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3 years ago

Find the distance between the points below. 4 + 3i and 9 – 9i

Mathematics

1 answer:

stich3 [128]3 years ago

7 0

Answer:

13 units.

Step-by-step explanation:

The complex numbers can be thought of as points on the xy plane, where their real part (denoted Re(z)), and their imaginary part (Im(z)) serve as the coordinates for these numbers, and since we know how to calculate distances between points we can calculate the distance between these numbers:

Formula: $d(z_1, z_2) = \sqrt{(\Re(z_2) - \Re(z_1))^2 + (\Im(z_2) - \Im(z_1))^2}{} =>\\d(4+3i, 9 - 9i) = \sqrt{(9-4)^2 + (-9-3)^2} = \sqrt{5^2 + 12^2} = \sqrt{169} = \sqrt{13^2} = 13$

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3 years ago

A helicopter is flying above a town. the local high school is directly to the east of the helicopter at a 20° angle of depressio

guapka [62]

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.

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3 years ago

Read 2 more answers

ABC is a right angled triangle right angled at B . A circle with centre O inscribed in the triangle . AB=6CM BC=8CM . Find the r

Vikki [24]

Answer:

Radius = 2 cm.

Step by step explanation:

By the Pythagoras theorem the third side of the triangle

= sqrt (6^2 + 8^2)cm = sqrt100 = 10cm.

The formula for the radius of the circle is

r = sqrt [ (s - a)(s-b)(s-c)/ s ] where a,b,c are side lengths and s = the semi perimeter.

Here s = ( 6+8+10) / 2 = 12

So the radius r

= sqrt [ (12-6)(12-8)(12-10)/ 12 ]

= sqrt 4

= 2 (answer).

3 0

3 years ago