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2 years ago

What expression has the same meaning as 2 7/4

Mathematics

1 answer:

Reptile [31]2 years ago

3 0

<h3><em><u>Question:What expression has the same meaning as 2 7/4?</u></em></h3>

<h3><em><u>Step-by-step explanation:15/4 also means 2 7/4 if that's what you mean.</u></em></h3>

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Find all the solutions for the equation:

Contact [7]

$2y^2\,\mathrm dx-(x+y)^2\,\mathrm dy=0$

Divide both sides by $x^2\,\mathrm dx$ to get

$2\left(\dfrac yx\right)^2-\left(1+\dfrac yx\right)^2\dfrac{\mathrm dy}{\mathrm dx}=0$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2\left(\frac yx\right)^2}{\left(1+\frac yx\right)^2}$

Substitute $v(x)=\dfrac{y(x)}x$ , so that $\dfrac{\mathrm dv(x)}{\mathrm dx}=\dfrac{x\frac{\mathrm dy(x)}{\mathrm dx}-y(x)}{x^2}$ . Then

$x\dfrac{\mathrm dv}{\mathrm dx}+v=\dfrac{2v^2}{(1+v)^2}$

$x\dfrac{\mathrm dv}{\mathrm dx}=\dfrac{2v^2-v(1+v)^2}{(1+v)^2}$

$x\dfrac{\mathrm dv}{\mathrm dx}=-\dfrac{v(1+v^2)}{(1+v)^2}$

The remaining ODE is separable. Separating the variables gives

$\dfrac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=-\dfrac{\mathrm dx}x$

Integrate both sides. On the left, split up the integrand into partial fractions.

$\dfrac{(1+v)^2}{v(1+v^2)}=\dfrac{v^2+2v+1}{v(v^2+1)}=\dfrac av+\dfrac{bv+c}{v^2+1}$

$\implies v^2+2v+1=a(v^2+1)+(bv+c)v$

$\implies v^2+2v+1=(a+b)v^2+cv+a$

$\implies a=1,b=0,c=2$

Then

$\displaystyle\int\frac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=\int\left(\frac1v+\frac2{v^2+1}\right)\,\mathrm dv=\ln|v|+2\tan^{-1}v$

On the right, we have

$\displaystyle-\int\frac{\mathrm dx}x=-\ln|x|+C$

Solving for $v(x)$ explicitly is unlikely to succeed, so we leave the solution in implicit form,

$\ln|v(x)|+2\tan^{-1}v(x)=-\ln|x|+C$

and finally solve in terms of $y(x)$ by replacing $v(x)=\dfrac{y(x)}x$ :

$\ln\left|\frac{y(x)}x\right|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C$

$\ln|y(x)|-\ln|x|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C$

$\boxed{\ln|y(x)|+2\tan^{-1}\dfrac{y(x)}x=C}$

7 0

3 years ago

Which point lies on the graph of the finite sequence shown?<br> 5, –1, 6, 0, 7, 1, 8

djyliett [7]

Hello,

$u_{1} =5\\
 u_{2} = u_{1}-6=5-6=-1\\
 u_{3} = u_{2}+7=-1+7=6\\
 u_{4} = u_{3}-6=6-6=0\\
 u_{5} = u_{4}+7=0+7=7\\
 u_{6} = u_{5}-6=7-6=1\\
 u_{7} = u_{6}+7=1+7=8\\
...\\

\boxed{ u_{2n} = u_{2n-1}-6}\\\\

\boxed{ u_{2n+1} = u_{2n}+7}\\

$

7 0

2 years ago

Read 2 more answers

Whats 1.64 as a mixed number in simplest form

raketka [301]

It is 1 16/25

Hope it helps ;-)

8 0

2 years ago

My teacher wouldn't help me.. and this is my last question. I need to know how to find the perimeter of the geometric figure (it

nika2105 [10]

This isn't really a geometry problem. It's just an addition of fractions.

You know that 'perimeter' means 'the distance all the way around'.
And you know the length of all the sides of the parallelogram.
All you need to do is add them up !

(13/12) + (3/13) + (13/12) + (3/13) = the perimeter

Notice that two of the sides are equal, and the other two sides are also equal.
So you can make the job a little easier if you add up the twelfths first

(13/12) + (13/12) = 26/12

and then add up the thirteenths ...

(3/13) + (3/13) = 6/13 .

Now, the perimeter looks a little bit less complicated.
It's just
(26/12) + (6/13) = the perimeter.

This is the tough part. Before you can add fractions, they need to have
a common denominator.

The smallest common denominator for 12ths and 13ths is <em>156 </em>!
Change each fraction to (<em>something over 156</em>), and add um up.
I'll leave that part to you.

5 0

3 years ago

Find the 65th term of the arithmetic sequence –10,9, 28; ...

SOVA2 [1]

Answer:

1206

Step-by-step explanation:

find the pattern and add. ;)

7 0

3 years ago