Compound interest is given by:
A=p(1+r/(100*n))^(nt)
where;
A=future amount
p=principle amount=$35,000
r=rate=10%=0.1
n=number of terms=2
t=time=6
Hence,
A=35,000(1+0.05)^(2*6)
A=35000(1.05)^12
A=$62,854.97
The amount of money after 6 years will be $62,854.97
16 because its an even number
Answer:
x² + y² = 4
Step-by-step explanation:
We need to write the standard equation of circle with , centre (0,0) and radius 2 unit . The Standard equation of the circle ⭕ is ,
=> ( x - h)² + (y -k)² = r²
=> ( x -0)² + (y-0)² = 2²
=> x² + y² = 4 .
<h3>• Hence the equation of the circle is x² + y² = 4.</h3>
Answer:
The answer is below
Step-by-step explanation:
The slope of a line (m) is given by:
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Two lines are parallel if they have the same slope and perpendicular if the product of their slope is -1.
1)
![Slope\ of\ PQ=\frac{1-(-2)}{9-(-3)}=\frac{1}{4} \\\\Slope\ of\ UV=\frac{-2-6}{5-3}=-4](https://tex.z-dn.net/?f=Slope%5C%20of%5C%20PQ%3D%5Cfrac%7B1-%28-2%29%7D%7B9-%28-3%29%7D%3D%5Cfrac%7B1%7D%7B4%7D%20%20%5C%5C%5C%5CSlope%5C%20of%5C%20UV%3D%5Cfrac%7B-2-6%7D%7B5-3%7D%3D-4)
Since the product of their slope is -1, they are perpendicular
2)
![Slope\ of\ PQ=\frac{1-7}{2-(-10)}=-\frac{1}{2} \\\\Slope\ of\ UV=\frac{1-0}{6-4}=\frac{1}{2}](https://tex.z-dn.net/?f=Slope%5C%20of%5C%20PQ%3D%5Cfrac%7B1-7%7D%7B2-%28-10%29%7D%3D-%5Cfrac%7B1%7D%7B2%7D%20%20%5C%5C%5C%5CSlope%5C%20of%5C%20UV%3D%5Cfrac%7B1-0%7D%7B6-4%7D%3D%5Cfrac%7B1%7D%7B2%7D)
Since the slope is not the same or product of their slope is not -1, they are neither parallel or perpendicular
3)
![Slope\ of\ PQ=\frac{8-1}{9-1}=\frac{7}{8} \\\\Slope\ of\ UV=\frac{8-1}{2-(-6)}=\frac{7}{8}](https://tex.z-dn.net/?f=Slope%5C%20of%5C%20PQ%3D%5Cfrac%7B8-1%7D%7B9-1%7D%3D%5Cfrac%7B7%7D%7B8%7D%20%20%5C%5C%5C%5CSlope%5C%20of%5C%20UV%3D%5Cfrac%7B8-1%7D%7B2-%28-6%29%7D%3D%5Cfrac%7B7%7D%7B8%7D)
Since the slopes are the same, they are parallel
4)
![Slope\ of\ PQ=\frac{3-0}{9-(-4)}=\frac{3}{4} \\\\Slope\ of\ UV=\frac{6-(-3)}{8-(-4)}=\frac{3}{4}](https://tex.z-dn.net/?f=Slope%5C%20of%5C%20PQ%3D%5Cfrac%7B3-0%7D%7B9-%28-4%29%7D%3D%5Cfrac%7B3%7D%7B4%7D%20%20%5C%5C%5C%5CSlope%5C%20of%5C%20UV%3D%5Cfrac%7B6-%28-3%29%7D%7B8-%28-4%29%7D%3D%5Cfrac%7B3%7D%7B4%7D)
Since the slopes are the same, they are parallel
5)
![Slope\ of\ PQ=\frac{1-2}{0-(-9)}=-\frac{1}{9} \\\\Slope\ of\ UV=\frac{-1-8}{-2-(-1)}=9](https://tex.z-dn.net/?f=Slope%5C%20of%5C%20PQ%3D%5Cfrac%7B1-2%7D%7B0-%28-9%29%7D%3D-%5Cfrac%7B1%7D%7B9%7D%20%20%5C%5C%5C%5CSlope%5C%20of%5C%20UV%3D%5Cfrac%7B-1-8%7D%7B-2-%28-1%29%7D%3D9)
Since the product of their slope is -1, they are perpendicular