Answer: 4.5 miles
Explanation:
When you draw the situation you find two triangles.
1) Triangle to the east of the helicopter
a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°
b) hypotensue = distance between the high school and the helicopter
c) opposite-leg to angle 20° = heigth of the helicopter
d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x
2) triangle to the west of the helicopter
a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°
b) distance between the helicopter and the elementary school = hypotenuse
c) opposite-leg to angle 62° = height of the helicopter
d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x
3) tangent ratios
a) triangle with the helicpoter and the high school
tan 20° = Height / x ⇒ height = x tan 20°
b) triangle with the helicopter and the elementary school
tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°
c) equal the height from both triangles:
x tan 20° = (5 - x) tan 62°
x tan 20° = 5 tan 62° - x tan 62°
x tan 20° + x tan 62° = 5 tan 62°
x (tan 20° + tan 62°) = 5 tan 62°
⇒ x = 5 tant 62° / ( tan 20° + tan 62°)
⇒ x = 4,19 miles
=> height = x tan 20° = 4,19 tan 20° = 1,525 miles
4) Calculate the hypotenuse of this triangle:
hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²
hipotenuse = 4.46 miles
Rounded to the nearest tenth = 4.5 miles
That is the distance between the helicopter and the high school.
Answer:
The amount of oil was decreasing at 69300 barrels, yearly
Step-by-step explanation:
Given
Required
At what rate did oil decrease when 600000 barrels remain
To do this, we make use of the following notations
t = Time
A = Amount left in the well
So:
Where k represents the constant of proportionality
Multiply both sides by dt/A
Integrate both sides
Make A, the subject
i.e. At initial
So, we have:
Substitute in
To solve for k;
i.e.
So:
Divide both sides by 1000000
Take natural logarithm (ln) of both sides
Solve for k
Recall that:
Where
= Rate
So, when
The rate is:
<em>Hence, the amount of oil was decreasing at 69300 barrels, yearly</em>
The classifications of the functions are
- A vertical stretch --- p(x) = 4f(x)
- A vertical compression --- g(x) = 0.65f(x)
- A horizontal stretch --- k(x) = f(0.5x)
- A horizontal compression --- h(x) = f(14x)
<h3>How to classify each function accordingly?</h3>
The categories of the functions are given as
- A vertical stretch
- A vertical compression
- A horizontal stretch
- A horizontal compression
The general rules of the above definitions are:
- A vertical stretch --- g(x) = a f(x) if |a| > 1
- A vertical compression --- g(x) = a f(x) if 0 < |a| < 1
- A horizontal stretch --- g(x) = f(bx) if 0 < |b| < 1
- A horizontal compression --- g(x) = f(bx) if |b| > 1
Using the above rules and highlights, we have the classifications of the functions to be
- A vertical stretch --- p(x) = 4f(x)
- A vertical compression --- g(x) = 0.65f(x)
- A horizontal stretch --- k(x) = f(0.5x)
- A horizontal compression --- h(x) = f(14x)
Read more about transformation at
brainly.com/question/1548871
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Answer:
The person has a speed of 12 miles per hour.
Step-by-step explanation:
The ratio is 12 miles to 1 hour.
This means, that in every hour, the person can move 12 miles and has a speed of 12 miles per hour.
