What is the perimeter of a square which has the same area as a circle with circumference of 4π?
1 answer:
Answer:
perimeter = 8
Step-by-step explanation:
We require to calculate the area (A) of the circle
A = πr² ← r is the radius
circumference = 4π = 2πr, hence
2πr = 4π ( divide both sides by 2π )
r = 2, hence
A = π × 4 = 4π
The area of the square is therefore 4π and area = s² ← s is the side length
s² = 4π ( take the square root of both sides )
s = = 2
, hence
perimeter = 4 × 2 = 8
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Answer:
Albert = $2159.07; Marie = $2244.99; Hans = $2188.35; Max = $2147.40
Marie is $10 000 richer
Step-by-step explanation:
Albert
(a) $1000 at 1.2 % compounded monthly
A = 1000(1 + 0.001)¹²⁰ = $1127.43
(b) $500 losing 2%
0.98 × 500 = $490
(c) $500 compounded continuously at 0.8%
(d) Balance
Total = 1127.43 + 490.00+ 541.64 = $2159.07
Marie
(a) 1500 at 1.4 % compounded quarterly
A = 1500(1 + 0.0035)⁴⁰ = $1724.99
(b) $500 gaining 4 %
1.04 × 500 = $520.00
(c) Balance
Total = 1724.99 + 520.00 = $2244.99
Hans
$2000 compounded continuously at 0.9 %
Max
(a) $1000 decreasing exponentially at 0.5 % annually
A = 1000(1 - 0.005)¹⁰= $951.11
(b) $1000 at 1.8 % compounded biannually
A = 1000(1 + 0.009)²⁰ = $1196.29
(c) Balance
Total = 951.11 + 1196.29 = $2147.40
Marie is $ 10 000 richer at the end of the competition.