Question

=the height in metres of a weather ballon above the ground after t seconds can be modelled by the function h(t)=-2t^3+3t^2+149, for 0<t<10. when is the ballon exactly 980 m above the ground?

Answer 1

h(t)=-2t^3+3t^2+149 = 980

-2 t^3 + 3 t^2 - 831 = 0

There is no positive real root. I think a typo
I bet you mean
h(t)=-2t^3+3t^2+149t
so
-2 t^3 + 3 t^2 + 149 t - 980 = 0
nope, no real + roots
I think a typo

Answer 2

let me rewrite the question:
the height,h, in metres, of a weather balloon above the ground after t seconds can be modelled by the function h(t)=-2t^3+3t^2+149+410, for 0<t<10. when is the balloon exactly 980 m above the ground
my bad i messed up the number

Answer 3

its *h(t)=-2t^3+3t^2+149t+410,

Answer 4

-2t^3+3t^2+149t+410 = 980
2t^3 - 3t^2 - 149t + 570 = 0

could try 1, 2, 3, 4, 5 ,6, 7, 8, 9 ,10
Well, what do you know,
t=5 works and so does t = 6
so there has to be 3 factors, I know the first two are
(t-5)(t-6)(? t + ?) = 0
by the "common sense" theorem, the third factor must be
2t + 19 , which would yield a negative t , no good

the balloon is above 980 m above after 5 minutes and again after 6 minutes

check one of them...
t = 6
h(6) = -2(6^3) + 3(6^2) + 149(6) + 410
= -432 + 108 + 894 +410
= 980

Answer 5

where do we get the 570 from?

Answer 6

Remember your algebra I?
Subtract 980 from both sides. You want to have f(x) = 0 to solve for x.