Step-by-step explanation:
k² + 5k + 13 = 0
Using the quadratic formula which is
From the question
a = 1 , b = 5 , c = 13
So we have
<u>Separate the solutions</u>
The equation has complex roots
<u>Separate the real and imaginary parts</u>
We have the final answer as
Hope this helps you
Using a graphing calculator you can find that the maximum is 1038, so the profit starts to decline at the t value for <span>1038</span>, which is 31
2x+y>-4, 2*5-12=10-12= - 2, -2 > -4 (5, -12) matched, 2*0 + 1= 1> - 4, (0,1) matched, 2*-1 + (-1) = -3 > -4, (-1,-1) matched, the solutions are (5, -12) , (0,1) and (-1,-1), if the question is 2x+y>-4,
Y=x i hope this helps you!
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
