Answer:
![x^2+y^2=81](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D81)
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The radius of the circle is the distance between the center and any point on the circle
the formula to calculate the distance between two points is equal to
![d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y2-y1%29%5E%7B2%7D%2B%28x2-x1%29%5E%7B2%7D%7D)
we have the points
(0,0) and (0,-9)
substitute in the formula
![r=\sqrt{-9-0)^{2}+(0-0)^{2}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B-9-0%29%5E%7B2%7D%2B%280-0%29%5E%7B2%7D%7D)
![r=\sqrt{-9)^{2}+(0)^{2}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B-9%29%5E%7B2%7D%2B%280%29%5E%7B2%7D%7D)
![r=9/ units](https://tex.z-dn.net/?f=r%3D9%2F%20units)
step 2
Find the equation of the circle
The equation of the circle in center radius form is equal to
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
we have
![(h,k)=(0,0)\\r=9\ units](https://tex.z-dn.net/?f=%28h%2Ck%29%3D%280%2C0%29%5C%5Cr%3D9%5C%20units)
substitute
![(x-0)^2+(y-0)^2=9^2](https://tex.z-dn.net/?f=%28x-0%29%5E2%2B%28y-0%29%5E2%3D9%5E2)
![x^2+y^2=81](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D81)
Answer:
Option 4th is correct
![2 \cdot (x-4)(x+4)](https://tex.z-dn.net/?f=2%20%5Ccdot%20%28x-4%29%28x%2B4%29)
Step-by-step explanation:
Using difference of square:
![a^2-b^2=(a-b)(a+b)](https://tex.z-dn.net/?f=a%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29)
GCF is the largest number that divide the given polynomial or expression.
Given the expression:
![2x^2-32](https://tex.z-dn.net/?f=2x%5E2-32)
We have to completely factor the expression.
GCF of
and 32 is, 2
then;
![2 \cdot (x^2-16)](https://tex.z-dn.net/?f=2%20%5Ccdot%20%28x%5E2-16%29)
Using difference of square
![2 \cdot (x-4)(x+4)](https://tex.z-dn.net/?f=2%20%5Ccdot%20%28x-4%29%28x%2B4%29)
therefore, the completely factor of
is, ![2 \cdot (x-4)(x+4)](https://tex.z-dn.net/?f=2%20%5Ccdot%20%28x-4%29%28x%2B4%29)
First convert both distances to the same unit.
1 mile is 5280 feet or 1760 yards.
Subtract 1760-880 and get 880 yards.
Noah swam 880 yards further than Liam ran.
Answer:
7 1/2 pints of water
Step-by-step explanation:
No. of pints of water drank by Ian during hike = 3
Given that he drinks 1 1/2 more cups of water when he gets home
No. of pints of water drank by Ian during return to home = No. of pints of water drank by Ian during hike + 1 1/2 = 3 + 1 1/2
No. of pints of water drank by Ian during return to home = 3 + (2*1 + 1)/2
= 3 + 3/2
Taking 2 as lCM for addition
= (3*2 + 3)/2
=9/2 = 4 1/2
Total water drank by Ian altogether = 3 + 4 1/2 = 7 1/2
Therefore, Ian drank 7 1/2 pints of water during Hike and return altogether.
Area = 1/4 πr²
Area = 1/4 π (32)²
Area = 804.25 cm²
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Answer: 804.25 cm²
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