Answer:
The population mean is 5 volts
Step-by-step explanation:
Output voltage is assumed to be normally distributed, with standard deviation 0.25 Volts
s=0.25
n = 8
Sample mean =
Since n < 30 and population standard deviation is unknown
So, we will use t test
Formula :
t=-1.69
Refer the t table for p value
Degree of freedom = n-1 = 8-1 = 7
So,
P value >α
So, We are failed to reject null hypothesis
Hence The population mean is 5 volts
Answer:Increasing in x∈(0,π/4)∪(5π/4,2π) decreasing in(π/4,5π/4)
Step-by-step explanation:
given f(x) = sin(x) + cos(x)
f(x) can be rewritten as
Using these result in equation a we get
f(x) =
Now we know that for derivative with respect to dependent variable is positive for an increasing function
Differentiating b on both sides with respect to x we get
f '(x) =
where x∈(0,2π)
we know that cox(x) > 0 for x∈[0,π/2]∪[3π/2,2π]
Thus for cos(π/4+x)>0 we should have
1) π/4 + x < π/2 => x<π/4 => x∈[0,π/4]
2) π/4 + x > 3π/2 => x > 5π/4 => x∈[5π/4,2π]
from conditions 1 and 2 we have x∈(0,π/4)∪(5π/4,2π)
Thus the function is decreasing in x∈(π/4,5π/4)