Answer:
y=t−1+ce
−t
where t=tanx.
Given, cos
2
x
dx
dy
+y=tanx
⇒
dx
dy
+ysec
2
x=tanxsec
2
x ....(1)
Here P=sec
2
x⇒∫PdP=∫sec
2
xdx=tanx
∴I.F.=e
tanx
Multiplying (1) by I.F. we get
e
tanx
dx
dy
+e
tanx
ysec
2
x=e
tanx
tanxsec
2
x
Integrating both sides, we get
ye
tanx
=∫e
tanx
.tanxsec
2
xdx
Put tanx=t⇒sec
2
xdx=dt
∴ye
t
=∫te
t
dt=e
t
(t−1)+c
⇒y=t−1+ce
−t
where t=tanx
its wrong
Step-by-step explanation:
Because the cos theta < 0 then theta must be an obtuse angle
so a^2 + b^2 < a^2
C
Answer: (0.1658, 0.2742)
Step-by-step explanation:
Formula to find the confidence interval for population proportion is given by :-
![\hat{p}\pm z^*\sqrrt{\dfrac{\hat{p}(1-\hat{p})}{n}}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%5Cpm%20z%5E%2A%5Csqrrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D)
, where n= sample size
z*= Critical value
= sample proportion.
As per given , we have
Significance level : ![\alpha=1-0.99=0.01](https://tex.z-dn.net/?f=%5Calpha%3D1-0.99%3D0.01)
According to z-table, Critical value for 99% confidence interval : z*=2.576
Let p be the proportion of people in the country that have red hair.
n= 388
![\hat{p}=0.22](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D0.22)
Now, required confidence interval for proportion of people in the country that have red hair will be :-
![0.22\pm (2.576)\sqrt{\dfrac{0.22(1-0.22)}{388}}](https://tex.z-dn.net/?f=0.22%5Cpm%20%282.576%29%5Csqrt%7B%5Cdfrac%7B0.22%281-0.22%29%7D%7B388%7D%7D)
![0.22\pm (2.576)\sqrt{0.000442268}](https://tex.z-dn.net/?f=0.22%5Cpm%20%282.576%29%5Csqrt%7B0.000442268%7D)
![0.22\pm (2.576)(0.02103)](https://tex.z-dn.net/?f=0.22%5Cpm%20%282.576%29%280.02103%29)
![(0.22-0.05417328,\ 0.22+0.05417328 )=(0.16582672,\ 0.27417328)\\\\\approx(0.1658,\ 0.2742)](https://tex.z-dn.net/?f=%280.22-0.05417328%2C%5C%200.22%2B0.05417328%20%29%3D%280.16582672%2C%5C%200.27417328%29%5C%5C%5C%5C%5Capprox%280.1658%2C%5C%200.2742%29)
The 99% confidence interval for the proportion of people in the country that have red hair= (0.1658, 0.2742)