Answer:
A = 20sinθ(6 + 5 cosθ) cm²
Step-by-step explanation:
Drop perpendiculars DE and CF to AB.
Then, we have congruent triangles ADE and BCF, plus the rectangle CDEF.
The formula for the area of the trapezium is
A = ½(a + b)h
DE = 10sinθ
AE = 10cosθ
BF = 10cosθ
EF = CD = 12 cm
AB = AE + EF + BF = 10cosθ + 12 + 10 cosθ = 12 + 20cosθ
A = ½(a + b)h
= ½(12 +12 + 20 cosθ) × 10 sinθ
=(24 + 20 cosθ) × 5 sinθ
= 4(6 + 5cosθ) × 5sinθ
= 20sinθ(6 + 5 cosθ) cm²
Answer:
5.93 years
Step-by-step explanation:
The continuous compounding formula tells you the amount after t years will be ...
A = Pe^(rt) . . . . principal P compounded continuously at annual rate r for t years
7400 = 5500e^(0.05t)
ln(7400/5500) = 0.05t . . . . divide by 5500, take natural logs
t = 20×ln(74/55) ≈ 5.93
It will take about 5.93 years for $5500 to grow to $7400.
Answer:
x = 4
Step-by-step explanation:
Given the 2 equations
2x - y = 11 → (1)
x + 3y = - 5 → (2)
Multiply (1) by 3 and add to (2) to eliminate the y- term
6x - 3y = 33 → (3)
Add (2) and (3) term by term to eliminate y, that is
7x = 28 ( divide both sides by 7 )
x = 4
Answer:
Step-by-step explanation:
