The statement- A cup with a hole in it loses 2 ounces of water in the first minute and then loses 2 ounces of water in the second minute is False,
and statement- A diver descends to the shipwreck and, after he is done exploring, returns to the surface of the water is True.
An integer plus its opposite sum to zero. The opposite of a number is called the additive inverse because the two number sum is zero.
Now in the first statement we have,
A cup with a hole in it loses 2 ounces of water in the first minute and then loses 2 ounces of water in the second minute.
Let x be the ounces of water in the cup.
Then amount of water lost in first minute = x-2 ounces
and amount of water lost in second minute = (x-2) - 2 ounces
Hence for additive inverse,
amount of water lost in first minute + amount of water lost in second minute = 0
⇒ x-2 + (x-2) - 2 = x - 2 + x -2 -2 = x - 6
⇒ x - 6 ≠ 0
Hence, the first statement is false.
Second Statement, A diver descends to the shipwreck and, after he is done exploring, returns to the surface of the water.
Let y be the distance from the surface to the site of exploring, then
⇒Distance travelled from surface to site of exploring = y
⇒ Distance travelled from site to surface = -y
Then for additive inverse,
Distance from surfe
Distance travelled from surface to site of exploring + Distance travelled from site to surface = 0
⇒ y + (-y) = y - y = 0
Hence second statement is true.
So,
The statement- A cup with a hole in it loses 2 ounces of water in the first minute and then loses 2 ounces of water in the second minute is False,
and statement- A diver descends to the shipwreck and, after he is done exploring, returns to the surface of the water is True.
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