Follow the given formula. The initial amount of money invested, P, becomes 2P (same thing as "doubles) after t years. Since compounding is quarterly, n=4. The annual interest rate is 12%. That is, r=0.12.
Then we have 2P = P (1 + 0.12/4)^(4t) and need only solve for time, t.
Simplifying the above equation: 2 = (1.03)^(4t)
We must isolate 4t, and then isolate t. To do this, take the common log of both sides of the above equation. We get:
log 2 = (4t) log 1.03. This gives us 4t = [log 2] / [log 1.03], or
4t = 23.4498
Dividing both sides by 4, we get t = 5.86 (years).
Answer:
Write the problem as a mathematical expression.
y=−x²+18x−72
Rewrite the equation in vertex form.
y=−(x−9)²+9
Use the vertex form, y=a(x−h)2+k , to determine the values of a, h, and k.
a=−1
h=9
k=9
Find the vertex (h,k).
(9,9)
Good Luck !
Step-by-step explanation:
Answer:
Area segment = 3/2 π - (9/4)√3 units²
Step-by-step explanation:
∵ The hexagon is regular, then it is formed by 6 equilateral Δ
∵ Area segment = area sector - area Δ
∵ Area sector = (Ф/360) × πr²
∵ Ф = 60° ⇒ central angle of the sector
∵ r = 3
∴ Area sector = (60/360) × (3)² × π = 3/2 π
∵ Area equilateral Δ = 1/4 s²√3
∵ The length of the side of the Δ = 3
∴ Area Δ = 1/4 × (3)² √3 = (9/4)√3
∴ Area segment = 3/2 π - (9/4)√3 units²
Answer:
3 days
Step-by-step explanation
50 multiplied by 6 is 300 cupcakes a day. 900/300= 3