(a) This is the same as computing 4⁵⁵ (mod 11). We have
4² ≡ 16 ≡ 5 (mod 11)
4³ ≡ 4 • 5 ≡ 20 ≡ 9 (mod 11)
4⁴ ≡ 4 • 9 ≡ 36 ≡ 3 (mod 11)
4⁵ ≡ 4 • 3 ≡ 12 ≡ 1 (mod 11)
Then from here,
4⁵⁵ ≡ (4⁵)¹⁰ • 4⁵ ≡ 1¹⁰ • 1⁵ ≡ 1 (mod 11)
(b) Each term in the sum
4ⁿ + 4ⁿ⁺¹ + 4ⁿ⁺² + 4ⁿ⁺³ + 4ⁿ⁺⁴
has a common factor of 4ⁿ, so this sum is the same as
4ⁿ (1 + 4 + 16 + 64 + 256) = 4ⁿ • 341 = 4ⁿ • 11 • 31
So the sum is indeed divisible by 11 for all integers <em>n</em>.
(c) Since 4ⁿ = (2ⁿ)², we know the sum is also divisible by 11 when <em>a</em> = 2.
Answer:
P = 0.09r²
Step-by-step explanation:
Price, p is proportional to the square of its radius, r
P = k*r²
a mirror with radius 20cm has a price of £36
P = k * r²
36 = k * 20²
36 = k * 400
36 = 400k
k = 36/400
k = 0.09
Substitute the value of k into the equation:
P = k * r²
P = 0.09 * r²
P = 0.09r²
Do you really need an answer 1 hour later<span />
I'm pretty sure a strong steel manufactures would be a corporation. I hope this helps!
Answer: 1200 milliliters.
Step-by-step explanation: 1 liter has 100 milliliters of milk in it. So you have to multiply 1.2 by 100 to get 1200.
