50/10 reduces to 5/1 so your answer is 5
Given that
![x=6\tan\theta \\ \\ \Rightarrow\tan\theta= \frac{x}{6}](https://tex.z-dn.net/?f=x%3D6%5Ctan%5Ctheta%20%5C%5C%20%20%5C%5C%20%5CRightarrow%5Ctan%5Ctheta%3D%20%5Cfrac%7Bx%7D%7B6%7D%20)
Consider a right triangle with angle θ, the side opposite the angle θ is x and that side adjacent angle x is 6.
Then the hypothenus is given by
![\sqrt{x^2+36}](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%5E2%2B36%7D%20)
![\sin{ \frac{2\theta}{4}} =\sin{2\left( \frac{\theta}{2} \right)} \\ \\ =2\sin{\frac{\theta}{2}}\cos{\frac{\theta}{2}}=2\cdot \sqrt{\frac{1-\cos{\theta}}{2}} \cdot \sqrt{\frac{1+\cos{\theta}}{2}} \\ \\ =\sqrt{1-\cos^2\theta}](https://tex.z-dn.net/?f=%5Csin%7B%20%5Cfrac%7B2%5Ctheta%7D%7B4%7D%7D%20%3D%5Csin%7B2%5Cleft%28%20%5Cfrac%7B%5Ctheta%7D%7B2%7D%20%5Cright%29%7D%20%5C%5C%20%20%5C%5C%20%3D2%5Csin%7B%5Cfrac%7B%5Ctheta%7D%7B2%7D%7D%5Ccos%7B%5Cfrac%7B%5Ctheta%7D%7B2%7D%7D%3D2%5Ccdot%20%5Csqrt%7B%5Cfrac%7B1-%5Ccos%7B%5Ctheta%7D%7D%7B2%7D%7D%20%5Ccdot%20%5Csqrt%7B%5Cfrac%7B1%2B%5Ccos%7B%5Ctheta%7D%7D%7B2%7D%7D%20%20%5C%5C%20%20%5C%5C%20%3D%5Csqrt%7B1-%5Ccos%5E2%5Ctheta%7D)
Recall that
![\cos\theta= \frac{adjacent}{hypothenuse} = \frac{6}{\sqrt{x^2+36}}](https://tex.z-dn.net/?f=%5Ccos%5Ctheta%3D%20%5Cfrac%7Badjacent%7D%7Bhypothenuse%7D%20%3D%20%5Cfrac%7B6%7D%7B%5Csqrt%7Bx%5E2%2B36%7D%7D%20)
Therefore,
Answer:
The amount $15000 is divided as
in 2% = $7000
in 5% = $8000
Step-by-step explanation:
It is given that the total amount is $15000 and rates of interests are 2% and 5%.
<em>Let the amount invested in 2% be "x", so the amount invested in 5% is (15000 - x).</em>
The annual interest on x part is given as,
= ![(\frac{2}{100})(x)](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%7D%7B100%7D%29%28x%29)
Similarly, The annual interest on (15000 - x) part is given as,
= ![(\frac{5}{100})(15000 - x)](https://tex.z-dn.net/?f=%28%5Cfrac%7B5%7D%7B100%7D%29%2815000%20-%20x%29)
the total annual interest is given as $540
Thus, <em>540 =
</em>
<em>54000 =
</em>
<em>21000 = 3(x)</em>
x =
= 7000
Thus the shares are $7000 and (15000 - 7000) $8000 .