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SOVA2 [1]
3 years ago
15

Find the directional derivative of f at the given point in the direction indicated by the angle θ.

Mathematics
1 answer:
anygoal [31]3 years ago
4 0

Answer:

Directional derivative = 1/√2

Step-by-step explanation:

We are given f(x, y) = y cos(xy)

Now, we know that;

∇f(x, y) = ycos xy

Thus, applying that to the question, we have;

∇f(x, y) = [-y² sin xy, cos (xy) - xy sin xy]

At coordinates (0,1),we now have;

∇f(0, 1) = [-1²•sin0, (cos 0) - 0]

∇f(0, 1) = [0, 1]

Now, unit vector indicated by the angle θ is given as; u = [cos θ, sin θ]

From the question, since θ = π/4, thus

u = [cos π/4, sin π/4]

Cos π/4 in surd form is; 1/√2

Also, sin π/4 in surd form is; 1/√2

So, u = [1/√2, 1/√2]

Directional derivative = [∇f(0, 1)] • u

= [0, 1] × [1/√2, 1/√2] = 0 + 1/√2 = 1/√2

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idk

Step-by-step explanation:

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3 years ago
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Four cookies and three cupcakes code $13.25. Five cookies and two cupcakes cost $11.75. Give the system of equations that could
Kaylis [27]

Answer:

  • cookie: $1.25
  • cupcake: $2.75

Step-by-step explanation:

Let x and y represent the cost of a cookie and a cupcake, respectively.

  4x +3y = 13.25

  5x +2y = 11.75 . . . . . . the system of equations

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By Cramer's rule:

  x = (3(11.75) -2(13.25))/(3(5) -2(4)) = 8.75/7 = 1.25

  y = (13.25(5) -11.75(4))/7 = 19.25/7 = 2.75

The cost of one cookie is $1.25; the cost of one cupcake is $2.75.

_____

Cramer's rule gives the solution to the system of equations ...

  ax +by =c

  dx +ey = f

as ...

  ∆ = bd -ea

  x = (bf -ec)/∆

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7 0
3 years ago
Twenty-five percent of the students had forgotten the year of the Declaration of Independence. If 57 students had not forgotten,
Phantasy [73]

Answer:

76,

Step-by-step explanation:

If you divide 57 by 3, you get 19. If you times 19 by 4 that is the total number of students there were in all.

4 0
3 years ago
15,000 blue trout were released into the Meherrin River for a scientific study. The function, f(x) = 15,000 (9/8)^x represents t
Ainat [17]
I'm guessing you mean f(x)=15,000(9/8)^x. If this is what you mean, the population would increase by about 12,000 (12030.4870605 to be exact).
Step-by-step explanation:
Starting equation: f(x)=15,000(9/8)^x
You can clean up the 9/8 to be 1.125
Now what you want to do is find the answer to (9/8)^5 which is 1.8020324707
Next multiply 1.8020324707 by 15,000 and you get 27030.4870605
Finally 27,030.4870605 - 15,000 gives you 12030.4870605. Which means that the population increased by about 12,000.

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5 0
3 years ago
In 2015, Ed spent $800 buying lunches. In 2017, he spent $550 buying lunches. What was the rate of change from 2015 to
marta [7]

9514 1404 393

Answer:

  $125 per year

Step-by-step explanation:

In the 2 years from 2015 to 2017, the spending on lunches increased by ...

  $800 -550 = $250

That is an average per year of ...

  $250/(2 yr) = $125/yr . . . . average dollar increase per year

_____

<em>Additional comment</em>

For costs, it is often true that they follow an exponential curve, not a linear one. Ed's spending increased by a factor of 800/550 = 16/11 in the two years, so an average percentage increase of √(16/11) -1 = 20.6% per year.

7 0
3 years ago
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