An advertising blimp hovers over a stadium at an altitude of 125 m. The pilot sights a tennis court at and 8° angle of depressio
n. Find the ground distance in a straight line between the stadium and the tennis court. Round to the nearest 100 m.
1 answer:
Answer:
Hence the ground distance is about 889m between stadium and Tennis court.
Step-by-step explanation:
Given:
A pilot at height of 125 m(flying the advertising blimp)
angle of depression=8 degrees.
To find :
The ground distance stadium and tennis court.
Solution :
Using Trigonometric Function we can solve it ,
(Refer the attachment for fig)
Considering above data we get a triangle(ABC)
with point A represent pilot position and C court position and B as stadium.
The height AB=125 m
angle of depression= 8 degrees.
Using
<em>tan∅ =AB/BC</em>
tan(8)=125/BC
BC=125/tan(8)
=125/0.14054
=889.2
=889 m
Hence the ground distance is about 889m between stadium and Tennis court.
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Answer:
Santos should run approximately 36.145 meters along the shore
Step-by-step explanation:
The given parameters are;
The distance along the shore of the child = 50 meters
The distance from the shore of the child = 60 meters
The rate at which Santos can run = 4 m/s
The rate he can swim = 0.9 m/s
Let 'x' represent the distance he runs along the shore
We have;
The time he spends running on the shore, t₁ = x/4
The time he spends swimming, t₂ = (√(60² + (50 - x)²)/0.9
The total time, T = t₁ + t₂ = x/4 + (√(60² + (50 - x)²)/0.9
To find the maximum, we have;
dT/dx = 0 = d(x/4 + (√(60² + (50 - x)²)/0.9)/dx = 1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0
1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0
Simplifying using a graphing calculator gives;
1519·x² - 151900·x + 3505900 = 0
x = (151900 ± √((-151900)² - 4×1519×3505900))/(2 × 1519)
x ≈ 63.86 m or x ≈ 36.145 m
We note that the distance from a point x = 63.83 meters and 36.145 meters from where Santos spots the girl to the location of the girl are the same
Therefore, Santos should run approximately 36.145 meters along the shore before jumping into to the water in order to save the child
Answer: Second option.
Step-by-step explanation:
Given the functions f(x) and g(x):
You need to divide them in order to find asked in the exercise. Then:
Now, it is important to remember that, by definition, the division by zero is not defined. Therefore, the denominator of the function cannot be zero.
Let's find the value of "x" for which the denominator of the function would be zero:
1. You need to make the denominator equal to zero:
2. Finally, you must solve for "x":
Therefore, as you can see, the answer is:
,