Answer: After 1 year: $5,610
After 2 years: $5,722.20
Step-by-step explanation: Use the formula for periodic compounding interest, which is
A = P(1 + r/n)^(nt), where A is the final amount, P is the initial deposit, r is the interest rate as a decimal, n is the number of times the interest is compounded per year, and t is how many years.
Here, P = 5,500, r = 0.02 (that's 2% as a decimal), n = 1,
t = 1 for the first answer, t = 2 for the second answer (1 year, then for 2 years)
Plug the known values in to solve...
For 1 year...
A = 5,500(1 + 0.02/1)^(1*1)
A = 5,500(1.02)^1
A = 5,610
For 2 years...
A = 5,500(1 + 0.02/1)^(1*2)
A = 5,500(1.02)²
A = 5,722.20
Answer:
180:4 and 816:12
Step-by-step explanation:
7 stamps* ($2.20/ 5 stamps)= $3.08.
(Note that the unit cancels out so you get the answer)
The final answer is $3.08~
The angle between the planes is the same as the angle between their normal vectors, which are
<em>n</em><em>₁</em> = ⟨1, 1, 1⟩
<em>n</em><em>₂</em> = ⟨4, 3, 1⟩
The angle <em>θ</em> between the vectors is such that
⟨1, 1, 1⟩ • ⟨4, 3, 1⟩ = ||⟨1, 1, 1⟩|| ||⟨4, 3, 1⟩|| cos(<em>θ</em>)
Solve for cos(<em>θ</em>) :
4 + 3 + 1 = √(1² + 1² + 1²) √(4² + 3² + 1²) cos(<em>θ</em>)
8 = √3 √26 cos(<em>θ</em>)
cos(<em>θ</em>) = 8/√78
