Answer:
1) ![m=-3\,;\,\, m=\frac{1}{3}](https://tex.z-dn.net/?f=%20m%3D-3%5C%2C%3B%5C%2C%5C%2C%20m%3D%5Cfrac%7B1%7D%7B3%7D)
2) ![m=1\pm\sqrt{6}\\\\](https://tex.z-dn.net/?f=%20m%3D1%5Cpm%5Csqrt%7B6%7D%5C%5C%5C%5C)
Step-by-step explanation:
As differential equation is not give so we consider both equations attached in figure below one by one.
![1) \,3x^{2}\frac{d^2y}{dx^2}+11x\frac{dy}{dx}-3y=0](https://tex.z-dn.net/?f=1%29%20%5C%2C3x%5E%7B2%7D%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%2B11x%5Cfrac%7Bdy%7D%7Bdx%7D-3y%3D0)
Writing in terms of ∅
![3x^{2}\frac{d^2\phi}{dx^2}+11x\frac{d\phi}{dx}-3\phi=0](https://tex.z-dn.net/?f=3x%5E%7B2%7D%5Cfrac%7Bd%5E2%5Cphi%7D%7Bdx%5E2%7D%2B11x%5Cfrac%7Bd%5Cphi%7D%7Bdx%7D-3%5Cphi%3D0)
Substitute
![\phi=x^m\\\\\phi'=mx^{m-1}\\\\\phi''=m(m-1)x^{m-2}](https://tex.z-dn.net/?f=%5Cphi%3Dx%5Em%5C%5C%5C%5C%5Cphi%27%3Dmx%5E%7Bm-1%7D%5C%5C%5C%5C%5Cphi%27%27%3Dm%28m-1%29x%5E%7Bm-2%7D)
![3x^{2}(m(m-1)x^{m-2})+11x(mx^{m-1})-3x^m=0\\\\3x^{m}(m(m-1))+11mx^{m}-3x^m=0\\\\x^{m}(3m^2-3m+11m-3)=0\\\\3m^2+8m-3=0\\\\By \,\,factorization\\\\3m^2-m+9m-3=0\\\\m(3m-1)+3(3m-1)=0\\\\(m+3)(3m-1)=0\\\\\implies m=-3\,;\,\, m=\frac{1}{3}](https://tex.z-dn.net/?f=3x%5E%7B2%7D%28m%28m-1%29x%5E%7Bm-2%7D%29%2B11x%28mx%5E%7Bm-1%7D%29-3x%5Em%3D0%5C%5C%5C%5C3x%5E%7Bm%7D%28m%28m-1%29%29%2B11mx%5E%7Bm%7D-3x%5Em%3D0%5C%5C%5C%5Cx%5E%7Bm%7D%283m%5E2-3m%2B11m-3%29%3D0%5C%5C%5C%5C3m%5E2%2B8m-3%3D0%5C%5C%5C%5CBy%20%5C%2C%5C%2Cfactorization%5C%5C%5C%5C3m%5E2-m%2B9m-3%3D0%5C%5C%5C%5Cm%283m-1%29%2B3%283m-1%29%3D0%5C%5C%5C%5C%28m%2B3%29%283m-1%29%3D0%5C%5C%5C%5C%5Cimplies%20m%3D-3%5C%2C%3B%5C%2C%5C%2C%20m%3D%5Cfrac%7B1%7D%7B3%7D)
![2)\, x^2\frac{d^2y}{dx^2}-x\frac{dy}{dx}-5y=0---(2)](https://tex.z-dn.net/?f=2%29%5C%2C%20x%5E2%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D-x%5Cfrac%7Bdy%7D%7Bdx%7D-5y%3D0---%282%29)
Writing in terms of ∅
![x^2\frac{d^2\phi}{dx^2}-x\frac{d\phi}{dx}-5\phi=0](https://tex.z-dn.net/?f=x%5E2%5Cfrac%7Bd%5E2%5Cphi%7D%7Bdx%5E2%7D-x%5Cfrac%7Bd%5Cphi%7D%7Bdx%7D-5%5Cphi%3D0)
Substitute
![\phi=x^m\\\\\phi'=mx^{m-1}\\\\\phi''=m(m-1)x^{m-2}](https://tex.z-dn.net/?f=%5Cphi%3Dx%5Em%5C%5C%5C%5C%5Cphi%27%3Dmx%5E%7Bm-1%7D%5C%5C%5C%5C%5Cphi%27%27%3Dm%28m-1%29x%5E%7Bm-2%7D)
![x^2(m(m-1)x^{m-2})-x(mx\phix^{m-1})-5x^{m}=0\\\\(m^2-m)x^m-mx^m-5x^m=0\\\\x^m(m^2-m-m-5)=0\\\\m^2-2m-5=0\\\\Using\,\,quadratic\,\,formula\\\\m=\frac{2\pm \sqrt{20+4}}{2}\\\\m=\frac{2\pm \sqrt{24}}{2}\\\\m=1\pm\sqrt{6}\\\\](https://tex.z-dn.net/?f=x%5E2%28m%28m-1%29x%5E%7Bm-2%7D%29-x%28mx%5Cphix%5E%7Bm-1%7D%29-5x%5E%7Bm%7D%3D0%5C%5C%5C%5C%28m%5E2-m%29x%5Em-mx%5Em-5x%5Em%3D0%5C%5C%5C%5Cx%5Em%28m%5E2-m-m-5%29%3D0%5C%5C%5C%5Cm%5E2-2m-5%3D0%5C%5C%5C%5CUsing%5C%2C%5C%2Cquadratic%5C%2C%5C%2Cformula%5C%5C%5C%5Cm%3D%5Cfrac%7B2%5Cpm%20%5Csqrt%7B20%2B4%7D%7D%7B2%7D%5C%5C%5C%5Cm%3D%5Cfrac%7B2%5Cpm%20%5Csqrt%7B24%7D%7D%7B2%7D%5C%5C%5C%5Cm%3D1%5Cpm%5Csqrt%7B6%7D%5C%5C%5C%5C)
3yds because 1 yards is 3 feet so 3 times 3=9 feet greater than 8feet
Answer:
Obi's age is 18 and Oba's age is 9
Step-by-step explanation:
Let Obi's age be x and Oba's age be y
<u><em>Condition 1:</em></u>
x = 2y -----------(1)
<u><em>Condition 2:</em></u>
(x-4) = 3(y-4)
=> x -4 = 3y-12
=> x - 3y = -9 -----(2)
<u><em>Putting eq (1) in (2)</em></u>
2y - 3y = -9
=> -y = -9
=> y = 9
Now,
x = 2y
=> x = 2(9)
=> x= 18
Answer:
That separeates the problem
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Volume of sphere:
4/3 * pi * r^3
Surface Area of Sphere:
4 * pi * r^2
So if V = SA
4/3 * pi * r^3 = 4 * pi * r^2
<u>4</u>/3 * <u>pi</u> * r^3 = <u>4</u> * <u>pi</u> * r^2
1/3 * r^3 = r^2
1/3 * r = 1
r = 3