Which number is rational , square root 2 , pi , square root 10 or square 16

Mathematics

2 answers:

melamori03 [73]3 years ago

8 0

The square root of 16 is rational.

vova2212 [387]3 years ago

4 0

Answer: The only rational number in your list is "square 16" - I am assuming you mean square root of 16.

Explanation:

Square root of 2 is irrational. This has been proven by the Pythagoreans (there is a simple proof of that).

pi is also known to be irrational although the proof is a bit more demanding.

Square root of 10 can be written as a product of square root of 5 and square root of 2, which themselves are irrational. Any product involving an irrational number is irrational

Square root of 16 = 4. 4 can be written as a fraction 4/1, or 8/2, 16/4, etc. and therefore is rational by definition.

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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

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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:

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