Answer:
Using 3.14 for pi A = 113.0 ft^2
Using the pi button A = 113.1 ft^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi ( 6)^2
A = 36 pi
Using 3.14 for an approximation for pi
A = 36(3.14) = 113.04
To 1 decimal
113.0
Using the pi button
A = 113.0973355
A = 113.1
Answer:
Step-by-step explanation:
Equation of circle: (x - h)² + (y - k)² = r² where (h,k) is the center.
Center( -4 , 4) and r = 5
(x -[-4])² + (y - 4)²= 5²
(x + 4)² + (y-4)² = 25
x² + 2*4*x +4² + y² - 2*y*4 + 4² = 25
x² +8x + 16 + y² - 8y + 16 = 25
x² + 8x + y² - 8y + 16 + 16 -25 = 0
x² + 8x + y² - 8y +7 = 0
Answer:
{ x : x = 2^n -1 , n ∈ N}
Where N is the set of natural numbers
Step-by-step explanation:
Mathematically, we can rewrite each term in the set as follows;
1 = 2^1 - 1
3 = 2^2 -1
7 = 2^3 -1
15 = 2^4-1
31 = 2^5-1
63 = 2^6 -1
so we can conclude that the nth term is 2^n -1
So writing this in set builder notation, we have;
{ x : x = 2^n -1 , n ∈ N}
Where N is the set of natural numbers
Answer:
![a=[2q^{2}r]](https://tex.z-dn.net/?f=a%3D%5B2q%5E%7B2%7Dr%5D)
![b=[3s^{2}t]](https://tex.z-dn.net/?f=b%3D%5B3s%5E%7B2%7Dt%5D)
Step-by-step explanation:
we have

we know that
![8q^{6}r^{3}=(2^{3})(q^{2})^{3}r^{3}=[2q^{2}r]^{3}](https://tex.z-dn.net/?f=8q%5E%7B6%7Dr%5E%7B3%7D%3D%282%5E%7B3%7D%29%28q%5E%7B2%7D%29%5E%7B3%7Dr%5E%7B3%7D%3D%5B2q%5E%7B2%7Dr%5D%5E%7B3%7D)
![27s^{6}t^{3}=(3^{3})(s^{2})^{3}t^{3}=[3s^{2}t]^{3}](https://tex.z-dn.net/?f=27s%5E%7B6%7Dt%5E%7B3%7D%3D%283%5E%7B3%7D%29%28s%5E%7B2%7D%29%5E%7B3%7Dt%5E%7B3%7D%3D%5B3s%5E%7B2%7Dt%5D%5E%7B3%7D)
therefore
![a=[2q^{2}r]](https://tex.z-dn.net/?f=a%3D%5B2q%5E%7B2%7Dr%5D)
![b=[3s^{2}t]](https://tex.z-dn.net/?f=b%3D%5B3s%5E%7B2%7Dt%5D)
substitute

![[2q^{2}r]^{3} +[3s^{2}t]^{3}=([2q^{2}r]+[3s^{2}t])([2q^{2}r]^{2} -[2q^{2}r][3s^{2}t]+[3s^{2}t]^{2})](https://tex.z-dn.net/?f=%5B2q%5E%7B2%7Dr%5D%5E%7B3%7D%20%2B%5B3s%5E%7B2%7Dt%5D%5E%7B3%7D%3D%28%5B2q%5E%7B2%7Dr%5D%2B%5B3s%5E%7B2%7Dt%5D%29%28%5B2q%5E%7B2%7Dr%5D%5E%7B2%7D%20-%5B2q%5E%7B2%7Dr%5D%5B3s%5E%7B2%7Dt%5D%2B%5B3s%5E%7B2%7Dt%5D%5E%7B2%7D%29)
![[2q^{2}r]^{3} +[3s^{2}t]^{3}=([2q^{2}r]+[3s^{2}t])([4q^{4}r^{2}] -6[q^{2}r][s^{2}t]+[9s^{4}t^{2}])](https://tex.z-dn.net/?f=%5B2q%5E%7B2%7Dr%5D%5E%7B3%7D%20%2B%5B3s%5E%7B2%7Dt%5D%5E%7B3%7D%3D%28%5B2q%5E%7B2%7Dr%5D%2B%5B3s%5E%7B2%7Dt%5D%29%28%5B4q%5E%7B4%7Dr%5E%7B2%7D%5D%20-6%5Bq%5E%7B2%7Dr%5D%5Bs%5E%7B2%7Dt%5D%2B%5B9s%5E%7B4%7Dt%5E%7B2%7D%5D%29)
It would be 15 because 2/3 of $12 is $8. she has enough money to buy 10 bags from the gift shop which means she has $120. at the pharmacy, $120 would buy her 15 bags.