Answer:
The answer to your question is 14.5 weeks
Step-by-step explanation:
Data
Total cost = C = $87
money earned = m = $6
Number of weeks to have the money = w = ?
Process
1.- Write an equation that represents the situation
Weeks = Total cost / Money earned
w = C/m
2.- Substitute the values
w = 87 / 6
3.- Result
w = 14.5
4.- Conclusion
Niki will last 14.5 weeks to have enough money to buy a dog bed.
Answer:
max{x²-4x²+5} = 5 at x = 0
Step-by-step explanation:
1. Find the critical numbers by finding the first derivative of f(x), set it to 0 and solve for x.
We get:
So the critical number is x = 0.
2. Evaluate the first derivative by plugging in the critical number and see if the derivative is positive or negative on both sides:
is positive when the x < 0 (for example: -6*(-1)=+)
is negative when the x > 0 (for example: -6*(1)=-)
Therefore, you have a local maximum.
Now just get the Y value by plugging in the critical number in the original function.
local maximum is (0,5)
Answer:
(-2.4, 37.014)
Step-by-step explanation:
We are not told how to approach this problem.
One way would be to graph f(x) = x^5 − 10x^3 + 9x on [-3,3] and then to estimate the max and min of this function on this interval visually. A good graph done on a graphing calculator would be sufficient info for this estimation. My graph, on my TI83 calculator, shows that the relative minimum value of f(x) on this interval is between x=2 and x=3 and is approx. -37; the relative maximum value is between x= -3 and x = -2 and is approx. +37.
Thus, we choose Answer A as closest approx. values of the min and max points on [-3,3]. In Answer A, the max is at (-2.4, 37.014) and the min at (2.4, -37.014.
Optional: Another approach would be to use calculus: we'd differentiate f(x) = x^5 − 10x^3 + 9x, set the resulting derivative = to 0 and solve the resulting equation for x. There would be four x-values, which we'd call "critical values."
This might not be super helpful but it’s either 50 or 130. Sorry i haven’t done this for a while!!
In the table shown below:
Let N be the number of bottles filled,
Let T be the time in hours.
Given that the number of bottles filled is proportional to the amount of time the machine runs, we have
Let's evaluate the value of k for each day.
Thus, on monday,
Tuesday:
Wednesday:
Thursday:
It is observed that all exept wednesday have the same value of k.
Thus, the amount of time required for the number of bottles filled on wednesday is evaluated as
Hence, the incorrect day is Wednesday. The amount of time for that many bottles should be 6.85 hours.