-6-0&-9-1\end{array}\right]$

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Now, we have a problem similar to A.X=B. To solve it and because we don't divide matrices, we do X=A⁻¹·B. In this case,

X= $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ ⁻¹· $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Now, a matrix with index -1 is called Inverse Matrix and is calculated as: A . A⁻¹ = I.

So,

$\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ · $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

9a - 3b = 1

7a - 6b = 0

9c - 3d = 0

7c - 6d = 1

Resolving these equations, we have a= $\frac{2}{11}$ ; b= $\frac{7}{33}$ ; c= $\frac{-1}{11}$ and d= $\frac{-3}{11}$ . Substituting:

X= $\left[\begin{array}{ccc}\frac{2}{11} &\frac{-1}{11} \\\frac{7}{33}&\frac{-3}{11} \end{array}\right]$ · $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Multiplying the matrices, we have

X= $\left[\begin{array}{ccc}\frac{8}{11} &\frac{26}{11} \\\frac{39}{11}&\frac{198}{11} \end{array}\right]$

6 0

2 years ago

A cylinder of height 16 is inscribed in a sphere of radius 10. What is the radius of the cylinder?

alexdok [17]

Answer:

6

Step-by-step explanation:

10² = r² + 8²

100 = r² + 64

r² = 36

r = 6

7 0

3 years ago

What is the mean number of hours worked that week?

Veseljchak [2.6K]

Answer:

well how menny hours per day?

Step-by-step explanation:

Mean is the middle

Median is the average

Mode is most often.

4 0

3 years ago

Two-step equations with decimals and fractions<br><br> Solve for p.<br><br> −5(p+ 3/5 )=−4

GrogVix [38]

Answer:

1/5 or 0.2

Step-by-step explanation:

-5(p+3/5)=-4

Let's convert 3/5 to decimal form:

-5(p+0.6)=-4

Expand parentheses:

-5p-3=-4

Add -3 to both sides:

-5p=-1

Divide both sides by -5:

p=1/5 or 0.2

Hope this helps!

4 0

2 years ago

Read 2 more answers

A circle as 75 square centimeters . Which answer is closest of the measure of its radius

olchik [2.2K]

Answer:

≈ 4.89

Step-by-step explanation:

A = πr²

75 = 3.14 x r²

r² = 75 / 3.14 = 23.89

r = 4.89

4 0

2 years ago