First of all, when I do all the math on this, I get the coordinates for the max point to be (1/3, 14/27). But anyway, we need to find the derivative to see where those values fall in a table of intervals where the function is increasing or decreasing. The first derivative of the function is
. Set the derivative equal to 0 and factor to find the critical numbers.
, so x = -3 and x = 1/3. We set up a table of intervals using those critical numbers, test a value within each interval, and the resulting sign, positive or negative, tells us where the function is increasing or decreasing. From there we will look at our points to determine which fall into the "decreasing" category. Our intervals will be -∞<x<-3, -3<x<1/3, 1/3<x<∞. In the first interval test -4. f'(-4)=-13; therefore, the function is decreasing on this interval. In the second interval test 0. f'(0)=3; therefore, the function is increasing on this interval. In the third interval test 1. f'(1)=-8; therefore, the function is decreasing on this interval. In order to determine where our points in question fall, look to the x value. The ones that fall into the "decreasing" category are (2, -18), (1, -2), and (-4, -12). The point (-3, -18) is already a min value.
Observation that we can make is min = 10, max = 19, range = 9, Maximum frequency of a number is 12, Average = 12.9, median = 12, mode = 12 it is slightly skewed on the right.
Step-by-step explanation:
- It is imperative to create a data in a tabular column before analyzing.
- Once the data is created use tally marks or frequency distribution.
- Frequency distribution helps the data to provide occurrence of event.
- Very important to number which is a counting numbers are discrete.
- Continuous of data are ones which are in decimal.
- Descriptive statistics is the 1st level of Statistics.
- It finds, where the data stands. Minimum, Maximum is understandable.
- Range is at what level data is expanded.
- Average is the one numeric of a number.
- Median is the mid point of data
- Mode is the repetitive number of the data.
- Skewness is whether data is having extreme directions.
For this case we have the following variables:
x = the number of drill-based workouts
y = the number of conditioning workouts
The system of equations that adapts to the situation is:
"According to her schedule, she can complete at most 10 workouts this week":
x + y <= 10
"It takes Gianna 45 minutes to complete her drill-based workouts and 30 minutes to complete her conditioning workouts. She is required to spend more than 450 minutes on workouts every week"
45x + 30y> 450
Answer:
A system of inequalities can that be used is:
x + y <= 10
45x + 30y> 450
That would be
cos x
sin x + cos x * --------
sin x
sin x
Mult sin x by ----------
sin x
to obtain
(sin x)^2
------------
sin x
and then add
(cos x)^2
-------------
sin x
with the outcome being
(sin x)^2 + (cos x)^2 1
--------------------------- = --------- = cos x (answer)
sin x sin x
