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Maksim231197 [3]
4 years ago
11

Help with 1 and 3 if possible show work

Mathematics
1 answer:
Vinvika [58]4 years ago
5 0
1)

\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+r\right)^{t}
\quad 
\begin{cases}
A=\textit{compounded amount}\\
P=\textit{original amount deposited}\to &\$600\\
r=rate\to 1.6\%\to \frac{1.6}{100}\to &0.016\\
t=years\to &2
\end{cases}
\\\\\\
A=600\left(1+0.016\right)^{2}

3)

\bf V(t)=1350(1.017)^t\implies 
\begin{array}{llllll}
V(t)&=&1350(&1 +& 0.017&)^t\\
A&=&P(&1+&\boxed{r}&)^t
\end{array}

notice the rate "r"... now, is in decimal format, as you saw on 1) is just r/100 so 1.6% was really 1.6/100 or 0.016  anyhow

to get the percentage form, just multiply it by 100

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Given the equation 9x+3/4 y=6 and 2x+1/2 y=9, by what factor would you multiply the second equation to eliminate y and solve the
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Find x. Round your answer to the nearest hundredth
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Use the Newton-Raphson method to find the root of the equation f(x) = In(3x) + 5x2, using an initial guess of x = 0.5 and a stop
xxMikexx [17]

Answer with explanation:

The equation which we have to solve by Newton-Raphson Method is,

 f(x)=log (3 x) +5 x²

f'(x)=\frac{1}{3x}+10 x

Initial Guess =0.5

Formula to find Iteration by Newton-Raphson method

  x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}\\\\x_{1}=x_{0}-\frac{f(x_{0})}{f'(x_{0})}\\\\ x_{1}=0.5-\frac{\log(1.5)+1.25}{\frac{1}{1.5}+10 \times 0.5}\\\\x_{1}=0.5- \frac{0.1760+1.25}{0.67+5}\\\\x_{1}=0.5-\frac{1.426}{5.67}\\\\x_{1}=0.5-0.25149\\\\x_{1}=0.248

x_{2}=0.248-\frac{\log(0.744)+0.30752}{\frac{1}{0.744}+10 \times 0.248}\\\\x_{2}=0.248- \frac{-0.128+0.30752}{1.35+2.48}\\\\x_{2}=0.248-\frac{0.17952}{3.83}\\\\x_{2}=0.248-0.0468\\\\x_{2}=0.2012

x_{3}=0.2012-\frac{\log(0.6036)+0.2024072}{\frac{1}{0.6036}+10 \times 0.2012}\\\\x_{3}=0.2012- \frac{-0.2192+0.2025}{1.6567+2.012}\\\\x_{3}=0.2012-\frac{-0.0167}{3.6687}\\\\x_{3}=0.2012+0.0045\\\\x_{3}=0.2057

x_{4}=0.2057-\frac{\log(0.6171)+0.21156}{\frac{1}{0.6171}+10 \times 0.2057}\\\\x_{4}=0.2057- \frac{-0.2096+0.21156}{1.6204+2.057}\\\\x_{4}=0.2057-\frac{0.0019}{3.6774}\\\\x_{4}=0.2057-0.0005\\\\x_{4}=0.2052

So, root of the equation =0.205 (Approx)

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 Approximate relative error in terms of Percentage

   =0.41 × 100

   = 41 %

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