3 years ago

A right triangle with one angle that is 50*

Mathematics

1 answer:

denis-greek [22]3 years ago

7 0

Its an acute triangle

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Suppose you inherited a house that was purchased in 1950 for 20,000. It is now 2015 and the value of the house has increased by

sleet_krkn [62]

This deals with exponential growth.
house value = 20,000 * (1.05)^years
(where years is # of years from 1950 - so 1950 = 0, 1951 = 1, etc)
house value = 20,000 * (1.05)^65
house value = 20,000 * 23.8399005592 
house value = 476,798.01

7 0

3 years ago

A certificate of deposit with $600 principal earns 2. 5% interest for 6 years. How much is the interest earned for 6 years?

mario62 [17]

$~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (600)(0.025)(6)\implies I=90$

5 0

2 years ago

Integrate sin²2x cos²2x dx

DochEvi [55]

$\sin^2x=\dfrac{1-\cos2x}2$
$\cos^2x=\dfrac{1+\cos2x}2$

From the identities above, you have

$\sin^22x\cos^22x=\dfrac{(1-\cos4x)(1+\cos4x)}4=\dfrac{1-\cos^24x}4$

Applying once more, you have

$\dfrac{1-\cos^24x}4=\dfrac{1-\dfrac{1+\cos8x}2}4=\dfrac{1-\cos8x}8$

So,

$\displaystyle\int\sin^22x\cos^22x\,\mathrm dx=\frac18\int(1-\cos8x)\,\mathrm dx=\frac x8-\frac1{64}\sin8x+C$