Answer:
(507.05, 592.95)
Step-by-step explanation:
Given data:
sample mean = $550, sample standard deviation S = $60.05
95% confidence interval , n = 10
For 95% confidence interval for the mean
mean ± M.E.
where M.E. is margin of error = ![t_{n-1}, \alpha/2\times\frac{S}{\sqrt{n} }](https://tex.z-dn.net/?f=t_%7Bn-1%7D%2C%20%5Calpha%2F2%5Ctimes%5Cfrac%7BS%7D%7B%5Csqrt%7Bn%7D%20%7D)
Substituting the values in above equation
![=t_{10-1}, 0.05/2\times\frac{60.05}{\sqrt{10} }](https://tex.z-dn.net/?f=%3Dt_%7B10-1%7D%2C%200.05%2F2%5Ctimes%5Cfrac%7B60.05%7D%7B%5Csqrt%7B10%7D%20%7D)
= 2.62×18.99
=42.955
= 550±42.95
=(507.05, 592.95)
Answer
Given,
Mass of the Uranus, M = 8.68 x 10²⁵ Kg
Radius of Uranus, R = 2.56 x 10⁷ m
Distance of Uranus, D = 2.87 x 10¹² days
a) Rotational Kinetic energy of the Uranus
moment of inertia of the Uranus
I = 22.75 x 10³⁹ kg.m²
Angular speed
\
![\omega = 1 \times 10^{-4}](https://tex.z-dn.net/?f=%5Comega%20%3D%201%20%5Ctimes%2010%5E%7B-4%7D)
Rotational Kinetic energy
![KE = \dfrac{1}{2}I\omega^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cdfrac%7B1%7D%7B2%7DI%5Comega%5E2)
![KE = \dfrac{1}{2}\times 22.75\times 10^{39}\times (10^{-4})^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%2022.75%5Ctimes%2010%5E%7B39%7D%5Ctimes%20%2810%5E%7B-4%7D%29%5E2)
![KE = 11.38\times 10^{31}\ J](https://tex.z-dn.net/?f=KE%20%3D%2011.38%5Ctimes%2010%5E%7B31%7D%5C%20J)
b) Rotational Kinetic energy of Uranus in its orbit around sun
moment of inertia of the Uranus
I = 7.15 x 10⁵⁰ kg.m²
Angular speed
\
![\omega =2.36\times 10^{-9}](https://tex.z-dn.net/?f=%5Comega%20%3D2.36%5Ctimes%2010%5E%7B-9%7D)
Rotational Kinetic energy
![KE = \dfrac{1}{2}I\omega^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cdfrac%7B1%7D%7B2%7DI%5Comega%5E2)
![KE = \dfrac{1}{2}\times 7.15\times 10^{50}\times (2.36\times 10^{-9})^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%207.15%5Ctimes%2010%5E%7B50%7D%5Ctimes%20%282.36%5Ctimes%2010%5E%7B-9%7D%29%5E2)
![KE = 1.99\times 10^{33}\ J](https://tex.z-dn.net/?f=KE%20%3D%201.99%5Ctimes%2010%5E%7B33%7D%5C%20J)
Answer:
Step-by-step explanation:
3844 x 10²
all you need to do is think about the 10th power