A two-digit number is twice the sum of its digit. If the tens digit is 7 less than the unit digit, find the number.
Let x= the unit digit
Then y= the tens digit
<span>And 10y+x= the number
</span>x+y= the sum of the digits
<span>Now we are told that 10y+x=2(x+y) ------1st equation </span>
<span>We are also told that y=x-7 ----------- 2nd Equation </span>
<span>So our equations to solve are: </span>
(1) 10y+x=2(x+y)
<span>(2) y=x-7
</span>
Hope it helps
Answer:
0
Step-by-step explanation:
Given that,
6m - 2n=0
=>6m=2n
=>n=3m [divide both side by 2]
& mn=12
Now,
216c - 8n³
= 216m³- 8(3m)³
=216m³- 8 .27m³
=216m³- 216m³
=0
![xe^y+4\ln y=x^2](https://tex.z-dn.net/?f=xe%5Ey%2B4%5Cln%20y%3Dx%5E2)
Differentiate both sides with respect to <em>x</em>, assuming <em>y</em> = <em>y</em>(<em>x</em>).
![\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%28xe%5Ey%2B4%5Cln%20y%29%7D%7B%5Cmathrm%20dx%7D%3D%5Cdfrac%7B%5Cmathrm%20d%28x%5E2%29%7D%7B%5Cmathrm%20dx%7D)
![\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%28xe%5Ey%29%7D%7B%5Cmathrm%20dx%7D%2B%5Cdfrac%7B%5Cmathrm%20d%284%5Cln%20y%29%7D%7B%5Cmathrm%20dx%7D%3D2x)
![\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%28x%29%7D%7B%5Cmathrm%20dx%7De%5Ey%2Bx%5Cdfrac%7B%5Cmathrm%20d%28e%5Ey%29%7D%7B%5Cmathrm%20dx%7D%2B%5Cdfrac4y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D2x)
![e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x](https://tex.z-dn.net/?f=e%5Ey%2Bxe%5Ey%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%2B%5Cdfrac4y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D2x)
Solve for d<em>y</em>/d<em>x</em> :
![e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x](https://tex.z-dn.net/?f=e%5Ey%2B%5Cleft%28xe%5Ey%2B%5Cdfrac4y%5Cright%29%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D2x)
![\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y](https://tex.z-dn.net/?f=%5Cleft%28xe%5Ey%2B%5Cdfrac4y%5Cright%29%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D2x-e%5Ey)
![\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D%5Cdfrac%7B2x-e%5Ey%7D%7Bxe%5Ey%2B%5Cfrac4y%7D)
If <em>y</em> ≠ 0, we can write
![\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D%5Cdfrac%7B2xy-ye%5Ey%7D%7Bxye%5Ey%2B4%7D)
At the point (1, 1), the derivative is
![\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cbigg%7C_%7Bx%3D1%2Cy%3D1%7D%3D%5Cboxed%7B%5Cdfrac%7B2-e%7D%7Be%2B4%7D%7D)