We will use double angle identities:
cos (5x ) = sin (10x )
cos (5x ) = 2 cos (5x ) sin ( 5x )
cos ( 5 x) - 2 cos ( 5 x ) sin ( 5x ) = 0
cos ( 5 x ) · [ 1 - 2 sin (5 x) ] = 0
cos ( 5 x ) = 0 or : 1 - 2 sin (5 x) = 0
5 x = π/2 +kπ, k∈Z sin (5 x) = 1/2
x1 = π/10 + kπ/5 5 x = π/6+2kπ , k∈ Z
5 x = 5π/6 +2kπ , k∈ Z
x 2 = π/30 +2kπ/5
x 3 = π/9 + 2kπ/5
C=pi(radius)^2
c=pi(5)^2
c=pi(25)
c=78.5398163397...
c is about 78.5
Answer:
F⁻¹(x) = 
Step-by-step explanation:
Inverse of 5 would be 1/5, and
Inverse of -1 would be +1
Hope this helps!
1. Mean of the data: 8
2. Median: 8
3. IQR = 4
4. Members that use the facility 10 days a month is: 2.
See reasons below.
<h3>What is the Mean, Median, and Interquartile Range of a Data?</h3>
Mean = sum of all values ÷ number of data values (easily solved using a dot plot
Median = middle value (easily found using a box plot).
Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).
1. Mean of the data: use the dot plot.
Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8
2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.
Median = 8
3. IQR = Q3 - Q1 = 10 - 6
IQR = 4
4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.
Learn more about the mean, median, and interquartile range on:
brainly.com/question/9821103
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Answer:
The length is 23 inches and the width is 6 inches.
Step-by-step explanation:
The perimeter for a rectangular shape is represented as:
P = 2L + 2W, where L represents length and W represents width
We can represent the length as:
L = 3W + 5
Substituting this into the perimeter function, we get:
P = 2 (3W + 5) + 2W
Substituting 58 for P, we get:
58 = 2 (3W + 5) + 2W
58 = 6W + 10 + 2W
58 = 8W + 10
58 - 10 = 8W + 10 - 10
48 = 8W
48 / 8 = 8W / 8
6 = W
With 6 being the established value for the width, we can substitute this back into the equation for length:
L = 3W + 5
L = 3(6) + 5
L = 18 + 5
L = 23
To check our work, we can substitute both the width and length into the perimeter equation:
P = 2L + 2W
58 = 2(23) + 2(6)
58 = 46 + 12
58 = 58
Therefore, length is 23 inches and the width is 6 inches.
