Answer:
The standard form of the equation of the circle is
.
Step-by-step explanation:
A circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center.
The equation of a circle in standard form is
where <em>r</em> is the radius of the circle, and <em>h</em>, <em>k</em> are the coordinates of its center.
When the center of the circle coincides with the origin
, so
![(x-0)^2+(y-0)^2=r^2\\x^2+y^2=r^2](https://tex.z-dn.net/?f=%28x-0%29%5E2%2B%28y-0%29%5E2%3Dr%5E2%5C%5Cx%5E2%2By%5E2%3Dr%5E2)
We are also told that the circle contains the point (0, 1), so we will use that information to find the radius <em>r</em>.
![0^2+1^2=r^2\\r^2=0^2+1^2\\r^2=1\\r=\sqrt{1}](https://tex.z-dn.net/?f=0%5E2%2B1%5E2%3Dr%5E2%5C%5Cr%5E2%3D0%5E2%2B1%5E2%5C%5Cr%5E2%3D1%5C%5Cr%3D%5Csqrt%7B1%7D)
Therefore, the standard form of the equation of the circle is
.
Answer:
6 hours
Step-by-step explanation:
6 inches burns at rate .8 inches in 1 hour
to be 1.2 inches has to burn 6 -1.2 = 4.8 inches of the candle
4.8 inches / .8 inches in 1 hour = 6 hours
Answer:
Time=
years
Step-by-step explanation:
Let total time![=t](https://tex.z-dn.net/?f=%3Dt)
Initial Amount![=5000](https://tex.z-dn.net/?f=%3D5000)
Final Amount![=10000](https://tex.z-dn.net/?f=%3D10000)
Total interest = Final Amount - Initial Amount
![=10000-5000\\=5000](https://tex.z-dn.net/?f=%3D10000-5000%5C%5C%3D5000)
Simple Interest ![=\frac{Initial Amount\times time\times rate}{100} \\\\5000=\frac{5000\times t \times 10}{100}\\\frac{t}{10} =1\\t=10 \ years](https://tex.z-dn.net/?f=%3D%5Cfrac%7BInitial%20Amount%5Ctimes%20time%5Ctimes%20rate%7D%7B100%7D%20%5C%5C%5C%5C5000%3D%5Cfrac%7B5000%5Ctimes%20t%20%5Ctimes%2010%7D%7B100%7D%5C%5C%5Cfrac%7Bt%7D%7B10%7D%20%3D1%5C%5Ct%3D10%20%5C%20years)