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3 years ago

What is the total volume of the cube below? Each block represents 1 unit.

Mathematics

2 answers:

Galina-37 [17]3 years ago

6 0

The answer is D. 125
Can you please mark me brainiest!!!!

Marrrta [24]3 years ago

4 0

Answer:125

Step-by-step explanation:firts you count your width height and thength which are all 5 them multiply them together which with give you your answer

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Determine the values of the constants r and s such that i(x, y) = x rys is an integrating factor for the given differential equa

garri49 [273]

$\underbrace{y(7xy^2+6)}_{M(x,y)}\,\mathrm dx+\underbrace{x(xy^2-1)}_{N(x,y)}\,\mathrm dy=0$

For the ODE to be exact, we require that $M_y=N_x$ , which we'll verify is not the case here.

$M_y=21xy^2+6$
$N_x=2xy^2-1$

So we distribute an integrating factor $i(x,y)$ across both sides of the ODE to get

$iM\,\mathrm dx+iN\,\mathrm dy=0$

Now for the ODE to be exact, we require $(iM)_y=(iN)_x$ , which in turn means

$i_yM+iM_y=i_xN+iN_x\implies i(M_y-N_x)=i_xN-i_yM$

Suppose $i(x,y)=x^ry^s$ . Then substituting everything into the PDE above, we have

$x^ry^s(19xy^2+7)=rx^{r-1}y^s(x^2y^2-x)-sx^ry^{s-1}(7xy^3+6y)$
$19x^{r+1}y^{s+2}+7x^ry^s=rx^{r+1}y^{s+2}-rx^ry^s-7sx^{r+1}y^{s+2}-6sx^ry^s$
$19x^{r+1}y^{s+2}+7x^ry^s=(r-7s)x^{r+1}y^{s+2}-(r+6s)x^ry^s$
$\implies\begin{cases}r-7s=19\\r+6s=-7\end{cases}\implies r=5,s=-2$

so that our integrating factor is $i(x,y)=x^5y^{-2}$ . Our ODE is now

$(7x^6y+6x^5y^{-1})\,\mathrm dx+(x^7-x^6y^{-2})\,\mathrm dy=0$

Renaming $M(x,y)$ and $N(x,y)$ to our current coefficients, we end up with partial derivatives

$M_y=7x^6-6x^5y^{-2}$
$N_x=7x^6-6x^5y^{-2}$

as desired, so our new ODE is indeed exact.

Next, we're looking for a solution of the form $\Psi(x,y)=C$ . By the chain rule, we have

$\Psi_x=7x^6y+6x^5y^{-1}\implies\Psi=x^7y+x^6y^{-1}+f(y)$

Differentiating with respect to $y$ yields

$\Psi_y=x^7-x^6y^{-2}=x^7-x^6y^{-2}+\dfrac{\mathrm df}{\mathrm dy}$
$\implies\dfrac{\mathrm df}{\mathrm dy}=0\implies f(y)=C$

Thus the solution to the ODE is

$\Psi(x,y)=x^7y+x^6y^{-1}=C$

4 0

3 years ago

Sorting an excel table

Lana71 [14]

Sort data in a table

Select a cell within the data.

Select Home > Sort & Filter. Or, select Data > Sort.

Select an option: Sort A to Z - sorts the selected column in an ascending order. Sort Z to A - sorts the selected column in a descending order. Custom Sort - sorts data in multiple columns by applying different sort criteria.

6 0

3 years ago

The solutions to the equation 2x2+x-1=2 are X= -3/2 or x=

Brilliant_brown [7]

Answer:

positive 3/2

Step-by-step explanation:

3 0

3 years ago

What are the answers

gulaghasi [49]

Answer and Step-by-step explanation:

7. 70 - 180 = 110

8. 39 - 180 = 141

9. 81 - 180 = 99

10. 81 - 180 = 99

11. 115 - 180 = 65

12. 41+36 = 77 - 180 = 103

x = answer

4 0

3 years ago

A researcher is interested in the texting habits of high school students in the United States. The researcher selects a group of

vlabodo [156]

Answer:

(a)High school students in the United States.

(b)100 Students

(c)Statistic

Step-by-step explanation:

(a)Since the researcher is interested in the texting habits of high school students in the United States, the population for this study consists of all high school students in the United States.

(b)It is most often improbable to carry out research on an entire population of study. A <u>sample is taken to represent the population</u> and the results obtained from the sample are assumed to hold for the entire population.

In the given study, the researcher selects a group of 100 students to represent the High School students in the United States. This is the sample for the study.

(c)The researcher calculated the average number of text messages that each individual sends each day from the sample of 100 Students. This is an example of a Statistic. A statistic is a numerical data obtained from a sample.

Note: If the data were obtained from the entire population, it would be a <u>parameter.</u>

3 0

3 years ago