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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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a) the largest y-intercept is 1

b) 13.5

c) y=x-3

d) 8

Step-by-step explanation:

the question was worded very strangely and I will answer the way I precieved it.

for question d, I simply considered the question to be asking what is X when y is 17 and since the equation of that line is 2x-1

5 0
3 years ago
Complete the table to summarize what you know about each player's throw: (2 points: 1 point for each row of the chart) tre and h
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3 years ago
If f(x) = 3x and g(x)=2x, what is (g o f)(x)?<br> 5x<br> 5x2<br> 6x<br> 6x2
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If you would like to solve (g ° f)(x), you can calculate this using the following steps:<span>

(g ° f)(x) = g(f(x))

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5 0
3 years ago
Original amount = 80 dollars. 20 percent off is 64 dollars. 20 percent off is question mark.
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Answer:

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7 0
2 years ago
Frank invests $1,000 in simple interest investment account that pays 8% a year. After a number of years, he withdraws his balanc
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There are 15 years was his money invested.

<h3>What is simple interset?</h3>

Simple Interest is an easy method of calculating the interest for a loan/principal amount.

Given

Frank invests $1,000 in simple interest investment account that pays 8% a year.

After a number of years, he withdraws his balance of $2,200.

The number of years was his money inversted is;

\rm I= P\times r \times t

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Hence, in the 15 years was his money invested.

To know more about investing click the link given below.

brainly.com/question/26677076

7 0
2 years ago
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