<u>Given</u>:
The equation of the circle is 
We need to determine the center and radius of the circle.
<u>Center</u>:
The general form of the equation of the circle is 
where (h,k) is the center of the circle and r is the radius.
Let us compare the general form of the equation of the circle with the given equation
to determine the center.
The given equation can be written as,

Comparing the two equations, we get;
(h,k) = (0,-4)
Therefore, the center of the circle is (0,-4)
<u>Radius:</u>
Let us compare the general form of the equation of the circle with the given equation
to determine the radius.
Hence, the given equation can be written as,

Comparing the two equation, we get;


Thus, the radius of the circle is 8
L = 2 W
B = L x W = 2 W²
Side Area = 2 W H + 2 L H = 2 H ( W + L ) = 6 H W
V = 2 W² H = 10
H = 5 / W²
Cost = 15 * 2 W² + 9 * 5/W
= 30 W² + 270/ W
C ` = 60 W - 270 / W²
= ( 60 W² - 270 ) / W² = 0
60 W² = 270
W ² = 270 : 60
W² = 4.5
W = √ 4.5 = 2.12
Cost (min) = 15 * 2 * 4.5 + 30 / 2.12 = 135 + 14.15 = $149.15
Answer: The cost of materials for the cheapest such container is $149.15.
Answer:
1.
31, 37, 43, 49, 55
2.
for nth number the value is 31+6(n-1)
3.
24th number, 169-31=138 and 138/6=23
Answer:
Distance = 8.6
M = (-13.5,27.5)
Step-by-step explanation:
Distance = 
= 
= 
= 
= 
= 
= 8.6
Midpoint = 
= (-10+(-17)) ÷ 2 ; (30+25) ÷ 2
= -27 ÷2 ; 55 ÷ 2
= -13.5, 27.5
24 divided by 3 = 8
So if the barge takes only 2 hours during the return trip. We multiply 2 hours by 8 miles to get a total of 16 hours.
The answer is 16