What is the distance between points (4, −7) and (−5, 9)?
1 answer:
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Answer: Any irrational number
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a fraction of two integers where the denominator is different from zero, it is also characterized by the fact that its decimal expression is neither exact nor periodic.
As an example of this we have
On the other hand, it is necessary to know the following:
-The multiplication of two rational numbers results in a rational number.
-The multiplication of a <u>rational number</u> by <u>any irrational number</u> results in an <u>irrational number.</u>
This means that if we multiply 1/4 (which is rational) by any irrational number, the result will be irrational.
Therefore, the answer is: Any irrational number.
<h3>Rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr</h3><h3><u>Solution:</u></h3>
Given that,
A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream
Therefore,
Upstream distance = 165 km
Upstream time = 3 hours
<h3><u>Find upstream speed:</u></h3>Thus upstream speed is 55 km per hour
Downstream distance = 510 km
Downstream time = 6 hours
<h3><u>Find downstream speed:</u></h3>Thus downstream speed is 85 km per hour
<em><u>If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then</u></em>
Speed downstream = u + v km/hr
Speed upstream = u - v km/hr
Therefore,
u + v = 85 ----- eqn 1
u - v = 55 ----- eqn 2
Solve both
Add them
u + v + u - v = 85 + 55
2u = 140
u = 70
<em><u>Substitute u = 70 in eqn 1</u></em>
70 + v = 85
v = 85 - 70
v = 15
Thus rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr