Let f(x,y)=(5y^2)ln(3x). Then ∇f =? , and Duf(2,5) in the direction of the vector 〈2,−2〉 is ?
Let f(x,y)=((x^3)(y^3))/9. Then ∇f =? , and Duf(−5,−4) in the direction of the vector 〈−2,−2〉 is ? .

Answers

Answer 1

Duf(−5,−4) in the direction of the vector 〈−2,−2〉 is 〈((-5)^2)(-4)^3/3, (-5)^3((-4)^2)/3〉 · 〈-1/√2, -1/√2〉 = 500/3.

For the function f(x, y) = (5y^2)ln(3x), we have:

∂f/∂x = (5y^2)/(3x)

∂f/∂y = 10y ln(3x)

Therefore, ∇f = 〈(5y^2)/(3x), 10y ln(3x)〉.

To find Duf(2, 5) in the direction of the vector 〈2, -2〉, we first need to find the unit vector in the direction of 〈2, -2〉:

||〈2, -2〉|| = √(2^2 + (-2)^2) = 2√2

u = 〈2, -2〉 / ||〈2, -2〉|| = 〈1/√2, -1/√2〉

Then, we have:

Duf(2, 5) = ∇f(2, 5) · u = 〈(5(5)^2)/(3(2)), 10(5) ln(3(2))〉 · 〈1/√2, -1/√2〉

= (125/6√2) - (50/√2) ln3.

For the function f(x, y) = ((x^3)(y^3))/9, we have:

∂f/∂x = (x^2)(y^3)/3

∂f/∂y = (x^3)(y^2)/3

Therefore, ∇f = 〈(x^2)(y^3)/3, (x^3)(y^2)/3〉.

To find Duf(-5, -4) in the direction of the vector 〈-2, -2〉, we first need to find the unit vector in the direction of 〈-2, -2〉:

||〈-2, -2〉|| = √((-2)^2 + (-2)^2) = 2√2

u = 〈-2/√8, -2/√8〉 = 〈-1/√2, -1/√2〉

Then, we have:

Duf(-5, -4) = ∇f(-5, -4) · u = 〈((-5)^2)(-4)^3/3, (-5)^3((-4)^2)/3〉 · 〈-1/√2, -1/√2〉

= 500/3.

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Related Questions

Find The Area of the parallelogram...

Answers

Answer:

162 ft^2

Step-by-step explanation:

the formula for finding the area of a triangle is [tex]\frac{b*h}{2}[/tex]

the base is 27 and the height is 12

[tex]\frac{27*12}{2}=\frac{324}{2} = 162[/tex]

the area of a triangle is (base X height)/2

(27 X 12)/2 = 324/2 = 162ft^2

In the number 8246315 what sigit is in the ones place​

Answers

Answer:

5

Step-by-step explanation:

The ones place is the one most to the right that isn't after a decimal point.

Answer:

5, since it is all the way to the right

Step-by-step explanation:

if you ever have a big number, the number in thes ones place is ALWAYS on the far right, except if its a decimal !

i hope this helps !! :D

Gabriella made 5 waffles for breakfast. She has 25 strawberries and 15 blueberries to put on top of the waffles. She will put a equal number of berries on each waffle.How many berries will gabrielle put on each waffle?

Answers

She will use 3 blueberries on each and 5 strawberries on each hope this helps <3

15x=12x+15 whats the angle measures.

Answers

Answer:

x = 5 (please read the step by step explanation)

Step-by-step explanation:

So, I'm just going to solve for x because the instructions aren't too clear. I believe there is supposed to be an image attached to it, but seeing as I don't have that, I'll just solve for x and you can plug in with the values.

15x = 12x + 15

Same to both sides:

3x = 15

Isolate x:

x = 5

Just plug in those values and you'll be good to go! Have a good day!

HELP ASAP HELPPP MARKING BRAINLIEST

Answers

The answer is 68 1/8

Answer:

answer is 68 1/8

Step-by-step explanation:

The area of circle can be expressed by the
formula A = ar?where r is a radius of circle.
express radius in terms of area of circle.

Answers

9514 1404 393

Answer:

  r = √(A/π)

Step-by-step explanation:

Solve for r. Do this by dividing by the coefficient of the r² term, then taking the square root.

  A = πr²

  A/π = r²

  r = √(A/π)

there are 5 red marbles, 7 green marbles, 4 black marbles, and 8 blue marbles in a bag. Find P(not yellow

Answers

Total number of Marbles is = 5 + 8 + 7 = 20

Total number of non-red marbles = 5 + 7 = 12.

P( Not yellow) 12/20 = 3/5.

The answer is 3/5.

Answer:

3/5

Step-by-step explanation:

A set of 25 two digit numbers are listed below 10,17,20,23,24,28,32,39,42,25,26,52,55,58,61,65,66,72,75,78,79,85,94,97,98. What is the probability of the sum of the number's digits is odd?

Answers

Answer:

0.48

Step-by-step explanation:

Given the data:

X:

10,17,20,23,24,28,32,39,42,25,26,52,55,58,61,65,66,72,75,78,79,85,94,97,98

Sum of each of the numbers :

1, 8, 2, 5, 6, 10, 6, 12, 6, 7, 8, 7, 20, 13, 7, 11, 12, 9, 12, 15, 16, 13, 13, 16, 17

Probability that sum of the number's digit is odd:

Number of odd sum / total numbers

Number of odd sum = 12

Total numbers = 25

12 / 25

= 0.48

y-2=1/2(x-4) in slope intercept form

Answers

Answer:

y = 1/2x

Step-by-step explanation:

y - 2 = 1/2 (x-4)

y = 1/2x - 2 + 2

y = 1/2x

(The y - intercept is 0 because -2 and 2 cancels each other out)

Hope this helps :)

Let me know if there are any mistake!!

The slope intercept form of the equation y - 2 = 1/2 (x - 4) will be

⇒ y = 1/2x

What is equation of line?

The equation of line in slope intercept form is defined as;

y = mx + b

Where, 'm' is slope of line and 'b' is y-intercept.

Given that;

The equation of line is;

y - 2 = 1/2 ( x - 4 )

Now,

We can change the equation of line in slope intercept form as,

y - 2 = 1/2 ( x - 4)

Solve as;

y - 2 = 1/2 x - 1/2 × 4

y - 2 = 1/2 x - 2

Add 2 both side,

y - 2 + 2 = 1/2 x - 2 + 2

y = 1/2 x

Thus, The slope intercept form of the equation y - 2 = 1/2 (x - 4) will be;

⇒ y = 1/2x

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If A = 56° then find C.

Answers

Answer:

124

Step-by-step explanation:

If you are talking about angles, then the answer is 124 degrees. Question is a little open, though.

I hope this helps!

− 2/3m = −1/2 solve for m

Answers

Answer:

m=-18

Step-by-step explanation:

-12=2/3m

Identify the exponential function for the given graph.
A)
f(x) = (şs* +2
f(%) (şyx - 2
f(x) = (-3;* + 2
f(x) = (–33* - 2
9.
D)

Answers

Answer:

Step-by-step explanation:

C - 3(2^x).

Find the distance between the two points rounding to the nearest tenth (if necessary).
(-3,0) and (5, -3)

Answers

Use the distance formula to find the distance.

uM ANY help pls?
Hopely someone can help!

Answers

Answer:

He made 35% of his shots he did not make 65& of his shots

Step-by-step explanation:

7/20=35%, 20/7=65%

What is the value of the expression 11 - (34.48?
1) 3
O2) 5
O 3) 8
4) 9

Answers

Answer:

-23.48

Step-by-step explanation:

Hoped this helped!!

Need answer pizza ???

Answers

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Surface areas and Volumes.

Since, we know that the lateral area of a Right circular cone is given as,

AL = πrl

here, l = slant height , r = radius of the circular base.

so now, we have to find first slant height to get the lateral surface area,

[tex]l \: = \sqrt{ {r}^{2} + {h}^{2} } [/tex]

here, r = 8 cm and h = 15,

hence,

[tex]l \: = \sqrt{64 + 225} = \sqrt{289} = 17cm[/tex]

hence, now we apply the formula,

AL = π(8) (17) cm^2

===> AL = 136 π cm^2

help me plz plz i need my grades up​

Answers

Answer:

Decimal: 2.1

Fraction: 21/10

Answer:
2.1
Explanation

geometry: help needed, it’s urgent!
angle 1 measures 75 degrees, is this table right?

