5(x² + 6x + 10)
That's the best way to factor it
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:
∠ XMN = 50°
Step-by-step explanation:
∠ XNM and ∠ XKL are alternate angles and are congruent, then
∠ XNM = 35°
The sum of the 3 angles in a triangle = 180° , so
∠ XMN = 180° - (95 + 35)° = 180° - 130° = 50°
Answer:
5 x^2 - x + 6
Step-by-step explanation:
- (x^2 + 2) + 6 x^2 - x + 8
- x^2 - 2 + 6 x^2 - x + 8
(6 x^2 - x^2) - x + (8 - 2)
5 x^2 - x + (8 - 2)
= 5 x^2 - x + 6
