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OlgaM077 [116]
3 years ago
14

11000 is compounded semiannually at a rate of 12% for 21 years. Find the total amount in the compound interest account

Mathematics
1 answer:
marishachu [46]3 years ago
5 0

\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\dotfill &\$11000\\
r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semiannually, thus twice}
\end{array}\dotfill &2\\
t=years\dotfill &21
\end{cases}


\bf A=11000\left(1+\frac{0.12}{2}\right)^{2\cdot 21}\implies A=11000(1.06)^{42}\implies A\approx 127127.359416

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Root 3 cosec140° - sec140°=4<br>prove that<br><br>​
Lorico [155]

Answer:

Step-by-step explanation:

We are to show that \sqrt{3} cosec140^{0} - sec140^{0} = 4\\

<u>Proof:</u>

From trigonometry identity;

cosec \theta = \frac{1}{sin\theta} \\sec\theta = \frac{1}{cos\theta}

\sqrt{3} cosec140^{0} - sec140^{0} \\= \frac{\sqrt{3} }{sin140} - \frac{1}{cos140} \\= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\

From trigonometry, 2sinAcosA = Sin2A

= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\\\=  \frac{\sqrt{3}cos140-sin140 }{sin280/2}\\=  \frac{4(\sqrt{3}/2cos140-1/2sin140) }{2sin280}\\\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{sin280}\\since sin420 = \sqrt{3}/2 \ and \ cos420 = 1/2  \\ then\\\frac{4(sin420cos140-cos420sin140) }{sin280}

Also note that sin(B-C) = sinBcosC - cosBsinC

sin420cos140 - cos420sin140 = sin(420-140)

The resulting equation becomes;

\frac{4(sin(420-140)) }{sin280}

= \frac{4sin280}{sin280}\\ = 4 \ Proved!

3 0
3 years ago
Find the equation of the line shown.
Luda [366]

Answer:

y = -x + 9

Step-by-step explanation:

✔️Find the slope using (9, 0) and (7, 2):

slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{7 - 9} = \frac{2}{-2} = -1

Slope (m) = -1

✔️Find the y-intercept (b):

The line intercepts the y-axis when y = 9. Therefore, y-intercept (b) = 9

✔️Substitute m = -1 and b = 9 into y = mx + b

Thus,

y = -1(x) + 9

y = -x + 9

5 0
3 years ago
a company promises to release model every month. each model's battery life will be 6% longer than the previous model's. if the c
Ratling [72]

The number of months that it will take the latest model's battery life to reach 1,008.9 minutes is; 8 months

<h3>How to solve geometric progression?</h3>

Each month, there is an increase by a factor of 0.06 of the previous months model.

From geometric sequence formula of aₙ = ar^(n - 1),

where;

a is first term

r is common ratio

aₙ is nth term

we have;

1,008.9 = 671 * 1.06^(n - 1)

1008.9/671 = 1.06^(n - 1)

In 1.504 = (n - 1) In 1.06

0.408 = (n - 1) * 0.058

n - 1 = 0.408/0.058

n = 7.03 + 1

n ≈ 8 months

Read more about geometric sequence at; brainly.com/question/24643676

#SPJ1

5 0
2 years ago
Sovle 4 pls and thank you
max2010maxim [7]

Answer:

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Step-by-step explanation:

6 0
3 years ago
Min is twice as tall as her brother . If min is 5feet 3 inches tall how tall is her brother
liubo4ka [24]
5’3 is 63 inches since her brother is 1/3 larger so 63/3= 21 inches
3 0
3 years ago
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