I'll explain how to do the first one:-
y = cos-1(x2)
This can be described as ' a function of a function' x^2 is a function of x and cos-1(x^2) is a function of x^2.
We need to apply the chain rule.
Personally I find this easier to understand if i let u = x^2, so
If y = f(u) and u is a function of x then
dy/dx = dy/ du * du/dx
Here u = x^2 and y = cos-1(u)
du/dx = 2x
so dy/dx = d(cos-1(x^2) dx = dy/du * du/dx
= -1 / √(1 - u^2) * 2x
= -2x / √(1 - u^2)
= -2x / √(1 - (x^2)^2)
= -2x / √(1 - x^4)
I hope this helps. but if not. you might like to employ the formulae in the question - The square boxes contain the 'u' s in my answer. These formulae are equivalent to my explanation.
<h3>3
Answers:</h3>
- B) Mean
- C) Mean absolute deviation
- E) Mode
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Explanation:
The box plot, aka "box-and-whisker plot", visually represents five things. These things are:
- Minimum
- Q1 = first quartile
- Median (sometimes referred to as Q2 or second quartile)
- Q3 = third quartile
- Maximum
This list of five items is known as the five number summary.
The min is the tip of the left most whisker, assuming there aren't any small outliers. The max is the opposite side, being the tip of the right most whisker (assuming no large outliers). If there are any outliers, then they'll be shown as "island" dots on their own separated from the main box plot. The left and right edges of the box are Q1 and Q3 respectively. The median is the vertical line inside the box. The vertical line does not have to be at the midpoint of the left and right edges of the box. It simply needs to be somewhere in the box.
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Since the box plot lets us know the min and max, we can compute the range because
range = max - min
and we can also calculate the interquartile range (IQR) because
IQR = Q3 - Q1
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So to summarize so far, the five number summary is visually represented as the box plot. The range and IQR can be computed using items from the five number summary.
We cannot compute the mean because we would need the actual data set of values, rather than the summary data. The same goes for the mean absolute deviation (MAD) and the mode. Since your teacher is looking for things that cannot be determined from a box plot, we'll go for answers B, C and E.
In other words, we rule out choices A, D, and F because we can compute or determine those values from a box plot.
a) 2/5(n)=6 n=15
b) 4/7(x)=16/3 x=28/3 x=9.33333 x=9 1/3
any option for b works
i hope this is right and helps
Answer:
Step-by-step explanation:
value after five years = $18,000×(1-0.12)⁵ = 18,000×0.88⁵ = $9,499.17
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The value drops below $2,000 in the 17th year.
Step-by-step explanation:
12 is rounded to 10
22 is rounded to 20
20×10= 200
