Answer:
x = {kπ, arccos(1/5) +2kπ, 2kπ -arccos(1/5)}
Step-by-step explanation:
The double-angle trig identity for sine is useful:
5(2sin(θ)cos(θ)) -2sin(θ) = 0
2sin(θ)(5cos(θ) -1) = 0
This has solutions that make the factors zero:
θ = arcsin(0) = kπ
and ...
cos(θ) = 1/5
θ = arccos(1/5) +2kπ . . . . or . . . . 2kπ -arccos(1/5)
_____
Some numerical values are shown on the graph attached. values for multiples of pi are ...
{..., -12.566, -9.425, -6.283, -3.142, 0, 3.142, 6.283, 9.425, 12.566, ...}
<u>Answer-</u>
<em>In </em><em>25.15%</em><em> cases their response times is over 30 minutes.</em>
<u>Solution-</u>
Hint- Calculating the z-score (how much standard deviations away from the mean) and then getting the corresponding probability value from normal distribution table we can get solution.
Applying the formula for Z-score,
Here,
X = score = 30,
μ = mean = 22,
σ = standard deviation = 11.9
Putting the values,
(Subtracted from 1 as the values of area to the left of the Z score is given in table, but we need the area right to Z score as response times more than 30 minutes is asked)
Answer:
To empty the aquarium it takes 26 minutes
Step-by-step explanation:
step 1
Find the volume of the aquarium
The volume of rectangular prism is
we have
substitute the given values
step 2
Divide the volume by the rate of 396 in^3 per minute
therefore
To empty the aquarium it takes 26 minutes
