Answer:
$9261
$1261
Step-by-step explanation:
Principal: $8000
Interest rate: 5% PA compounded annually
Time: 3 years
- Sum = $8000*(1.05)³ = $9261
- Interest = $9261 - $8000 = $1261
13/8 or 1 5/8
3/4 becomes 7/8 when add it is 13/8
Answer:
![x=33\\y=-41](https://tex.z-dn.net/?f=x%3D33%5C%5Cy%3D-41)
Step-by-step explanation:
Let:
![2x+y=25\hspace{5}(1)\\and\\4x+3y=9\hspace{5}(2)](https://tex.z-dn.net/?f=2x%2By%3D25%5Chspace%7B5%7D%281%29%5C%5Cand%5C%5C4x%2B3y%3D9%5Chspace%7B5%7D%282%29)
We need to eliminate one of the variables, so let's use elimination method. First multiply (1) by 2
![2*(1)\equiv\hspace{5}4x+2y=50](https://tex.z-dn.net/?f=2%2A%281%29%5Cequiv%5Chspace%7B5%7D4x%2B2y%3D50)
Now subtract (2) from 2*(1) in order to eliminate x:
![2*(1)-(2)\\4x-4x+2y-3y=50-9\\-y=41](https://tex.z-dn.net/?f=2%2A%281%29-%282%29%5C%5C4x-4x%2B2y-3y%3D50-9%5C%5C-y%3D41)
Solving for y:
Multiplying both sides by -1
![y=-41](https://tex.z-dn.net/?f=y%3D-41)
Finally, replacing the value of y in (1)
![2x-41=25](https://tex.z-dn.net/?f=2x-41%3D25)
Solving for x:
add 41 to both sides:
![2x=66](https://tex.z-dn.net/?f=2x%3D66)
Multiply both sides by 1/2:
![x=\frac{66}{2} =33](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B66%7D%7B2%7D%20%3D33)
So the circle is 39.25
And the area of triangle 30 together about 39.25
Answer:
![\sin(90^{\circ} - x)=\frac{1}{3}](https://tex.z-dn.net/?f=%5Csin%2890%5E%7B%5Ccirc%7D%20-%20x%29%3D%5Cfrac%7B1%7D%7B3%7D)
Step-by-step explanation:
Given: ![\cos (x)=\frac{1}{3}](https://tex.z-dn.net/?f=%5Ccos%20%28x%29%3D%5Cfrac%7B1%7D%7B3%7D)
We have to find the value of ![\sin(90^{\circ} - x)](https://tex.z-dn.net/?f=%5Csin%2890%5E%7B%5Ccirc%7D%20-%20x%29)
Since Given ![\cos (x)=\frac{1}{3}](https://tex.z-dn.net/?f=%5Ccos%20%28x%29%3D%5Cfrac%7B1%7D%7B3%7D)
Using trigonometric identity,
![\sin(90^{\circ} - \theta)=\cos\theta](https://tex.z-dn.net/?f=%5Csin%2890%5E%7B%5Ccirc%7D%20-%20%5Ctheta%29%3D%5Ccos%5Ctheta)
Thus, for
comparing , we have,
![\theta=x](https://tex.z-dn.net/?f=%5Ctheta%3Dx)
We get,
![\sin(90^{\circ} - x)=\cos x=\frac{1}{3}](https://tex.z-dn.net/?f=%5Csin%2890%5E%7B%5Ccirc%7D%20-%20x%29%3D%5Ccos%20x%3D%5Cfrac%7B1%7D%7B3%7D)
Thus, ![\sin(90^{\circ} - x)=\frac{1}{3}](https://tex.z-dn.net/?f=%5Csin%2890%5E%7B%5Ccirc%7D%20-%20x%29%3D%5Cfrac%7B1%7D%7B3%7D)