Please solve this for 15 points
1 answer:
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I think you are asked to find the value of the first derivative of <em>f(x)</em> at <em>π</em>/4. Given
use the quotient to differentiate and you get
Then at <em>x</em> = <em>π</em>/4, you have
tan(<em>π</em>/4) = 1
cos(4•<em>π</em>/4) = cos(<em>π</em>) = -1
sin(<em>π</em>/4) = 1/√2
sin(4•<em>π</em>/4) = sin(<em>π</em>) = 0
cos(<em>π</em>/4) = 1/√2
sec(<em>π</em>/4) = √2
==> <em>f '</em> (<em>π</em>/4) = (1•(-4 + 1/√2) - (0 - 1/√2)•(√2)²) / 1² = -4 + 1/√2 + √2
Answer:
The horizontal distance between the lifeguard and the person is approximately 24.751 feet.
Step-by-step explanation:
At first we include a geometrical representation of the statement, which is shown in the image attached below. We can determine the horizontal distance between the lifeguard and the person by means of the following trigonometrical relationship:
(1)
Where:
- Angle of depression to the person, measured in sexagesimal degrees.
- Height of the lifeguard above the ground, measured in feet.
- Horizontal distance between the lifeguard and the person, measured in feet.
If we know that and
, then the horizontal distance between the lifeguard and the person is:
The horizontal distance between the lifeguard and the person is approximately 24.751 feet.
