The speed of sound in different gases at a certain temperature T depends on the molar mass of the gases. Show that

$${\frac{v_1}{v_2}} = \sqrt{\frac{M_2}{M_1}},$$

where

$$v_1$$

is the speed of sound in a gas of molar mass

$$M_1$$

and

$$v_2$$

is the speed of sound in a gas of molar mass

$$M_2$$

.

Polonium-210 decays exponentially with a half-life of 140 days. (a)At time t = 0 a sample of polonium-210 has a mass of 100 grams. Find an expression that gives the mass at an arbitrary time t. (b)How long will it take for the 100-gram mass to decay to 75 grams?

There are 32 students in the school drill team performance. Each row of team members must have the same number of students. If there are at least 8 students in each row, what are all the possible arrangements?

Use reference triangles in an appropriate quadrant, to find the angles. $\sin ^{-1}\left(\frac{-1}{\sqrt{2}}\right)$

Provide two different methods of calculating $\cos \left(195^{\circ}\right) \cos \left(105^{\circ}\right)$, one of which uses the product to sum. Which method is easier?

Evaluate the expression.

(a) $\log _3\left(\frac{1}{27}\right)$

(b) $\log _{10} \sqrt{10}$

(c) $\log _5 0.2$

Evaluate the variable expression when x = 3.

6 x

On a sheet of paper, use the given term in a sentence 'periphery'.

When 25.0 mL of a solution containing both $\mathrm{Fe}^{2+}$ and $\mathrm{Fe}^{3+}$ ions is titrated with 23.0 mL of 0.0200 M $\mathrm{KMnO}_4$, all of the $\mathrm{Fe}^{2+}$ ions are oxidized to $\mathrm{Fe}^{3+}$ ions. Next, the solution is treated with Zn metal to convert all of the $\mathrm{Fe}^{3+}$ ions to $\mathrm{Fe}^{2+}$ ions. Finally, 40.0 mL of the same $\mathrm{KMnO}_4$ solution are added to the solution in order to oxidize the $\mathrm{Fe}^{2+}$ ions to $\mathrm{Fe}^{3+}$. Calculate the molar concentrations of $\mathrm{Fe}^{2+}$ and $\mathrm{Fe}^{3+}$ in the original solution.

Fructose is a type of a. disaccharide$\hspace{1.53cm}$ c. polysaccharide b. monosaccharide$\hspace{1cm}$ d. amino acid

A free electron has a wave function where x is in meters. Find its (a) de Broglie wavelength, (b) momentum, and (c) kinetic energy in electron volts. $\psi ( x ) = A e ^ { i \left( 5.00 \times 10 ^ { 10 } x \right) }$

In this exercise, find the reference angle $\theta^{\prime}$, and sketch $\theta$ and $\theta^{\prime}$ in standard position.

$$\theta=-145^{\circ}$$

Find the value of the variable.

$$2 p+5=13$$

On a sheet of paper, use each of these terms in a sentence 'linkage'.