Serena has 6 photo albums with 15 photos in each
so serena has (6 * 15) = 90 photos.
maya has 8 albums with 13 photos in each.
so maya has (8 * 13) = 104 photos
if serena add another 12 photos to her album....(90 + 12) = 102 photos
so in total, serena and maya have 102 + 104 = 206 photos <=
<span>Take the integral:
integral (cos(x))/sqrt(cos(x)+1) dx
For the integrand (cos(x))/sqrt(1+cos(x)), substitute u = 1+cos(x) and du = -sin(x) dx:
= integral (u-1)/(sqrt(2-u) u) du
For the integrand (-1+u)/(sqrt(2-u) u), substitute s = sqrt(2-u) and ds = -1/(2 sqrt(2-u)) du:
= integral -(2 (1-s^2))/(2-s^2) ds
Factor out constants:
= -2 integral (1-s^2)/(2-s^2) ds
For the integrand (1-s^2)/(2-s^2), cancel common terms in the numerator and denominator:
= -2 integral (s^2-1)/(s^2-2) ds
For the integrand (-1+s^2)/(-2+s^2), do long division:
= -2 integral (1/(s^2-2)+1) ds
Integrate the sum term by term:
= -2 integral 1/(s^2-2) ds-2 integral 1 ds
Factor -2 from the denominator:
= -2 integral -1/(2 (1-s^2/2)) ds-2 integral 1 ds
Factor out constants:
= integral 1/(1-s^2/2) ds-2 integral 1 ds
For the integrand 1/(1-s^2/2), substitute p = s/sqrt(2) and dp = 1/sqrt(2) ds:
= sqrt(2) integral 1/(1-p^2) dp-2 integral 1 ds
The integral of 1/(1-p^2) is tanh^(-1)(p):
= sqrt(2) tanh^(-1)(p)-2 integral 1 ds
The integral of 1 is s:
= sqrt(2) tanh^(-1)(p)-2 s+constant
Substitute back for p = s/sqrt(2):
= sqrt(2) tanh^(-1)(s/sqrt(2))-2 s+constant
Substitute back for s = sqrt(2-u):
= sqrt(2) tanh^(-1)(sqrt(1-u/2))-2 sqrt(2-u)+constant
Substitute back for u = 1+cos(x):
= sqrt(2) tanh^(-1)(sqrt(sin^2(x/2)))-2 sqrt(1-cos(x))+constant
Factor the answer a different way:
= sqrt(1-cos(x)) (csc(x/2) tanh^(-1)(sin(x/2))-2)+constant
Which is equivalent for restricted x values to:
Answer: |
| = (2 cos(x/2) (2 sin(x/2)+log(cos(x/4)-sin(x/4))-log(sin(x/4)+cos(x/4))))/sqrt(cos(x)+1)+constant</span>
Answer:
B) 22.0
Step-by-step explanation:
We solve using the Trigonometric function of Tangent
tan θ = Opposite/Adjacent
Adjacent = x
Opposite = 8
θ = 20°
tan θ = 8/x
tan 20° = 0.364
0.364 = 8/x
Cross Multiply
0.364 × x = 8
Divide both sides by 0.364
x = 8/0.364
x = 21.978021978
Approximately, x ≈ 22.0
Option B is the correct option
Answer:
The mean for Z is 40.
The standard deviation for Z is 25.
Step-by-step explanation:
We are given the following in the question:
X: daily work hours.
The average daily work hours are 8 hours, with a standard deviation of 5.
Z denote weekly work hours.
We have to find the mean and standard deviation for Z.
The mean for Z is 40.
We use the property:
Thus, the standard deviation for Z is 25.