If an angle is on a straight line, x is less than y by 40. find the values of x and y

Mathematics

1 answer:

notsponge [240]2 years ago

5 0

Answer:

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Step-by-step explanation:

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Two boats leave the same place at the same time. The first boat heads due north at 10 kilometers per hour. The second boat heads

Maksim231197 [3]

Answer:

18.87 km/hr

Step-by-step explanation:

First boat is heading North with a speed of 10 km/hr.

Second boat is heading West with a speed of 16 km/hr.

Time for which they move = 2.5 hours

To find:

The speed at which the distance is increasing between the two boats.

Solution:

Let the situation be represented by the attached diagram.

Their initial position is represented by point O from where they move towards point A and point B respectively.

$Distance = Speed \times Time$

$Distance\ OA = 10 \times 2.5 = 25\ km$

$Distance\ OB = 16 \times 2.5 = 40\ km$

We can use Pythagorean Theorem to find the distance AB.

AB is the hypotenuse of the right angled $\triangle AOB$ .

According to Pythagorean theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^2 = 25^2 + 40^2\\\Rightarrow AB^2 = 2225^2\\\Rightarrow AB^2 \approx 47.17\ km$