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3 years ago

What is the simplest form of 18/24?

Mathematics

2 answers:

Zepler [3.9K]3 years ago

8 0

$\frac{18}{24}=\frac{3 \times 6}{4 \times 6}=\boxed{\frac{3}{4}}$

jeka943 years ago

3 0

The simplest form of 18/24 is 3/4.
18 can be divided by 6 to get 3.
24 can be divided by 6 to get 4.
The answer should be 3/4.

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Use the given transformation to evaluate the integral. double integral 9xy dA R , where R is the region in the first quadrant bo

lianna [129]

It looks like the boundaries of $R$ are the lines $y=\dfrac23x$ and $y=3x$ , as well as the hyperbolas $xy=\frac23$ and $xy=3$ . Naturally, the domain of integration is the set

$R = \left\{(x,y) ~:~ \dfrac{2x}3 \le y \le 3x \text{ and } \dfrac23 \le xy \le 3 \right\}$

By substituting $x=\frac uv$ and $y=v$ , so $xy=u$ , we have

$\dfrac23 \le xy \le 3 \implies \dfrac23 \le u \le 3$

and

$\dfrac{2x}3 \le y \le 3x \implies \dfrac{2u}{3v} \le v \le \dfrac{3u}v \implies \dfrac{2u}3 \le v^2 \le 3u \implies \sqrt{\dfrac{2u}3} \le v \le \sqrt{3u}$

so that

$R = \left\{(u,v) ~:~ \dfrac23 \le u \le 3 \text{ and } \sqrt{\dfrac{2u}3 \le v \le \sqrt{3u}\right\}$

Compute the Jacobian for this transformation and its determinant.

$J = \begin{bmatrix}x_u & x_v \\ y_u & y_v\end{bmatrix} = \begin{bmatrix}\dfrac1v & -\dfrac u{v^2} \\\\ 0 & 1 \end{bmatrix} \implies \det(J) = \dfrac1v$

Then the area element under this change of variables is

$dA = dx\,dy = \dfrac{du\,dv}v$

and the integral transforms to

$\displaystyle \iint_R 9xy \, dA = \int_{2/3}^3 \int_{\sqrt{2u/3}}^{\sqrt{3u}} \frac{dv\,du}v$

Now compute it.

$\displaystyle \iint_R 9xy \, dA = \int_{2/3}^3 \ln|v|\bigg|_{v=\sqrt{2u/3}}^{v=\sqrt{3u}} \,du \\\\ ~~~~~~~~ = \int_{2/3}^3 \ln\left(\sqrt{3u}\right) - \ln\left(\sqrt{\frac{2u}3}\right) \, du \\\\ ~~~~~~~~ = \frac12 \int_{2/3}^3 \ln(3u) - \ln\left(\frac{2u}3\right) \, du \\\\ ~~~~~~~~ = \frac12 \int_{2/3}^3 \ln\left(\frac{3u}{\frac{2u}3}\right) \, du \\\\ ~~~~~~~~ = \frac12 \ln\left(\frac92\right) \int_{2/3}^3 du \\\\ ~~~~~~~~ = \frac12 \ln\left(\frac92\right) \left(3-\frac23\right) = \boxed{\frac76 \ln\left(\frac92\right)}$

7 0

2 years ago

17+(−8)+(−8) CAN YOU HELP GUY pls

professor190 [17]

Answer:

Step-by-step explanation:

17 + (-8) + (-8) = 17 + (-16)

= 1

If two numbers have same sign, then add and put the sign.

So, add (-8)and (-8), the result will have the sign (-). -16

If two numbers have different sign, subtract and the result will have the sign of the bigger number.

17 and (-16) have different sign and the bigger number sign is +

So, the result is 1

3 0

3 years ago

Read 2 more answers

Which quadrant would the ordered pair (-10, 8) be located in?

goldfiish [28.3K]

Answer:

Quadrant 2

Step-by-step explanation:

Hope this helps :D Have a great day

5 0

3 years ago

Ok if you can figure this out right your legend

Zigmanuir [339]

-20 + -3

-10 + -13

-15 + -8

-5 + -18

I hope this helps!

8 0

3 years ago

a book charges a member fee of $15.Each book costs $2 to buy .Write an expression that represents the amount a customer spends f

AleksandrR [38]

2b+15
2 dollars for each book so you multiply it by the number of books and add 15 because it is a one time fee.

4 0

3 years ago