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4 years ago

15

The start-up cost to join eTunes music is $7.95 plus $0.95 per song downloaded. If Will spent $26, write and solve a linear equa

tion to find how many songs he downloaded .

1 answer:

Oksanka [162]4 years ago

6 0

Y = 0.95x + 7.95
26 = 0.95x + 7.95
Solve for x
26-7.95 =0.95x
18.05/0.95 = x
X = 19 songs

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Varun’s neighborhood is having a Halloween party. His family donated 9 bags of candy with 115 pieces in every bag. Christy’s fam

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Answer :

Step-by-step explanation:

His family donated 9 bags of candy with 115 pieces in every bag.

Christy’s family donated 25 bags of candy with 40 pieces of candy in every bag.

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Christy : 30

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If there are 50 kids in the neighborhood, how many pieces will each child receive?

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3 years ago

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3 years ago

Find the common ratio of the geometric sequence. 9,-18, 36, -72

Agata [3.3K]

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2 years ago

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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

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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.

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

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2 years ago

Haley makes earrings and packages them into cube boxes that measure 1/6 foot wide. How many 1/6 foot cubic boxes can she fit int

alexandr402 [8]

Answer: 28 cube boxes.

Step-by-step explanation:

The volume of a cube can be found with this formula:

$V_{(c)}=s^3$

Where "s" is the lenght of any edge of the cube.

You need to find the volume of a cube box:

$V_1=s^3=(\frac{1}{6}ft)^3=\frac{1}{216}ft^3$

To find the volume of the shipping box, first we must convert the mixed number to an improper fraction. To do it, multiply the whole number part by the denominator of the fraction and add this product to the numerator.

The denominator does not change.

Then:

$1\ \frac{1}{6}=\frac{(1*6)+1}{6}=\frac{7}{6}$

Knowing the dimensions of the shipping box, you can calculate its volume by multiplying its dimensions. Then, this is:

$V_2=(\frac{7}{6}\ ft)(\frac{1}{3}\ ft)(\frac{1}{3}\ ft)=\frac{7}{54}\ ft^3$

Finally, in order to find the number of cube boxes can Haley fits into a shipping box, you must divide the the volume of the shipping box by the volume of one cube:

$\frac{\frac{7}{54}ft^3}{\frac{1}{216}ft^3}=28$

5 0

3 years ago