MATHEMATICS HIGH SCHOOL

Let f be a function of two variables that has continuous partial derivatives and consider the pointsA(8, 9),

B(10, 9),

C(8, 10),

and

D(11, 13).

The directional derivative of f at A in the direction of the vector AB is 9 and the directional derivative at A in the direction of

AC is 2. Find the directional derivative of f at A in the direction of the vector AD.

(Round your answer to two decimal places.)

Answers

Answer 1

Answer:

Answer:

The directional derivative of f at A in the direction of $\vec{u}$ AD is 7.

Step-by-step explanation:

Step 1:

Directional of a function f in direction of the unit vector $\vec{u}=(a,b)$ is denoted by $D\vec{u}f(x,y)$ ,

$D\vec{u}f(x,y)=f_(x)\left ( x ,y\right ).a+f_(y)(x,y).b$ .

Now the given points are

$A(8,9),B(10,9),C(8,10) and D(11,13)$ ,

Step 2:

The vectors are given as

AB = (10-8, 9-9),the direction is

$\vec{u}_(AB) = (AB)/(\left \| AB \right \|)=(1,0)$

AC=(8-8,10-9), the direction is

$\vec{u}_(AC) = (AC)/(\left \| AC \right \|)=(0,1)$

AC=(11-8,13-9), the direction is

$\vec{u}_(AD) = (AD)/(\left \| AD \right \|)=\left ((3)/(5),(4)/(5) \right )$

Step 3:

The given directional derivative of f at A $\vec{u}_(AB)$ is 9,

$D\vec{u}_(AB)f=f_(x) \cdot 1 + f_(y)\cdot 0\nf_(x) =9$

The given directional derivative of f at A $\vec{u}_(AC)$ is 2,

$D\vec{u}_(AB)f=f_(x) \cdot 0 + f_(y)\cdot 1\nf_(y) =2$

The given directional derivative of f at A $\vec{u}_(AD)$ is

$D\vec{u}_(AD)f=f_(x) \cdot (3)/(5) + f_(y)\cdot (4)/(5)$

$D\vec{u}_(AD)f=9 \cdot (3)/(5) + 2\cdot (4)/(5)$

$D\vec{u}_(AD)f= (27+8)/(5) =7$

The directional derivative of f at A in the direction of $\vec{u}_(AD)$ is 7.

Related Questions

A regular quadrilateral has what type of symmetry?
You flip 3 coins. What is the probability that you get exactly 2 heads?
The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism. Find the volume of each figure. Rectangular prism: L= 6 ft. W= x H=3 ft. Triangular Prism: L= 7 ft W= x H=4 ft. Volume of rectangular prism: _ ft3 Volume of triangular prism: _ ft3 PLEASE ANSWER ASAP! I'M OFFERING A LOT OF POINTS!
2v2 -5v +3 = 0 how did I do this?
The data below were gathered on a random sample of 5 basking sharks, swimming through the water and filter-feeding, i.e. letting the water bring food into their mouths.Body Length (meters) Column 1Mean Speed (meters/seconds) Column 24 0.89 4.5 0.83 4 0.76 6.5 0.94 5.5 0.94 Construct a scatterplot of the data and answer the following questions:(a) What is the label for the horizontal axis?(b) What is the label for the vertical axis?(c) Interpret the scatterplot (comment on association, form, strength, and outliers).

What is the point of origin on a number line

Answers

0 is the point of origin because it's not really a number, it's more of a starting point for positive and negative numbers.

What is the product of the following? 22 × 26/11a. 44
b. 446/11
c. 89/14
d. 56

Answers

$22* (26)/(11) = 2*11* (26)/(11) =2*26=52$

any answer is correct, my is correct....

Write a conjecture for the following situation - the product of three odd numbers.

Answers

Answer:

Step-by-step explanation:

A raffle is held at MTHS ASB to draw for a $1000 plasma television. Two thousand tickets are sold at $1.00 each. Find the expected value of one ticket.

Answers

Answer:

$0.5

Step-by-step explanation:

"The expected value of one ticket" is what the cost of the television covers.

If 2000 tickets are sold for $ 1 the total amount of all tickets sold is

$2000.(1)= 2000$

To calculate the expected value of a single ticket, we have to divide the cost of the TV by the price of all tickets sold.

$(1000)/(2000)= 0.5$

The "expected value of a ticket" is the probability of being drawn multiplied by the earnings associated to being drawn.
($1 is the price of the ticket which of course can be different).

So in this case probability is 1/2000 and the earnings would be valued $1000 (value of the plasma TV).
The expected value is 1/2000*1000=1000/2000=$0,5

This means you should not buy a $1 ticket to play except if this really brings you LOTS of amusement ;)

Melissa compares the numbers 0.058 and 0.21. She thinks that 0.058 > 0.21 because 58 > 21 , but the reasoning that Melissa used is incorrect

Answers

Answer:

Step-by-step explanation:

What is the answer tho

A pyramid has a square base with sides 8" and a slant height of 5". Total Area =

Answers

The total area of the pyramid that has 8 inches as its base and 5 inches as its slant hieght is 144 square inches. This is computed by (perimeter of square times slant height) divided by two plus square of the base. It will be equal to (36 x 5) / 2 = 64, which will give us the answer of 144 square inches.

Answer:

144 square units

Step-by-step explanation:

Other Questions

What is -6x-4+(2x+-8

A publisher claims that the average salary paid at its company is $37,500 but it could differ as much as $4500. Write and solve an absolute value inequality to determine the range of salaries at this company.|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000 |x − 37,500| ≤ 4500; The salaries are less than $33,000 or greater than $42,000. |x − 37500| ≥ 4500; The salaries range from $33,000 to $42,000 |x − 37,500| ≥ 4500; The salaries are less than $33,000 or greater than $42,000.

2. What is the product of 713 and 82? A. 795 B. 58,466 C. 631 D. 8 r57

What number should be placed in the box to help complete the division calculation?