Yes they are equivalent expressions. If you take the z to the power of two, and subtract that from the other z to the power of two, it is zero. So you are left with four which is the answer
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.
60/ (30/100)
= 60* (100/30)
= 200
The final answer is 200~
The polar equation will be 
<h3> What is the polar equation?</h3>
A polar equation is any equation that expresses the relationship between r and theta, where r is the distance between the pole (origin) and a point on a curve, and theta is the counterclockwise angle formed by a point on a curve, the pole, and the positive x-axis.
From the equation, we are told that
The Eccentricity: e = 1
The Directrix is y = 4
Generally, the polar equation for e = 1 and y = + c is mathematically represented as
Therefore the polar equation will be
To know more about the polar equation follow
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Answer:
2 * 10 ^-4
Step-by-step explanation:
We need the first number to be between 1 and less than 10
.0002
2 * 10 ^ exponent
We move the decimal 4 places to the right. Since we move it to the right the exponent is negative and is the number of places we moved the decimal
2 * 10 ^-4
