I think we can use the identity sin x/2 = sqrt [(1 - cos x) /2]
cos x - sqrt3 sqrt ( 1 - cos x) /sqrt2 = 1
cos x - sqrt(3/2) sqrt(1 - cos x) = 1
sqrt(3/2)(sqrt(1 - cos x) = cos x - 1 Squaring both sides:-
1.5 ( 1 - cos x) = cos^2 x - 2 cos x + 1
cos^2 x - 0.5 cos x - 0.5 = 0
cos x = 1 , -0.5
giving x = 0 , 2pi, 2pi/3, 4pi/3 ( for 0 =< x <= 2pi)
because of thw square roots some of these solutions may be extraneous so we should plug these into the original equations to see if they fit.
The last 2 results dont fit so the answer is x = 0 , 2pi Answer
Answer:
B. Centers: the sea turtles have a greater median age than the koi
D. Spreads: the ages of the koi are more spread out
Step-by-step explanation:
The difference between the center and spread of the data distribution of koi and sea turtles as shown in the dot plots are as follows:
==>Median:
For Koi, the median value is the 14th value represented by the 14th dot on the plot, which is 30.
The median value for koi is between the 7th and the 8th value represented by dots on the plot. The average of both values will give us 55 as the median value for koi.
Therefore, the median age of sea turtle is greater than that of koi.
==>Spread:
Koi has a range of 45 (60-15), while sea turtles have a range of 20 (65-45). Invariably, mere looking at the dot plot, we can conclude that ages of the koi are more spread out.
Answer:
33.33%
Step-by-step explanation:
The oranges have decreased by one dollar per pound so you have to find the percentage of 3 that is 1. To do this is 1 over 3 multiplied by 100%
= 
* 100%
And this will give you 33.33%
Answer:
13 is the number.
Step-by-step explanation:
Given:
Twice the difference of a number and 9 equals 8.
Let the unknown number be 'x'.
Therefore, as per question:
The difference of 'x' and 9 = 
Twice the difference means 2 times the difference. So, we multiply 2 to the difference. Therefore,
Now, the above expression is equal to 8. So, we equate the above expression to 8. This gives,
Solving for 'x', we get:
Using distributive property of addition and distributing 2 inside the bracket. This gives,
Therefore, the unknown number is 13.
Now, we can verify our answer.
Therefore, the answer is correct.
