Answer:
a)
.
b) 
Step-by-step explanation:
Given a function
, this function has the following gradient:
.
(a) find the gradient of f
We have that
. So


.
.

(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.
The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.
We have that:

.

The vector is 
To use v as an unitary vector, we divide each component of v by the norm of v.

So

Now, we can calculate the scalar product that is the directional derivative.

Answer:
9 magazines
Step-by-step explanation:
To solve this problem you will want to work backwards. Start with the junk mail. There is 18 junk mail and if there are 1/3 as many bills as junk mail then you will need to multiply 18 * 1/3. This equals 6 bills. If there is twice as many bills as letters then you will need to divide bills(6) by 2 which equals 3. If there are 6 more magazines than letters then you need to add 6 to the letters (3). 3 + 6 = 9
Answer:
5.3333333333
Step-by-step explanation:
A number is called a rational if it can be written in the form of p/q where p/q are integers and q≠0.
The terminating numbers are always a rational number.
The number 5.3333333... is a rational number.
Step-by-step explanation:








Answer:
<em>Thus, the dimensions of the desk in the drawing are 4 cm long and 2 cm wide.</em>
Step-by-step explanation:
<u>Scaling</u>
The scale factor established to represent a desk 2 meters long and 1 meter wide is:
1 centimeter = 0.5 meter
We need to convert the real dimensions to the scaled dimensions. To complete the task, it's a good idea to multiply the real dimensions by the ratio:

to get the scaled dimensions.
The length of 2 meters is scaled to:

And the width of 1 meter is scaled to:
\displaystyle 1\ m\frac{1\ cm}{0.5\ m}=2 cm
Thus, the dimensions of the desk in the drawing are 4 cm long and 2 cm wide.