Ya, calculus and related rates, such fun!
everything is changing with respect to t
altitude rate will be dh/dt and that is 1cm/min
dh/dt=1cm/min
area will be da/dt which is increasing at 2cm²/min
da/dt=2cm²/min
base=db/dt
alright
area=1/2bh
take dervitivie of both sides
da/dt=1/2((db/dt)(h)+(dh/dt)(b))
solve for db/dt
distribute
da/dt=1/2(db/dt)(h)+1/2(dh/dt)(b)
move
da/dt-1/2(dh/dt)(b)=1/2(db/dt)(h)
times 2 both sides
2da/dt-(dh/dt)(b)=(db/dt)(h)
divide by h
(2da/dt-(dh/dt)(b))/h=db/dt
ok
we know
height=10
area=100
so
a=1/2bh
100=1/2b10
100=5b
20=b
so
h=10
b=20
da/dt=2cm²/min
dh/dt=1cm/min
therefor
(2(2cm²/min)-(1cm/min)(20cm))/10cm=db/dt
(4cm²/min-20cm²/min)/10cm=db/dt
(-16cm²/min)/10cm=db/dt
-1.6cm/min=db/dt
the base is decreasing at 1.6cm/min
2a-8a=12-8a
now add 8a to both side and you get
2a= 12
divide both sides by 2 and you get
a=6
Answer:
120.2 or in other words, the answer is the last option, D
<span>The factors of 36 are 36, 18, 12, 9, 6, 4, 3, 2, 1.
<span>The factors of 90 are 90, 45, 30, 18, 15, 10, 9, 6, 5, 3, 2, 1.</span></span>
Answer:
B. 26.99 ft.
Step-by-step explanation:
The formulas for circumference (C) and area (A) are ...
A = πr²
C = 2πr
Solving the area formula for r, we get ...
r = √(A/π)
Substituting this into the circumference formula gives ...
C = 2π√(A/π) = 2√(πA)
For the given circle, the numbers are ...
C = 2√(3.14×58 ft²) ≈ 26.99 ft
