Solve the Problem using elimination by addition

$$2 m-n=10$$

$$m-2 n--4$$

Balloons are often filled with helium gas because it weighs only about one-seventh of what air weighs under identical conditions. The buoyancy force, which can be expressed as $F_{\text{b}}=\rho_{\text{air}}gV_{\text{balloon}}$ will push the balloon upward. If the balloon has a diameter of 12 m and carries two people, 85 kg each, determine the acceleration of the balloon when it is first released. Assume the density of air is $\rho$= 1.16 kg/m^3, and neglect the weight of the ropes and the cage. Answer: 22.4 m/s^2

The distant star Deneb is thought by some astronomers to be 3,230 light-years away. Write this distance in scientific notation.

What values did Roman Stoic philosophers promote?

A certain neutron star has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster.

Some atomic properties depend on the average value of 1/r rather than the average value of ritsclf. Evaluate the expectation value of 1/r for (a) a hydrogenic 1s orbital, (b) a hydrogenic 2s orbital, (c) a hydrogenic 2p orbital. (d) Does $\langle 1/r \rangle = 1/ \langle r \rangle?$

Find the sum and demonstrate the addition on the real number line. -6 + 4

Find the magnitude and direction of the vector:

$$\vec{d}=\langle 4,-8\rangle$$

The Moon has a rest mass of $7.35 \times 10^{22} \mathrm{~kg}$ and an average orbital speed of $1.02 \times 10^3 \mathrm{~m} / \mathrm{s}$. Calculate the amount of mass that would need to be converted to energy to accelerate the Moon from rest to its final orbital speed.

What structure musta monomer have if it is to undergo addition polymerization?

Find the total charge on the surface $\mathbf{r}=e^{u} \cos v \mathbf{i}+e^{u} \sin v \mathbf{j}+u \mathbf{k}$, $(0 \leq u \leq 1,0 \leq v \leq \pi)$, if the charge density on the surface is $\delta=\sqrt{1+e^{2 u}}$.

If a planet has an average distance from the Sun of $2.0 \mathrm{AU}$, what is its orbital period?

Choose the best answer for the following. Explain your reasoning with one or more complete sentences.
After the helium flash in a low-mass star, the star’s luminosity
(a) goes up.
(b) goes down.
(c) stays the same

How many friends must you have to guarantee at least five of them will have birthdays in the same month?