Answers

Answer:

angle 1 and 3 are alternate INTERIOR angles cos they are on the inside of the lines but you were close

I need an explanation for the problem 4v2=-12v-9. I don't understand why it factors into 4v+3 and 4v+3

Answers

Answer:

The factors are [tex]2v+3,2v+3[/tex].

The factors are not [tex]4v+3,4v+3[/tex]

Step-by-step explanation:

Equation is [tex]4v^2=-12v-9[/tex].

This equation can be written as follows:

[tex]4v^2+12v+9=0[/tex]

Here,

[tex]12v=6v+6v[/tex]

Therefore,

[tex]4v^2+6v+6v+9=0\\2v(2v+3)+3(2v+3)=0\\(2v+3)(2v+3)=0[/tex]

So, the factors are [tex]2v+3,2v+3[/tex].

The factors are not [tex]4v+3,4v+3[/tex]

PLEASE HELP I WILL GIVE BRAINLIEST

Answers

Answer:

$67

Step-by-step explanation:

So 5x12+7=C

PEDMAS so:

5x12 = 60

60+7 = 67

67 = C

, describe how a translation is different from a rotation.

Answers

Answer:Rotation is rotating an object about a fixed point without changing its size or shape. Translation is sliding a figure in any direction without changing its size, shape or orientation.

Step-by-step explanation:

Which Triangle appears to be both right and isosceles?

Answers

Answer: B

Step-by-step explanation: An isosceles right triangle is an isosceles triangle and a right triangle. This means that it has two congruent sides and one right angle. Therefore, the two congruent sides must be the legs.

Answer:

B

Step By Step Explanation:

The corner of the triangle is at 90 degrees making it a right angle. Both legs are congruent and has corresponding angles.

tysm for whoever helps !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11

Answers

Answer:

21

Step-by-step explanation:

When you simply the fractions down, you will get this

[tex]16 + 5 = 21[/tex]

Hope this Helped

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents.

(b^4)2

Answers

Answer:

[tex](b^4)^2 = b^{8}[/tex]

Step-by-step explanation:

Given

[tex](b^4)^2[/tex]

Required

Simplify

In indices, we have:

[tex](a^m)^n = a^{m*n[/tex]

So:

[tex](b^4)^2 = b^{4*2}[/tex]

[tex](b^4)^2 = b^{8}[/tex]

in each diagram, BD bisects

Answers

Answer:

26. ∠ABC=44

27. ∠ABC=86

28. ∠ABC=116

Step-by-step explanation:

Since BD bisects ∠ABC in each diagram, ∠ABD=∠DBC.

26.

∠ABD=∠DBC

5x+2=7x-6

2x=8

x=4

∠ABC=∠ABD+∠DBC

=5(4)+2+7(4)-6

=20+2+28-6

=44

27.

∠ABD=∠DBC

11x-12=8x+3

3x=15

x=5

∠ABC=∠ABD+∠DBC

=11(5)-12+8(5)+3

=55-12+40+3

=86

28.

∠ABD=∠DBC

9x-23=5x+13

4x=36

x=9

∠ABC=∠ABD+∠DBC

=9(9)-23+5(9)+13

=81-23+45+13

=116

randy needs to save 2550$ for a vacation. he has 6 months to save the money. how much money must he save each month?

Answers

Answer:

425

Step-by-step explanation:

2550/6=425

Answer:

425

Step-by-step explanation:

I need help I am really struggling with math

Answers

Answer:

Okay what is it i might be able to help

Step-by-step explanation:

What is the conjugate of
(-5 + 4i)?

Answers

Answer:

the answer to that is -1i

Step-by-step explanation:

cause if you add negative and positve you get to subtract it and get the sign of the highest number

-3y>x+6 I need help w this math problem

Answers

Answer:

y< −x/3 −2

Step-by-step explanation:

I hope this is what you need if not let me know and ill edit the answer

The results of the first 100 students who voted are represented in the table. There are still 50 more students left to vote. Based on the early results, how many MORE votes do you expect Dan to get out of the 50 late voters?

Answers

Answer:

1-50

Step-by-step explanation:

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