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A100 -- Dan Swearingen

Math Practice Homework - Points earned on this assignment will be applied towards any points lost on the In Class math quiz. Due Tuesday, September 24 at the beginning of class.

Numerical Problems:

Show all work.

Do all work on your own paper.

All answers must be in proper scientific notation: "n.mmm... x 10^p".

Evaluate the following

1. 10⁶ x 10² =


2. 10¹¹/10⁴ =


3. (4 x 10^-6)/(8 x 10^-4) =


4. 1/(100 x 10⁵⁵ x 10^-16 x 10 x 10⁸²) =


5. 2 x 10^-5 - 4 x 10^-7 =


6. 3 x 10²⁷ + 5 x 10²⁸ =


7. 2 x 10^-125 x 5 x 10¹²² =


8. (10 x 2 x 10^-4 ) / (3 x 10² x 4 x 10² ) =


9. (7.5 x 10^-9) / (3 x 10^-9) =


10. (2 x 10^2A x 6 x 10^-2L ) / (3 x 10^12A x 7 x 10^4L ) =


11. 10¹⁸ + (3 x 10²¹) + (7 x 10²⁴) =

For the following problems, solve for the variable indicated.

12. If: what is m₁ = ?

13. If:what is M_wd ?

14. If: what is M_wd ?

Perform the following calculations:

The escape velocity v_esc and the thermal velocity v_Thermal are given by the formulas:

Calculate v_esc and v_Thermal.

Where:

G = 6.7 x 10^-11 [m³ kg^-1 sec^-2 ]

M = Mass of Earth = 5.9742 x 10²⁷ kg

R = Radius of Earth = 6,378.14 km

k = 1.38 x 10^-23 [J/^oK]

m_gas = mass of four protons = 4 x 1.67 x 10^-27 kg

T = room temperature in Kelvin which is about 300^o K

Note: make sure units are consistent. Answers should be velocities (a.k.a. speed) so final units should be in meters per second.

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