Answer:
The length of DF must be between 21 and 53.
Step-by-step explanation:
In a triangle, the length of two sides added together must exceed the length of the 3rd side. So, since EF is the shortest of the two givens, we know that EF + DF must be greater than DE. So we can plug in these numbers to find the minimum.
EF + DF > DE
16 + DF > 37
DF > 21
Now, for the upper maximum, we know that the two given lengths must be greater than the length of DF. So again, we can solve for the maximum using the amounts.
DE + EF > DF
37 + 16 > DF
53 > DF
With these two in mind, we know that DF must be between 21 and 53
Height of the water increasing is at rate of 
<h3>How to solve?</h3>
With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:
There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:
Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:
In the problem, we are given 
So we need to substitute this in:
Hence, Height of the water increasing is at rate of
<h3>Formula used: </h3>
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The angles in a triangle always add up to exactly 180 degrees. To see if this can be a triangle, add up the given angle measures. If the sum is not 180, then it cannot be a triangle.
140+43+7=190
A triangle CANNOT have the angles measures as 140, 43, and 7.
Hope this helps!!
Answer:
The first graph.
Step-by-step explanation:
The equation is x is greater than 2. Therefore, the graph needs to shade anything greater than 2, but not 2.
Answer: x= ±(√30) / 5
Step by step:
