7 - 3 2/5 =
7 - 17/5 =
35/5 - 17/5 = 18/5 = 3.6
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
The figure is equal to 102.5 cubic feet.
If Jan bought 3 lamps for $23.59 each, and a sofa for $769.99, then we can add these prices together for the total amount Jan spent:
23.59 + 23.59 + 23.59 + <span>769.99 = $840.76
</span>
Now we can find out how much sales tax she owes by multiplying the total cost by the sales tax rate:
$840.76 x 7.5% = <span>840.76 x 0.075 = $63.06
</span>
Therefore the answer is B. $63.06
