Complete parallel side 2

Mathematics

1 answer:

Gnoma [55]3 years ago

8 0

Step-by-step explanation:

Assume length of side 2 = L

Area of parallelogram is Height x L

So, 72 = 8 x L

L = 9

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The graph shows the number of handbags that mandy made in one day.What are the variables? Describe how the variables are related

tankabanditka [31]

The variables are: time(the independent variable or (x) variable) and number of handbags (the dependent variable or (y) variable). The variables helps to plot an accurate points on the graph.

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3 years ago

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What is the mass of 2.5 moles of carbon dioxide?

GarryVolchara [31]

Answer:

110 grams

Step-by-step explanation:

CO2 molecule is made up of Carbon (atomic mass =12) and oxygen (atomic mass=16).

So first finding the mass of 1 molecule of CO2 which is equals to

= mass of 1 carbon atom + masses of 2 oxygen atom, we get

= 12+(16*2)= 12+32= 44 a.m.u.

Now 1 molecule of CO2 has mass 44 amu so mass of 1 mole CO2 will be 44 grams.( 1 a.m.u.=1.6729*10^-33 grams. 1 mole = 6.022*10^23, so 44 a.m.u.=73.6076*10^-33 grams approx. For one mole CO2, 73.6076*10^-33*6.022*10^23 which is approximately equals to 44 grams. )

1 mole CO2= 44grams, so 2.5 moles = 44*2.5= 110 grams

So our answer is 110 grams.

lowkey hope this helped you, good luck whatever you need it for Imaooo

3 0

3 years ago

Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).

I am Lyosha [343]

Take the homogeneous part and find the roots to the characteristic equation:

$y''+4y=0\implies r^2+4=0\implies r=\pm2i$

This means the characteristic solution is $y_c=C_1\cos2x+C_2\sin2x$ .

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form $y_p=ax\cos2x+bx\sin2x$ . Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With $y_1=\cos2x$ and $y_2=\sin2x$ , you're looking for a particular solution of the form $y_p=u_1y_1+u_2y_2$ . The functions $u_i$ satisfy

$u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx$
$u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx$

where $W(y_1,y_2)$ is the Wronskian determinant of the two characteristic solutions.

$W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2$

So you have

$u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx$
$u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x$

$u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx$
$u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x$

So you end up with a solution

$u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x$

but since $\cos2x$ is already accounted for in the characteristic solution, the particular solution is then

$y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x$

so that the general solution is

$y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x$