Answer:
4013.45
Step-by-step explanation:
Given,
Purchased amount of the bond, P = 3500,
Annual rate of simple interest, r = 4.89% = 0.0489,
Time ( in years ), t = 3,
Since, the total amount of a bond that earns simple interest is,
![A=P(1+r\times t)](https://tex.z-dn.net/?f=A%3DP%281%2Br%5Ctimes%20t%29)
By substituting values,
The amount of the bond would be,
![=3500(1+0.0489\times 3)](https://tex.z-dn.net/?f=%3D3500%281%2B0.0489%5Ctimes%203%29)
![=3500(1.1467)](https://tex.z-dn.net/?f=%3D3500%281.1467%29)
![=4013.45](https://tex.z-dn.net/?f=%3D4013.45)
![\cos^2 x\sin x-3\sin x=0\\\\ \sin x\cdot (\cos^2 x-3)=0\\\\ \begin{array}{rcl} \sin x=0&~\text{ or }~&\cos^2 x - 3=0\\\\ \sin x=0&~\text{ or }~&\cos^2 x=3\\\\ \sin x=0&~\text{ or }~&\cos x=\pm \sqrt{3} \end{array}](https://tex.z-dn.net/?f=%5Ccos%5E2%20x%5Csin%20x-3%5Csin%20x%3D0%5C%5C%5C%5C%20%5Csin%20x%5Ccdot%20%28%5Ccos%5E2%20x-3%29%3D0%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Brcl%7D%20%5Csin%20x%3D0%26~%5Ctext%7B%20or%20%7D~%26%5Ccos%5E2%20x%20-%203%3D0%5C%5C%5C%5C%20%5Csin%20x%3D0%26~%5Ctext%7B%20or%20%7D~%26%5Ccos%5E2%20x%3D3%5C%5C%5C%5C%20%5Csin%20x%3D0%26~%5Ctext%7B%20or%20%7D~%26%5Ccos%20x%3D%5Cpm%20%5Csqrt%7B3%7D%20%5Cend%7Barray%7D)
Since
![|\cos x|\le 1,](https://tex.z-dn.net/?f=%7C%5Ccos%20x%7C%5Cle%201%2C)
the 2nd equation has no solutions for x. So
![\sin x=0\\\\ x=k\pi~~~~\text{where }k\text{ is an integer.}](https://tex.z-dn.net/?f=%5Csin%20x%3D0%5C%5C%5C%5C%20x%3Dk%5Cpi~~~~%5Ctext%7Bwhere%20%7Dk%5Ctext%7B%20is%20an%20integer.%7D)
Solution: