In Exercises $24-29$ find the measure of each angle. The measures of the angles of a hexagon are in the ratio $4 : 5 : 5 : 8 : 9 : 9 .$

The perimeter of a triangle is 132 $\mathrm{cm}$ and the lengths of its sides are in the ratio $8 : 11 : 14 .$ Find the length of each side.

The measures of the consecutive angles of a quadrilateral are in the ratio $5 : 7 : 11 : 13 .$ Find the measure of each angle. draw a quadrilateral that satisfies the requirements, and explain why two sides must be parallel.

What is the ratio of the measure of an interior angle to the measure of an exterior angle in a regular hexagon? A regular decagon? A regular $n$ -gon?

A team's best hitter has a lifetime batting average of $.320 .$ He has been at bat 325 times. a. How many hits has he made?b. The same player goes into a slump and doesn't get any hits at all in his next ten times at bat. What is his current batting average to the nearest thousandth?

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In Exercises $24-29$ find the measure of each angle. The measures of the angles of an isosceles triangle are in the ratio $3 : 3 : 2$

$\angle 1=67.5^{\circ} ; \angle 2=67.5^{\circ} ; \angle 3=45$

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In Exercises $24-29$ find the measure of each angle. The measures of the acute angles of a right triangle are in the ratio $5 : 7$ .

In Exercises $24-29$ find the measure of each angle. The ratio of the measures of two supplementary angles is $11 : 4$

One angle of an isosceles trapezoid has measure $57 .$ Find the measures of the other angles.

For the following exercises, graph the parabola, labeling the focus and the directrix.$$3 x^{2}+30 x-4 y+95=0$$

Mass Find the mass of the solid region bounded by the parabolic surfaces $z=16-2 x^{2}-2 y^{2}$ and $z=2 x^{2}+2 y^{2}$ if the density of the solid is $\delta(x, y, z)=\sqrt{x^{2}+y^{2}}$

For the following exercises, graph the parabola, labeling the focus and the directrix.$$x^{2}+4 x+2 y+2=0$$

Convert each angle in degrees to radians. Write the answer as a multiple of $\pi$.$$15^{\circ}$$

(II) The pressure variation in a sound wave is given by$\Delta P=0.0035 \sin (0.38 \pi x-1350 \pi t)$where $\Delta P$ is in pascals, $x$ in meters, and $t$ in seconds. Determine $(a)$ the wavelength, $(b)$ the frequency, $(c)$ the speed, and $(d)$ the displacement amplitude of the wave. Assume the density of the medium to be $\rho=2.3 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} .$

In Exercises 47-56, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

$f(x) = 3$

(a) If you combine two atomic orbitals on two different atoms to make a new orbital, is this a hybrid orbital or a molecular orbital? (b) If you combine two atomic orbitals on one atom to make a new orbital, is this a hybrid orbital or a molecular orbital? (c) Does the Pauli exclusion principle(Section 6.7) apply to MOs? Explain.

A wedge like the one in Exercise 22 has dimensions $a=2$ , $b=6,$ and $c=3 .$ The density is $\delta(x, y, z)=x+1 .$ Notice that if the density is constant, the center of mass will be $(0,0,0)$ .

An open barge has the dimensions shown in $\textbf{Fig. P12.63.}$ If the barge is made out of4.0-cm-thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in freshwater without sinking? Is there enough room in the barge to hold this amount of coal? (The density of coal is about 1500 kg/m$^3$.)

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## Recommended Questions

In Exercises $24-29$ find the measure of each angle.

The measures of the acute angles of a right triangle are in the ratio $5 : 7$ .

In Exercises $24-29$ find the measure of each angle.

The ratio of the measures of two supplementary angles is $11 : 4$

In Exercises $24-29$ find the measure of each angle.

The measures of the angles of a hexagon are in the ratio $4 : 5 : 5 : 8 : 9 : 9 .$

One angle of an isosceles trapezoid has measure $57 .$ Find the measures of the other angles.

For the following exercises, graph the parabola, labeling the focus and the directrix.

$$3 x^{2}+30 x-4 y+95=0$$

Mass Find the mass of the solid region bounded by the parabolic surfaces $z=16-2 x^{2}-2 y^{2}$ and $z=2 x^{2}+2 y^{2}$ if the density of the solid is $\delta(x, y, z)=\sqrt{x^{2}+y^{2}}$

For the following exercises, graph the parabola, labeling the focus and the directrix.

$$x^{2}+4 x+2 y+2=0$$

Convert each angle in degrees to radians. Write the answer as a multiple of $\pi$.

$$15^{\circ}$$

(II) The pressure variation in a sound wave is given by

$\Delta P=0.0035 \sin (0.38 \pi x-1350 \pi t)$

where $\Delta P$ is in pascals, $x$ in meters, and $t$ in seconds. Determine $(a)$ the wavelength, $(b)$ the frequency, $(c)$ the speed, and $(d)$ the displacement amplitude of the wave. Assume the density of the medium to be $\rho=2.3 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} .$

In Exercises 47-56, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

$f(x) = 3$

(a) If you combine two atomic orbitals on two different atoms to make a new orbital, is this a hybrid orbital or a molecular orbital? (b) If you combine two atomic orbitals on one atom to make a new orbital, is this a hybrid orbital or a molecular orbital? (c) Does the Pauli exclusion principle

(Section 6.7) apply to MOs? Explain.

A wedge like the one in Exercise 22 has dimensions $a=2$ , $b=6,$ and $c=3 .$ The density is $\delta(x, y, z)=x+1 .$ Notice that if the density is constant, the center of mass will be $(0,0,0)$ .

An open barge has the dimensions shown in $\textbf{Fig. P12.63.}$ If the barge is made out of

4.0-cm-thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in freshwater without sinking? Is there enough room in the barge to hold this amount of coal? (The density of coal is about 1500 kg/m$^3$.)