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Answer:
The highest altitude that the object reaches is 576 feet.
Step-by-step explanation:
The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be
, the first and second derivatives are, respectively:
First Derivative

Second Derivative

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:


(Critical value)
The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:


The highest altitude that the object reaches is 576 feet.
Answer:
Step-by-step explanation:
<u>Area of triangle:</u>
We have the value of b but not h.
Added auxiliary segments which help to find the value of h.
<em>See attached for details</em>
- sin 40° = h/4
- h = 4 sin 40°
- h = 2.57 km
<u>The area is:</u>
- A = 1/2*6*2.57 = 7.71 km²
Answer:
90.6m
Step-by-step explanation:
Initial speed = 8m/s
Time = 4.3 s
In studying the motion of an object, we often make use of kinematic equation
s = ut + 1/2at^2
v^2 = u^2 + 2as
a = (v - u) / t
v = final velocity
u = initial velocity
s = distance or height
t = time
a = acceleration due to gravity
Given time to hit the ground as 4.3s, we calculate the height by using
s = ut + 1/2at^2
Since the stone is moving against gravity, a is negative
u = 0
s = 0(4.3) +1/2(-9.8)(4.3)^2
s = -90.6m
The height of the cliff is 90.6m