A box with a height (x+5) has a square base with side x. A second box with height (x+2) has a square base with side (x+5). If th
1 answer:
Answer :
x = -1.43
Explanation :
As given ,
The first box has a height (x+5) has a square base with side x
So, the Length and Breadth of the box are x and x respectively.
Now,
The volume of first box = Length×Breadth×Height
= (x).(x).(x+5)
= x²(x+5)
⇒The volume of first box = x²(x+5)
Now,
Given that , the second box with height (x+2) has a square base with side (x+5).
So, the Length and Breadth of the box are (x+5) and (x+5) respectively.
Now,
The volume of second box = Length×Breadth×Height
= (x+5). (x+5).(x+2)
= (x+5)²(x+2)
⇒The volume of second box = (x+5)²(x+2)
Now,
Given that, the two boxes have the same volume
⇒x²(x+5) = (x+5)²(x+2)
⇒x² = (x+5)(x+2)
⇒x² = x² + 2x + 5x + 10
⇒x² - x² = 7x + 10
⇒0 = 7x + 10
⇒ 7x = -10
⇒ x = - = -1.43
⇒ x = -1.43
As volume of first box = x²(x+5) = (-1.43)²(-1.43+5) = 7.30 ≈ 7
As volume of second box = (x+5)²(x+2) = (-1.43+5)²(-1.43+2) = 7.26 ≈ 7
At x = -1.43, Volume of both the boxes are same.
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Answer:
(a) As time increases, the amount of water in the pool increases.
11 gallons per minute
(b) 65 gallons
Step-by-step explanation:
From inspection of the table, we can see that <u>as time increases, the amount of water in the pool increases</u>.
We are told that Ann adds water at a constant rate. Therefore, this can be modeled as a linear function.
The rate at which the water is increasing is the <em>rate of change</em> (which is also the <em>slope </em>of a linear function).
Choose 2 ordered pairs from the table:
Input these into the slope formula:
Therefore, the rate at which the water in the pool is increasing is:
<u>11 gallons per minute</u>
To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:
When Ann had added no water, x = 0. Therefore,
So there was <u>65 gallons</u> of water in the pool before Ann starting adding water.