A hovercraft takes off from a platform. Its height (in meters), 2 seconds after takeoff, is modeled by: h(x) = -3(x - 3)2 + 108
What is the height of the hovercraft at the time of takeoff?

81 m

Step-by-step explanation:

At take off t = 0, substitute x = 0 into h(x)

h(0) = - 3(0 - 3)² + 108 = - 3(9) + 108 = - 27 + 108 = 81 m

the expected value of the random variable : 0, 1 and 2

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°