Answer:
Step-by-step explanation:
To determine the slope, divide the rise by the run to calculate the slope.
Note that
1 ft = 12 in
Let
y ----> the rise
x ----> the run
m ----> the slope
the values are given as
substituting these values gives
Simplifying further
We can use a graphing tool to plot the <span> cosecant function
</span>check the attached image
the answer corresponds to option B
Given that the water in the tank doubles every minute, it implies that when the tank was full, it was half full just one minute prior. If it reaches fullness after 60 minutes, it was indeed double what it was a minute earlier. Hence, the opposite of doubling is halving. A minute before the tank filled completely, it was at half capacity. Therefore, it confirms that it was half full after 59 minutes.
Imagine a right triangle where vertex B is at the base of the hill, vertex S is at the top of the statue, and vertex Y represents your position. This triangle has a right angle at B, and angle Y measures 13.2°. Let h denote the height of the statue, making the lengths of sides YB and BS equal to 77 ft and 16+h ft, respectively.
With the lengths of two sides and one angle known, the height h can be determined using the tangent function:
ft.
Result: the height of the statue calculates to be 2.0565 ft.
For this scenario, we start with the function:
<span>w (x) = - 5 (x-8) (x + 4)
</span><span>Reorganizing yields:
</span><span>w (x) = - 5 (x² + 4x - 8x - 32)
</span><span>w (x) = - 5x² - 20x + 40x + 160
</span><span>w (x) = - 5x² + 20x + 160
</span><span>Next, we take the derivative:
</span><span>w '(x) = - 10x + 20
</span><span>Setting this to zero and solving for x:
</span><span>0 = -10x + 20
</span><span>10x = 20
</span><span>x = 20/10
</span><span>x = 2 seconds
</span><span>Substituting back:
</span><span>w (2) = - 5 (2-8) (2 + 4)
</span><span>w (2) = - 5 (-6) (6)
</span><span>w (2) = 180 meters
</span>Conclusion:
The peak height attained by the stone is:
w (2) = 180 meters
