Find all solutions of cos x -sqrt = 0.
1 answer:
Answer:
Option A
Step-by-step explanation:
Good question!
We assume that x lies on the interval 0<=x<=360. We can therefore identify the solution in degrees:
Now we can solve by substitution, and when simplified we get cos(x) = 1/2.
Take the inverse: x = cos^-1(1/2) = π/3 <--- angle in first quadrant
x = (2π-π/3) = 5π/3 <----- angle in fourth quadrant
As you know π/3 in degrees is 60, and 5π/3 = 360-60 = 300
Therefore your solution is the first option, x = 60+n360 and x = 300 + n360
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Answer:
Explanation below.
Step-by-step explanation:
For this case we have the following dataset:
46, 16, 41, 26, 22 ,33, 30, 22 ,36, 34,
63, 21, 26, 18, 27, 24, 31, 38, 26, 55,
31, 47, 27, 43 ,35, 22 ,64,40, 58, 20,
49, 37, 53, 25, 29, 32, 23, 49, 39, 40,
24, 56, 30, 51, 21, 45, 27, 34, 47, 35
So we have 50 values. The first step on this case would be order the dataset on increasing way and we got:
16, 18, 20, 21, 21, 22, 22, 22, 23, 24,
24, 25, 26, 26, 26, 27, 27, 27, 29, 30
30, 31, 31, 32, 33, 34, 34, 35, 35, 36,
37, 38, 39, 40, 40, 41, 43, 45, 46, 47,
47, 49, 49, 51, 53, 55, 56, 58, 63, 64
We can find the range for this dataset like this:
Then since we need 7 classes we can find the length for each class doing this:
And now we can define the classes like this and counting how many observations lies on each interval we got the frequency:
Class Frequency Midpoint RF CF
________________________________________________
[16-22.86) 8 19.43 (8/50)=0.16 0.16
[22.86-29.71) 11 26.29 (11/50)=0.22 0.38
[29.71-36.57) 11 33.14 (11/50)=0.22 0.6
[36.57-43.43) 7 40.0 (7/50)=0.14 0.74
[43.43-50.29) 6 46.86 (6/50)=0.12 0.86
[50.29-57.14) 4 53.72 (4/50)=0.08 0.94
[57.14-64] 3 60.57 (3/50)=0.06 1.0
________________________________________________
Total 50 1.00
RF= Relative frequency. CF= Cumulative frequency
The relative frequency was calculated as the individual frequency for a class divided by the total of observations (50)
The mid point is the average between the limits of the class.
And the cumulative frequency is calculated adding the relative frequencies for each class.