Answer:
New price = $210
Step-by-step explanation:
Given:
Original price = $120
Increase in cost = 75%
Find:
New price
Computation:
New price = Original price + Increase in cost
New price = 120 + 120(75%)
New price = 120 + 90
New price = $210
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:
x = 2 ± ![\sqrt{13}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D)
Step-by-step explanation:
Given
y = x² - 4x - 9
To find the zeros, set y = 0, that is
x² - 4x - 9 = 0 ( add 9 to both sides )
x² - 4x = 9
To complete the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(- 2)x + 4 = 9 + 4, that is
(x - 2)² = 13 ( take the square root of both sides )
x - 2 = ±
( add 2 to both sides )
x = 2 ±
← exact solutions
Answer:
r = 0.0424 cm (3sf)
Step-by-step explanation:
it makes 150 rev/sec
1 revolution = 1 circumference = 2pi*r
so every second the spool goes through 2*pi*r*150 of distance
we know that the rate of pulling is 40cm/sec
so 2pi*r*150 = 40
r = 40/(2pi*150), which is 0.04244131816 cm.
check: Circumference is 2pi*r = 0.2666
now multiply by 150rev/sec = 40 cm/sec
Answer:
b
Step-by-step explanation:
1 plus 2 equals three