Chapter 1.3, Problem 37E

a.

To determine

To find the total number of pixels.

Answer to Problem 37E

The total number of pixels is $1,310,720$ .

Explanation of Solution

Given information:

Number of pixels in a row is 1280.

Number of pixels in a column is 1024.

Calculation:

The total number of pixels is the product of the number of pixels in a row and the number of pixels in a column.

So, the expression for total number of pixels is $p=r\times c$

Number of pixels in a row is 1280.

Number of pixels in a column is 1024.

Now,

Substitute, $r=1280\text{ and }c=1024$ on $p=r\times c$ ,

So, total number of pixels is obtained as:

  $\begin{array}{l}p=1280\times 1024\\ p=1,310,720\end{array}$ [Multiply]

Hence,

The total number of pixels is $1,310,720$ .

b.

To determine

To find the number of megapixels in the image having 1280 pixels in a row and 1024 pixels in a column.

Answer to Problem 37E

The total number of megapixels is

Explanation of Solution

Given information:

One megapixel is equal to 1,000,000 pixels.

Calculation:

The total number of pixels is the product of the number of pixels in a row and the number of pixels in a column.

  $p=1,310,720$

Since, one megapixel is equal to 1,000,000 pixels.

So, the expression can be written as:

  $M=\frac{p}{1,000,000}$

Substitute, $1,310,720$ for $p$ on the above expression,

  $\begin{array}{l}M=\frac{1,310,720}{1,000,000}\\ M=1.31\left[\text{upto nearest tenth}\right]\end{array}$

The total number of megapixels is 1.31.

c.

To determine

To explain whether the print is clear if the length and width of the photo is 8 inches and 10 inches.

Answer to Problem 37E

Clear print of this photo is not possible.

Explanation of Solution

Given information:

The print will be clear if the value of the expression $\frac{m}{lw}$ (where $m=$ number of megapixel, $l=$ length of photo and $w=$ width of photo) is greater than or equal to 0.017.

Length of photo is 8 inchs.

Width of photo is 10 inches.

Calculation:

Total number of megapixels is 1.31 so, $m=1.31$

Length of photo is 8 inches so, $l=8$

Width of photo is 10 inches so, $w=10$

The print will be clear if the value of the expression $\frac{m}{lw}$ is greater than or equal to 0.017.

So, the expression is:

  $\frac{m}{lw}\ge 0.017$

Now, Substitute, $m=1.31$ , $l=8$ and $w=10$ on the above expression,

  $\begin{array}{l}\frac{1.31}{8\cdot 10}\\ =\frac{1.31}{80}\left[\text{Multiply}\right]\\ =0.016375\left[\text{Divide}\right]\end{array}$

Since, 0.016375 is less than 0.017.

Hence, the resulted ratio is less than the required factor, so a clear print of this photo is not possible.