The function that represents how much more water can be added to the bucket before it overflows is given as follows:
c(x) = 6x³ + 3x² - 2x - 2.
<h3>How to define the function?</h3>
The function to calculate the space remaining in the pool is given by the subtraction of the capacity function by the function representing the current amount of water in the pool.
The functions in this problem are defined as follows:
- f(x) = 8x³ + 4x² - 6x + 5.
- g(x) = 2x³ + x² - 4x + 7.
Then the capacity function is obtained as follows:
c(x) = f(x) - g(x)
c(x) = 8x³ + 4x² - 6x + 5 - (2x³ + x² - 4x + 7)
Then the distributive property is applied to the negative sign as follows:
c(x) = 8x³ + 4x² - 6x + 5 - 2x³ - x² + 4x - 7.
Finally, the like terms are combined, that is, the terms that have the same variable and exponent, as follows:
c(x) = 6x³ + 3x² - 2x - 2.
More can be learned about operations with functions at brainly.com/question/2723982
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0.92
Step-by-step explanation:
There are 4 cards in a deck of 52 cards that has a face value of 3. That means that the other 48 cards don't have a face value of 3. Therefore, the probability of picking a card of this deck that doesn't have a face value of 3 is
Answer:
$85
Step-by-step explanation:
5000 x $70 = $350,000
4950 x $71 = $351,450
4900 x $72 = $352,800
etc.
Create an equation for the monthly revenue:
f(n) = (5000 - 50n) x (70 + n)
= 350000 + 5000n - 3500n - 50n²
= 350000 + 1500n - 50n²
where n is the amount the ticket price is increased from $70.
Differentiate, equal to zero and solve for n to find the value of n when the monthly revenue is at its maximum:
f'(n) = 1500 - 100n
1500 - 100n = 0
1500 = 100n
15 = n
Therefore, the maximum monthly revenue is when n = 15.
So the cost of the ticket will be 70 + n = 70 + 15 = 85
The number is -3 because -3 minus 16 equals -19.
Answer:
:) good day mate
Step-by-step explanation:
:) indeed
