1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Natali [406]
3 years ago
6

(1 point) (a) Find the point Q that is a distance 0.1 from the point P=(6,6) in the direction of v=⟨−1,1⟩. Give five decimal pla

ces in your answer.
Q = ( , )

(b) Use P and Q to approximate the directional derivative of f(x,y)=√(x+3y) at P, in the direction of v.
fv ≈
(c) Give the exact value for the directional derivative you estimated in part (b).
fv =
Mathematics
1 answer:
natima [27]3 years ago
4 0

Answer:

following are the solution to the given points:

Step-by-step explanation:

In point a:

\vec{v} = -\vec{1 i} +\vec{1j}\\\\|\vec{v}| = \sqrt{-1^2+1^2}

    =\sqrt{1+1}\\\\=\sqrt{2}

calculating unit vector:

\frac{\vec{v}}{|\vec{v}|} = \frac{-1i+1j}{\sqrt{2}}

the point Q is at a distance h from P(6,6) Here, h=0.1  

a=-6+O.1 \times \frac{-1}{\sqrt{2}}\\\\= 5.92928 \\\\b= 6+O.1 \times \frac{-1}{\sqrt{2}} \\\\= 6.07071

the value of Q= (5.92928 ,6.07071  )

In point b:

Calculating the directional derivative of f (x, y) = \sqrt{x+3y} at P in the direction of \vec{v}

f_{PQ} (P) =\fracx{f(Q)-f(P)}{h}\\\\

            =\frac{f(5.92928 ,6.07071)-f(6,6)}{0.1}\\\\=\frac{\sqrt{(5.92928+ 3 \times 6.07071)}-\sqrt{(6+ 3\times 6)}}{0.1}\\\\= \frac{0.197651557}{0.1}\\\\= 1.97651557

\vec{v} = 1.97651557

In point C:

Computing the directional derivative using the partial derivatives of f.

f_x(x,y)= \frac{1}{2 \sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{2 \sqrt{22}}\\\\f_x(x,y)= \frac{1}{\sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{\sqrt{22}}\\\\f_{(PQ)}(P)= (f_x \vec{i} + f_y \vec{j}) \cdot \frac{\vec{v}}{|\vec{v}|}\\\\= (\frac{1}{2 \sqrt{22}}\vec{i} + \frac{1}{\sqrt{22}} \vec{j}) \cdot   \frac{-1}{\sqrt{2}}\vec{i} + \frac{1}{\sqrt{2}} \vec{j}

You might be interested in
What's the awnser to the one about Isabella
Irina18 [472]
I cant even see the picture clearly

6 0
3 years ago
6x-14<-14 or 3x+10>13
kow [346]

Step-by-step explanation:

not sure the question but I can solve the equations

6x-14<-14

6x<0

×<0

3x+10>13

3x>3

×>1

7 0
2 years ago
You and a partner tend 3 machines that run continuously. One prints 200 plastic bottles per hour, one prints 180 plastic bottles
strojnjashka [21]
The first machine does 200 in 1 hour, so in 8.5 hours it will then do 200 * 8.5.

the second machine does 180 in 1 hour, so in 8.5 hours it will then do 180 * 8.5.

the third machine does 150 in 1 hour, so in 8.5 hours it will do then 150 * 8.5.

how many bottles will they all do in total on that time?

(200 * 8.5) + (180 * 8.5) + (150 * 8.5)
6 0
3 years ago
Read 2 more answers
find the length of the base of a square pyramid if the volume is 1,024 cubic inches and has a height of 12 inches. (6 points) 4
Leokris [45]
To solve, we use the volume of a square pyramid formula which is expressed as the product of the area of the base (a²) and the height divided by three(h/3).

Volume = a² (h/3)
1024 in³ = (a²) (12 in/3)
a² = 1024 in³ · 3 /12
a = √256 in²
a = 16 in

Thus, the length of the base is 16 in.

5 0
3 years ago
Read 2 more answers
Product A requires 5 machine hours per unit to be produced, Product B requires only 3 machine hours per unit, and the company's
Lesechka [4]

Answer:

  Produce only Product B.

Step-by-step explanation:

The contribution margin per machine hour for product A is ...

  ($16 -$6)/(5 hour) = $2 per hour

The contribution margin per machine hour for product B is ...

  ($12 -$5)/(3 hour) ≈ $2.33 per hour

The company should produce the maximum possible number of the product that contributes the most per machine hour: Product B.

5 0
3 years ago
Other questions:
  • What is 6 whole and 1/5 as fraction to a decimal
    6·2 answers
  • a stainless steel garbage can is in the shape of a right circular cylinder. If its radius is 6 inches and its volume is 864 pi c
    5·2 answers
  • Tracey has 29 students in her class. She has 21 boys in her class. What is the ratio of girls to boys in her class
    15·1 answer
  • Please help 30 points!!!!!!! Convert 45.25 mL into ft3.
    8·1 answer
  • Evaluate numerical expression
    9·2 answers
  • Use a graphing calculator to sketch the graph of the quadratic equation, and then give the coordinates for the x-
    11·1 answer
  • (BRAINLIEST) What is the solution to this system of equations?
    10·2 answers
  • PLEASE HELP 7TH GRADE MATH
    12·2 answers
  • Triangle DEF is translated 3 units up to form triangle D'E'F'and 5 units to the left to form triangle D''E'' ''F'. The coordinat
    14·1 answer
  • Assuming that x=-2 and y=3 evaluate xy-x^3 ​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!