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SOVA2 [1]
1 year ago
15

two buses leave a station at the same time and travel in opposite directions. One bus travels 15 km/h faster than the other. If

the two buses are 1004 kilometers apart after 4 hours, what is the rate of each bus?
Mathematics
1 answer:
Marina CMI [18]1 year ago
8 0

The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr

<h3>What is speed?</h3>

Speed is a scalar quantity that refers to "how fast an object is moving".

Given that, two buses leave a station at the same time and travel in opposite directions, one bus travels 15 km/h faster than the other, the two buses are 1004 kilometres apart after 4 hours,

Speed = distance/ time

Let the speed of the slower bus be v and the faster bus be (v+15)

According to the question,

vt + (v+15)t = 1004

vt + vt + 15t = 1004

t = 4

4v + 4v + 60 = 1004

8v = 944

v = 118

Hence, The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr

For more references on speed, click;

brainly.com/question/7359669

#SPJ1

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1. Derive the half-angle formulas from the double
lilavasa [31]

1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

<h3>How to apply trigonometry on deriving formulas and transforming points</h3>

1) The following <em>trigonometric</em> formulae are used to derive the <em>half-angle</em> formulas:

sin² θ / 2 + cos² θ / 2 = 1                      (1)

cos θ = cos² (θ / 2) - sin² (θ / 2)           (2)

First, we derive the formula for the sine of a <em>half</em> angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a <em>half</em> angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a <em>half</em> angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in <em>rectangular</em> form to <em>polar</em> form are obtained by <em>trigonometric</em> functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in <em>polar</em> form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in <em>rectangular</em> form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the <em>linear</em> function y = 5 · x - 8, we proceed to use the following <em>substitution</em> formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

To learn more on trigonometric expressions: brainly.com/question/14746686

#SPJ1

4 0
2 years ago
The waiting time to ride a roller coaster is 20 minutes when 150 people are in line. How long is the waiting time when 240 peopl
laiz [17]

Answer: The waiting time will be 32 minutes when 240 people in line.

Step-by-step explanation:

Let us assume that the waiting time is directly proportional to the number of people in the queue.

Equation of direct proportion between variables x and y :  \dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}

Put x_1=20,\ y_1=150,\ y_2=150  to find  x_2.

\dfrac{20}{150}=\dfrac{x_2}{240}\\\\\Rightarrow\ x_2=\dfrac{20}{150}\times240\\\\\Rightarrow\ x_2=32

Hence, the waiting time will be 32 minutes when 240 people in line.

3 0
2 years ago
Read 2 more answers
Increase £30 by 2/5?
Sergeu [11.5K]
2/5 of 30 = 12
30 + 12 = 42
£42
6 0
3 years ago
Mira has breakfast at a restaurant. She leaves a 20% tip of $1.80.
Anvisha [2.4K]

Answer:          $9.00

.......................................

4 0
3 years ago
Help me PLEASEEEeeee
Harlamova29_29 [7]

Answer:

y=-2x-2

Step-by-step explanation:

Just ask.

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8 0
2 years ago
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