The amount of money she would have is $10,291.50.
The amount of money she would have to buy the gift is the sum of the amount deposited and the interest.
Simple interest is interest that only accrues on the amount of money deposited into the account.
The formula that can be used to determine simple interest is: principal x time x interest rate
Where:
- Principal = amount deposited = $10,000
- Time = 11/12
- Interest rate = 3.18%
$10,000 x 11/12 x 0.0318 = $291.50
$10,000 + $291.50 = $10,291.50
-9. first, add 14 on both sides = “-1=n/9
-9/9=-1
Answer:
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Hi,
x + 5x - 14 = 0
x + 5x - 14 + 14 = 0 + 14
6x = 14
x = 14/6 = 7/3
✅(◠‿◕)
Given:
![\cos 15^{\circ}](https://tex.z-dn.net/?f=%5Ccos%2015%5E%7B%5Ccirc%7D)
To find:
The exact value of cos 15°.
Solution:
![$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}](https://tex.z-dn.net/?f=%24%5Ccos%2015%5E%7B%5Ccirc%7D%3D%5Ccos%5Cfrac%7B%2030%5E%7B%5Ccirc%7D%7D%7B2%7D)
Using half-angle identity:
![$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}](https://tex.z-dn.net/?f=%24%5Ccos%20%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%3D%5Csqrt%7B%5Cfrac%7B1%2B%5Ccos%20%28x%29%7D%7B2%7D%7D)
![$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}](https://tex.z-dn.net/?f=%24%5Ccos%20%5Cfrac%7B30%5E%7B%5Ccirc%7D%7D%7B2%7D%3D%5Csqrt%7B%5Cfrac%7B1%2B%5Ccos%20%5Cleft%2830%5E%7B%5Ccirc%7D%5Cright%29%7D%7B2%7D%7D)
Using the trigonometric identity: ![\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Ccos%20%5Cleft%2830%5E%7B%5Ccirc%7D%5Cright%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
![$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%7B%5Cfrac%7B1%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D%7B2%7D%7D)
Let us first solve the fraction in the numerator.
![$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%7B%5Cfrac%7B%5Cfrac%7B2%2B%5Csqrt%7B3%7D%7D%7B2%7D%7D%7B2%7D%7D)
Using fraction rule: ![\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Ba%7D%7Bb%7D%20%7D%7Bc%7D%3D%5Cfrac%7Ba%7D%7Bb%20%5Ccdot%20c%7D)
![$=\sqrt{\frac {2+\sqrt{3}}{4}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%7B%5Cfrac%20%7B2%2B%5Csqrt%7B3%7D%7D%7B4%7D%7D)
Apply radical rule: ![\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3D%5Cfrac%7B%5Csqrt%5Bn%5D%7Ba%7D%7D%7B%5Csqrt%5Bn%5D%7Bb%7D%7D)
![$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%7D%7B%5Csqrt%7B4%7D%7D)
Using
:
![$=\frac{\sqrt{2+\sqrt{3}}}{2}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%7D%7B2%7D)
![$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}](https://tex.z-dn.net/?f=%24%5Ccos%2015%5E%5Ccirc%3D%5Cfrac%7B%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%7D%7B2%7D)