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ValentinkaMS [17]
3 years ago
12

Make r subject of the formula

Formula1" title="s = 4\pi \: r {}^{2} " alt="s = 4\pi \: r {}^{2} " align="absmiddle" class="latex-formula">
​
Mathematics
2 answers:
DerKrebs [107]3 years ago
4 0

Answer:

r = √( s/4π)

Step-by-step explanation:

s = 4πr²

s/4π = 4πr²/4π

r² = s/4π

√(r²) =+/-√( s/4π)

r = √( s/4π)     Because r is a radius of the circle , it should be positive.

xenn [34]3 years ago
4 0

Answer:

\boxed{r = \pm \frac{ \sqrt{s} }{2 \sqrt{\pi} } }

Step-by-step explanation:

Solve \:  for \:  r:  \\  =  > s=4\pi {r}^{2}  \\  \\ s =4\pi {r}^{2}  \:  is  \: equivalent \:  to  \: 4\pi {r}^{2}  = s:  \\  =  > 4\pi {r}^{2}  =s  \\  \\ Divide \:  both  \: sides  \: by \:  4\pi:  \\  {r}^{2}  =  \frac{s}{4\pi}  \\  \\ Take  \: the \:  square  \: root  \: of \:  both  \: sides:  \\ =  > r =  \frac{ \sqrt{s} }{2 \sqrt{\pi} }   \:  \:  \:  \: or \:  \:  \:  \:  r =   - \frac{ \sqrt{s} }{2 \sqrt{\pi} }

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B+alfa=45°
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3 years ago
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3 years ago
You have a map of an area in France. The scale used is 2cm:8km. You want to ride to a national park. The park is shown on the ma
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4 0
3 years ago
3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations d
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Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}

Where <em>A</em> is the final amount, <em>P</em> is the initial amount, <em>r</em> is the interest rate, <em>n</em> is the number of times compounded per year, and <em>t</em> is the number of years.

To obtain $4000 after two years, let <em>A</em> = 4000 and<em> t</em> = 2.

Because the account pays 3% interest compounded monthly, <em>r</em> = 0.03 and <em>n</em> = 12.

Substitute and solve for <em>P: </em>

<em />\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

\displaystyle A = Pe^{rt}

Where <em>e</em> is Euler's number.

Hence, let <em>A</em> = 4000, <em>r</em> = 0.04 and <em>t</em> = 2. Substitute and solve for <em>P: </em>

<em />\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}

In conclusion, about $3692.47 should be deposited.

8 0
2 years ago
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