Answer: 363
Step-by-step explanation:
The common difference is 7, so the explicit formula is 
.
Substituting in n=66,
Answer:
2³² -1
Step-by-step explanation:
The sequence has a₁ = 1 and r = 2. Filling in the numbers for n=32, we have ...
S₃₂ = 1·(1 -2³²)/(1 -2)
S₃₂ = 2³² -1
Answer: it would take 22 hours before you pay the same amount for both Garages.
Step-by-step explanation:
Let x represent the number of hours that you park at either Garage A or Garage B
Let y represent the total amount paid for x hours at Garage A
Let z represent the total amount paid for x hours at Garage B
Garage A charges $11 for the first 2 hours of parking there and then $3 per hour after the first 2 hours. This means that the total amount for x hours would be
y = 2 × 11 + 3x
y = 22 + 3x
Garage B charges $4 per hours. This means that the total amount for x hours would be
z = 4x
To determine the number of hours before the amount for both Garages becomes the same, we would equate y to z. It becomes
22 + 3x = 4x
4x - 3x = 22
x = 22
Answer:
( √15 + 8)/7
Step-by-step explanation:
TanA = -√15
.we are to find tan(A-π/4).
In trigonometry
Tan(A-B) = TanA - TanB/1+ tanAtanB
Hence:
tan(A-π/4) = TanA - Tanπ/4/1+ tanAtanπ/4
Substitute tan A value into the formula
tan(A-π/4) = -√15-tanπ/4 / 1+(-√15)(tanπ/4
tan(A-π/4) = -√15-1/1-√15
Rationalize
-√15-1/1-√15 × 1+√15/1+√15
= -√15-√225-1-√15/(1-√225)
= -2√15-15-1/1-15
= -2√15 -16/(-14)
= -2(√15+8)/-14
= √15 + 8/7
Hence the required value is ( √15 + 8)/7
