All categories

3 years ago

The symbol ≅ means...

Mathematics

2 answers:

SSSSS [86.1K]3 years ago

6 0

Congruent....hope this helped you out.

Xelga [282]3 years ago

5 0

The symbol means that it is congruent.

You might be interested in

Are 0.34 and 3/4 equivalent? Please explain your answer In complete sentences.

insens350 [35]

No

when 3 divided by 4 is converted into a decimal, it is 0.75 which does not equal 0.34

0.34 can also be written as 34/100
and 3/4 can be written as 75/100

therefore 0.34 and 3/4 are not equivalent

7 0

3 years ago

Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +

slava [35]

$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
$=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta$

When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
$=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta$

and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

6 0

3 years ago

How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the i

pishuonlain [190]

Answer:

In total, $120$ permutations of three items can be selected from a group of six distinct elements.

In particular, there are $6$ ways to order three distinct items.

$\begin{aligned}\rm B-D-F \\ \rm B-F-D \\ \rm D-B-F \\ \rm D-F-B \\ \rm F-B-D \\ \rm F-D-B\end{aligned}$ .

Step-by-step explanation:

The formula $\displaystyle P(n,\, r) = \frac{n!}{(n - r)!} = n \, (n - 1) \cdots (n - r + 1)$ gives the number of ways to select and order $r$ items from a group of $n$ distinct elements.

To select and order three items from a group six distinct elements, let $n = 6$ and $r = 3$ . Apply the formula:

$\begin{aligned} P(6,\, 3) &= \frac{6!}{(6 - 3)!} = \frac{6!}{3!} \\ &= \frac{6 \times 5 \times 4 \times 3\times 2 \times 1}{3 \times 2 \times 1} \\ &= 6 \times 5 \times 4 = 120 \end{aligned}$ .

In other words, there are $120$ unique ways to select and order three items (select a permutation of three items) from a group of six distinct elements.

Consider: what's the number of ways to order three distinct items? That's the same as asking: how many ways are there to select and order three items from a group of three distinct elements? Let $n =3$ and $r = 3$ . Apply the formula for permutation:

$\begin{aligned} P(3,\, 3) &= \frac{3!}{(3 - 3)!} = \frac{3!}{0!} && \left(\text{$0! = 1$ by convention.}\right) \\ &= 3! = 3 \times 2\times 1 \\ &= 6\end{aligned}$ .

To find the permutations, start by selecting one element as the first of the list. A tree diagram might be helpful. Refer to the attachment for an example.