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
Answer:
Step-by-step explanation:
42/4=10.5 pounds in one bushel
10.5/2=5.25≈5 pies
It's possible to make 5 pies with one peck of apples
Both sides are equal, so the equation has infinite solutions.
25 - 4x = 15 - 3x + 10 - x
= 25 - 4x = 25 - 3x - x
= 25 - 4x = 25 - 4x
Remember you can do anything to an equation as long as you do it to both sides
17-9x=-3+16x
add 9x to both sides
17=-3+25x
add 3 to both sides
20=25x
divide both sides by 25

