Yes, 0.069 is less than 0.07~
First, we compare the "one" place: 0 = 0.
Second, we compare the "tenth" place: 0 = 0.
Next, we compare the "hundredth" place: 6 < 7.
Because 6 < 7, 0.069 < 0.07 as a result~
Answer:
5/8
Step-by-step explanation:
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:
Step-by-step explanation:
Please use " ^ " to denote exponentiation: f(x) = x^2 + 4x - 21.
This function has a graph which is a parabola that opens up.
Its vertex is found by completing the square:
x² + 4x + 4 - 4 - 21, or
(x + 2)² - 25
Comparing this to the standard equation
(x - h)² + k, we see that h = -2 and k = -25.
Thus, the vertex (and the minimum of this function) is (-2, -25).
Thus, the range is [-25, ∞ ). This being a polynomial function, it has no restrictions on the domain: the domain is (-∞, ∞ )
