Question

The function h(t) = −5t2 + 15t shown in the graph models the supporting structure of a bridge:

Answer 1

Since the function is h(t) = −5t² + 15t, the domain of the function h(t) is  0 ≤ t ≤ 3

What is the domain of a function?

The domain of a function is the range of input values that make the function have real values.

Now given the function h(t) = −5t² + 15t, it will have real values when

h(t) ≥ 0

So, h(t) ≥ 0

⇒  −5t² + 15t ≥ 0

Factorizing, we have

-5t(t - 3) ≥ 0

5t(t - 3) ≤ 0

t(t - 3) ≤ 0

t ≤ 0 and t - 3 ≤ 0

t ≤ 0 and t ≤ 3

For t ≤ 0, say -1, t(t - 3) = -1(-1 - 3) = -1(-4) = 4 ≥ 0

For 0 ≤ t ≤ 3, say 2, t(t - 3) = 2(2 - 3) = 2(-1) = -2 ≤ 0

For t ≥ 3, say 4, t(t - 3) = 4(4 - 3) = 4(1) = 4 ≥ 0

Since we require  t(t - 3) ≤ 0, the domain of t is thus 0 ≤ t ≤ 3

So, the domain of the function h(t) is  0 ≤ t ≤ 3

Learn more about domain of a function here:

brainly.com/question/204418

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