Which of the following could be an equation of the line that is perpendicular to= 2x + 5
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The rate of change of the angle of elevation when the firework is 40 feet above the ground is 0.12 radians/second.
First we will draw a right angle triangle ΔABC, where ∠B = 90°
Lets, assume the height(AB) = h and base(BC)= x
If the angle of elevation, ∠ACB = α, then
tan(α) =
Taking inverse trigonometric function, α = tan⁻¹ () .............(1)
As we need to find the rate of change of the angle of elevation, so we will differentiate both sides of equation (1) with respect to time (t) :
Here, the firework is launched from point B at the rate of 10 feet/second and when it is 40 feet above the ground it reaches point A,
that means h = 40 feet and = 10 feet/second.
C is the observer's position which is 50 feet away from the point B, so x = 50 feet.
= 0.12 (Rounding up to two decimal places)
So, the rate of change of the angle of elevation is 0.12 radians/second.
ANSWER
EXPLANATION
Recall that,
That is why
is equivalent to
This implies that,
This is the same as,
When we are dividing by
we move the decimal point backwards two times.
This implies that,
EXPLANATION
Recall that,
That is why
is equivalent to
This implies that,
This is the same as,
When we are dividing by
we move the decimal point backwards two times.
This implies that,