The answer is 5/42. 1 x 5/7 x 6 = 5/42.
368, divide the amount of popsicles to the amount in each box
The given polynomial function has 1 relative minimum and 1 relative maximum.
<h3>What are the relative minimum and relative maximum?</h3>
- The relative minimum is the point on the graph where the y-coordinate has the minimum value.
- The relative maximum is the point on the graph where the y-coordinate has the maximum value.
- To determine the maximum and the minimum values of a function, the given function is derivated(since the maximum or minimum is obtained at slope = 0)
<h3>Calculation:</h3>
The given function is
f(x) = 2x³ - 2x² + 1
derivating the above function,
f'(x) = 6x² - 4x
At slope = 0, f'(x) = 0 (for maximum and minimum values)
⇒ 6x² - 4x = 0
⇒ 2x(3x - 2) = 0
2x = 0 or 3x - 2 = 0
∴ x = 0 or x = 2/3
Then the y-coordinates are calculated by substituting these x values in the given function,
when x = 0;
f(0) = 2(0)³ - 2(0)² + 1 = 1
So, the point is (0, 1)
when x = 2/3;
f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27
So, the point is (2/3, 19/27)
Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.
So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.
Thus, option A is correct.
Learn more about the relative minimum and maximum here:
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Answer:
Approximately
, assuming that
.
Step-by-step explanation:
Initial kinetic energy of the sled and its passenger:
.
Weight of the slide:
.
Normal force between the sled and the slope:
.
Calculate the kinetic friction between the sled and the slope:
.
Assume that the sled and its passenger has reached a height of
meters relative to the base of the slope.
Gain in gravitational potential energy:
.
Distance travelled along the slope:
.
The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:
.
In other words, the sled and its passenger would have lost (approximately)
of energy when it is at a height of
.
The initial amount of energy that the sled and its passenger possessed was
. All that much energy would have been converted when the sled is at its maximum height. Therefore, when
is the maximum height of the sled, the following equation would hold.
.
Solve for
:
.
.
Therefore, the maximum height that this sled would reach would be approximately
.
Answer:
IQR is 4, median is 58.
Step-by-step explanation:
Enter these values in a list, hit stat > calc > 1-var stats. That gives you the 5 number summary. To get IQR, subtract Q3 from Q1.