Answer:
65°
Step-by-step explanation:
180°-50°:130°
130°÷2:65°
130° divide by 2 because the shape was isosceles triangle
What’s da problem that u have?
Dave will have $12,728 after 15 years, if he has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly.
Step-by-step explanation:
The given is,
Investment = $ 8000
No. of years = 15 years
Interest rate, i = 3.1 %
( compounded monthly )
Step:1
For for calculating future value with compound interest monthly,
.................(1)
Where,
A = Future amount
P = Initial investment
r = Rate of interest
n = Number of compounding in a year
t = Time period
Step:2
From given values,
P = $8000
r = 3.1%
t = 15 years
n = 12 ( for monthly)
Equation (1) becomes,
![A = 8000( 1+\frac{0.031}{12} )^{(12)(15)}](https://tex.z-dn.net/?f=A%20%3D%208000%28%201%2B%5Cfrac%7B0.031%7D%7B12%7D%20%29%5E%7B%2812%29%2815%29%7D)
![= 8000 (1+0.002583)^{180}](https://tex.z-dn.net/?f=%3D%208000%20%281%2B0.002583%29%5E%7B180%7D)
![= 8000(1.002583)^{180}](https://tex.z-dn.net/?f=%3D%208000%281.002583%29%5E%7B180%7D)
![= 8000(1.591059)](https://tex.z-dn.net/?f=%3D%208000%281.591059%29)
![=12728.48](https://tex.z-dn.net/?f=%3D12728.48)
A = $ 12728.48
Result:
Dave will have $12,728 after 15 years, if he has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly.
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)
12 is the answer
Equilateral triangle means the three sides are the same length. You do 3 x 4 = 12