What restrictions must be made on $x$, $y$, and $z$ so that the triple $(x, y, z)$ will represent a point on the $y$ axis? On the $z$ axis? In the $xz$ plane? In the $yz$ plane?

Determine the Miller indices for the planes in the following unit cell:

Sandy charges each family that she babysits a flat fee of $10 for the night and an extra$5 per child. Kimmi charges $25 per night, no matter how many children a family has. a. Write a two-step equation that would compare what the two girls charge and find when their fees are the same. b. How many children must a family have for Sandy and Kimmi to charge the same amount? c. The Sanderson family has five children. Which babysitter should they choose if they wish to save some money on babysitting, and why?

Find the indices for the planes in the cubic unit cell shown in Figure $3-40$.

Use the rule from Exercise 4 to simplify each expression. a. $5^{3}2^{3}$
b. $4^{6}25^{6}$
c. $9^{10}\left(\dfrac{1}{9}\right)^{10}$
d. $20^{4}\left(\dfrac{1}{10}\right)^{4}$
e. $20^{4}5^{4}$
f. $\left(\dfrac{4}{3}\right)^{4}\left(\dfrac{15}{2}\right)^{4}$

Find the Miller indices for the directions in the cubic unit cell shown in Figure $3-37$.

Determine the Miller indices for the planes in the following unit cell:

For a simple cubic lattice, determine the Miller indices for the planes shown in the given figure.

What are the Miller indices of the cubic crystallographic planes shown in the mentioned Figure?

Determine the angle between covalent bonds in an $\mathrm{SiO}_{4}^{4}$ tetrahedron.

For a ceramic compound, what are the two characteristics of the component ions that determine the crystal structure?

Divide.

$$8 \frac { 1 } { 3 } \div 4 \frac { 2 } { 7 }$$

Evaluate the line integral $\int_{C} f d s$. f(x, y)=3x, C is the line segment from (0, 0) to (1, 0), followed by quarter-circle to (0, 1)

On January 1, 2016, the Shagri Company began construction on a new manufacturing facility for its own use. The building was completed in 2017. The only interest-bearing debt the company had outstanding during 2016 was long-term bonds with a book value of $10,000,000 and an effective interest rate of 8%. Construction expenditures incurred during 2016 were as follows: January 1$500,000 March 1 600,000 July 31 480,000 September 30 600,000 December 31 300,000. Required: Calculate the amount of interest capitalized for 2016.