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 object reaches the lowest height at 5 seconds
<h3>How to determine the time?</h3>
The function is given as:
f(t) = -2t² +22t + 6
Differentiate the function
f'(t) = -4t +22
Set to 0
-4t +22 = 0
Subtract 22 from both sides
-4t = -22
Divide both sides by -4
t = 5.5
Remove decimal points
t = 5
Hence, the object reaches the lowest height at 5 seconds
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Answer:
The three numbers are 341, 342, and 343
Step-by-step explanation:
We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 1026. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 1026
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 1026
3X + 3 = 1026
3X + 3 - 3 = 1026 - 3
3X = 1023
3X/3 = 1023/3
X = 341
Which means that the first number is 341, the second number is 341 + 1 and the third number is 341 + 2. Therefore, three consecutive integers that add up to 1026 are 341, 342, and 343.
341 + 342 + 343 = 1026
We know our answer is correct because 341 + 342 + 343 equals 1026 as displayed above.
Answer:
b. They can both be 90 degree angles
c. Acute angles are by definition 90 degrees, and acute is less than but not equal to 90 degrees
d. should be always
e. should be never (explanation: they have to be adjacent to be supplementary, and vertical angles are never adjacent)
Step-by-step explanation:
Answer:
first cross multiply
2x×4=3×8
8x=24
then, divide both sides by "8" so x could be alone
x=24/8
x=3
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Step-by-step explanation:
