7 / (x-3) = 1
(x-3) ((7 / (x-3)) = 1 (x-3) multiply both sides by (x-3), (x-3) on the left is cancelled
7 = x-3
3+7 = x - 3 + 3 add both sides by 3, 3 on the right is cancelled
x = 11
I think the answer is 36 but i could be wrong
![x=1+6t^2\implies\dfrac{\mathrm dx}{\mathrm dt}=12t](https://tex.z-dn.net/?f=x%3D1%2B6t%5E2%5Cimplies%5Cdfrac%7B%5Cmathrm%20dx%7D%7B%5Cmathrm%20dt%7D%3D12t)
![y=4+4t^3\implies\dfrac{\mathrm dy}{\mathrm dt}=12t^2](https://tex.z-dn.net/?f=y%3D4%2B4t%5E3%5Cimplies%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%3D12t%5E2)
The length of the curve
is given by
![\displaystyle\int_C\mathrm ds=\int_0^3\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_C%5Cmathrm%20ds%3D%5Cint_0%5E3%5Csqrt%7B%5Cleft%28%5Cfrac%7B%5Cmathrm%20dx%7D%7B%5Cmathrm%20dt%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%5Cright%29%5E2%7D%5C%2C%5Cmathrm%20dt)
![=\displaystyle\int_0^3\sqrt{144t^2+144t^4}\,\mathrm dt](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E3%5Csqrt%7B144t%5E2%2B144t%5E4%7D%5C%2C%5Cmathrm%20dt)
![=\displaystyle12\int_0^3t\sqrt{1+t^2}\,\mathrm dt](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle12%5Cint_0%5E3t%5Csqrt%7B1%2Bt%5E2%7D%5C%2C%5Cmathrm%20dt)
![=\displaystyle6\int_0^3 2t\sqrt{1+t^2}\,\mathrm dt](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle6%5Cint_0%5E3%202t%5Csqrt%7B1%2Bt%5E2%7D%5C%2C%5Cmathrm%20dt)
![=\displaystyle6\int_0^3\sqrt{1+t^2}\,\mathrm d(1+t^2)](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle6%5Cint_0%5E3%5Csqrt%7B1%2Bt%5E2%7D%5C%2C%5Cmathrm%20d%281%2Bt%5E2%29)
![=6\cdot\dfrac23(1+t^2)^{3/2}\bigg|_0^3](https://tex.z-dn.net/?f=%3D6%5Ccdot%5Cdfrac23%281%2Bt%5E2%29%5E%7B3%2F2%7D%5Cbigg%7C_0%5E3)
![=4(10^{3/2}-1)](https://tex.z-dn.net/?f=%3D4%2810%5E%7B3%2F2%7D-1%29)
![=40\sqrt{10}-4](https://tex.z-dn.net/?f=%3D40%5Csqrt%7B10%7D-4)
The correct answer is A) (1,-5)
Further explanation:
Given points are:
A(-8,7)=(x1,y1)
C(7,13)=(x2,y2)
IT is also given that
AB:BC=3:2
Which means that B divides the line segment in 3:2
Here,
m=3
n=2
To find the coordinates of B
![x_B=\frac{mx_2+nx_1}{m+n}\\ = \frac{(3)(7)+(2)(-8)}{3+2}\\=\frac{21-16}{5}\\=\frac{5}{5}\\=1\\y_B=\frac{my_2+ny_1}{m+n}\\=\frac{(3)(-13)+(2)(7)}{3+2}\\=\frac{-39+14}{5}\\=\frac{-25}{5}\\=-5](https://tex.z-dn.net/?f=x_B%3D%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%5C%5C%20%3D%20%5Cfrac%7B%283%29%287%29%2B%282%29%28-8%29%7D%7B3%2B2%7D%5C%5C%3D%5Cfrac%7B21-16%7D%7B5%7D%5C%5C%3D%5Cfrac%7B5%7D%7B5%7D%5C%5C%3D1%5C%5Cy_B%3D%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5C%5C%3D%5Cfrac%7B%283%29%28-13%29%2B%282%29%287%29%7D%7B3%2B2%7D%5C%5C%3D%5Cfrac%7B-39%2B14%7D%7B5%7D%5C%5C%3D%5Cfrac%7B-25%7D%7B5%7D%5C%5C%3D-5)
The coordinates of point B are (1,-5)
The correct answer is A) (1,-5)
Keywords: Coordinate geometry, mid-point
Learn more about coordinate geometry at:
#learnwithBrainly