Answer:
the answer to #9 is (½, 1½)
Step-by-step explanation:
to find the midpoint, you need to use the midpoint formula
the midpoint formula is (x₁ + x₂ / 2 , y₁ + y₂ / 2)
for #9 you have to plug in the appropriate numbers in the formula
(-4 + 5 / 2 , 4 - 1 / 2)
(½ , 1½)
<em>Hope</em><em> </em><em>this</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em><em>.</em>
![\ln(4x+y)=2x-3](https://tex.z-dn.net/?f=%5Cln%284x%2By%29%3D2x-3)
Differentiate both sides wrt
:
![\dfrac{\mathrm d(\ln(4x+y))}{\mathrm dx}=\dfrac{\mathrm d(2x-3)}{\mathrm dx}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%28%5Cln%284x%2By%29%29%7D%7B%5Cmathrm%20dx%7D%3D%5Cdfrac%7B%5Cmathrm%20d%282x-3%29%7D%7B%5Cmathrm%20dx%7D)
By the chain rule, we get
![\dfrac1{4x+y}\dfrac{\mathrm d(4x+y)}{\mathrm dx}=2](https://tex.z-dn.net/?f=%5Cdfrac1%7B4x%2By%7D%5Cdfrac%7B%5Cmathrm%20d%284x%2By%29%7D%7B%5Cmathrm%20dx%7D%3D2)
![\dfrac{4+\frac{\mathrm dy}{\mathrm dx}}{4x+y}=2](https://tex.z-dn.net/?f=%5Cdfrac%7B4%2B%5Cfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%7D%7B4x%2By%7D%3D2)
Solve for
:
![4+\dfrac{\mathrm dy}{\mathrm dx}=8x+2y](https://tex.z-dn.net/?f=4%2B%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D8x%2B2y)
![\boxed{\dfrac{\mathrm dy}{\mathrm dx}=8x+2y-4}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D8x%2B2y-4%7D)
Answer:
5/4
Step-by-step explanation:
2(8x-3)-4(3x-5)=19
16x-6-12x+20=19
16x-12x-6+20=19
4x+14=19
4x=19-14
4x=5
x=5/4