Locate and classify all the critical points of the function. (If an answer does not exist, enter DNE.)

f(x, y) = 2x² + 3y² + 4

Answers

Answer 1

Answer:

Step-by-step explanation:

f(x,y)=2x2+3y2−4x−1 ⇒ ∇f =⟨4x−4,6y⟩=⟨0,0⟩ ⇒ x=1, y = 0. Thus (1,0) is the only critical point of f, and it lies in the region x2+y2<16.Ontheboundary,g(x,y)=x2+y2=16 ⇒ λ∇g=⟨2λx,2λy⟩,so6y=2λy ⇒ eithery=0orλ=3. Ify=0,then x=±4;ifλ=3,then4x−4=2λx ⇒ x=−2andy=±2√3. Now f(1,0) = −3, f(4,0) = 15, f(−4,0) = 47, and f−2,±2√3 = 51. Thus the maximum value of f(x,y) on the disk x2+y2 ≤ 16 is f−2,±2√3 = 51, and the minimum value is f (1, 0) = −3.


Related Questions

Jenniter's bill for lunch was $15.00 if Jennifer left a 20% tip, which proportion would BEST represent how to find how much tip she should leave? 15 100 20 B — 20 100 15 15 20 100 O D 15 100​

Answers

Answer:

Well, I usually multiply this which would be 15 x .2 which would equal the tip.

Step-by-step explanation:

If you order 3 hamburgers, 2 orders of fries, and 3 milkshakes for your friends, how much do they owe you?

Answers

Answer:

31.55

Step-by-step explanation:

1/4 ÷ (−3/8) Can anyone help me with this?

Answers

Answer:

Fraction:

- 2 over 3

Decimal: -0.66666666

(- Repeating Decimal-)

Step-by-step explanation:

Add negative 8 + positive 8

Answers

Answer: 0

Step-by-step explanation: -8+8=0

Answer:

0

Step-by-step explanation:

So if you have -8 and 8 and you add them together they cancel out each other and make 0

Dale made $105 for 7 hours of work. At the same rate, how much would he make for 9 hours of work? helppp please

Answers

You would have to divide 105 by 7 and get an answer then you times that answer by nine and get your answer

Answer:

135

Step-by-step explanation:

105/7 = 15

15*9 = 135

Graphing Ratios Which line includes the ratios in the table? Reading a Graph All the ratios lie on line

Answers

Answer:

b

Step-by-step explanation:

Write an equation in slope intercept form that passes through the point (2,-2), and has a slope that equals -2 (please hurry)

Answers

Answer:

y = -2x + 2

Step-by-step explanation:

Plug in the point and slope into y = mx + b, and solve for b:

y = mx + b

-2 = -2(2)  + b

-2 = -4 + b

2 = b

Plug in the slope and y intercept into y = mx + b

y = -2x + 2

So, the equation is y = -2x + 2

Simplify (2V5 - 4)(3 V5+2).
a.
4
c.
b.
8-4v5
d. 22-8v5

Answers

Answer:

[tex](2\sqrt{5} - 4)(3\sqrt{5}+2)= 22 - 8\sqrt{5}[/tex]

Step-by-step explanation:

Given

[tex](2\sqrt{5} - 4)(3\sqrt{5}+2)[/tex]

Required

Simplify

[tex](2\sqrt{5} - 4)(3\sqrt{5}+2).[/tex]

Expand brackets

[tex]2\sqrt{5}(3\sqrt{5}+2). - 4(3\sqrt{5}+2).[/tex]

Open each bracket

[tex]2\sqrt{5}*3\sqrt{5}+2\sqrt{5}*2 - 4*3\sqrt{5}-4*2[/tex]

[tex]6 * 5 + 4\sqrt{5} - 12\sqrt{5} - 8[/tex]

[tex]30 + 4\sqrt{5} - 12\sqrt{5} - 8[/tex]

Collect Like Terms

[tex]- 8+30 + 4\sqrt{5} - 12\sqrt{5}[/tex]

[tex]22 - 8\sqrt{5}[/tex]

Hence:

[tex](2\sqrt{5} - 4)(3\sqrt{5}+2)= 22 - 8\sqrt{5}[/tex]

Factor the polynomial 8x² − 24x − 224 completely. help now!

Answers

Answer:

8 ( x  −  7 )  ( x  +  4 )

Step-by-step explanation:

can someone help me plz

Answers

14,606 is the right answer

heyyy can someone help really quickly

Answers

Answer:

10x+16

Step-by-step explanation:

4x-1+6x+2+15

10x-1+2+15

10x+16

if Susan finished her lunch at 1:00 and it took her 45 minutes to eat. what time did the class start

Answers

Answer:

12:15

Step-by-step explanation:

i dont really have an explanation

but i am in 6th grade not sure how

to explain it lol

Solve distance 120 meters time 30 seconds

Answers

Answer:

4 meters per second

Step-by-step explanation:

120 divided by 30 = 4

The perimeter of a picture frame is 68 inches. The difference between the length of the frame and th
times its width is 2. The system of equations

Answers

Answer:

L - W = 2 and 2L + 2W = 68

Step-by-step explanation:

The two equations here are going to be-

Length minus width equals 2

L - W = 2

And

Length x 2 + Width x 2 = 68

2L + 2W = 68

3n^2-1 find the 2nd and 5th term

Answers

Answer:

2nd term = 11

5th term = 74

Step-by-step explanation:

3n² - 1

n = 2 , 2nd term = 3*2²  - 1

                           = 3*4 -1

                          = 12 - 1

                          = 11

n= 5 , 5th term = 3*5² - 1

                        = 3*25 - 1

                      = 75 - 1

                      = 74

Step-by-step explanation:

in[tex]\tt{3n^2-1 }[/tex] ⠀

If n=2

so,

2nd term=⠀

[tex]\rightsquigarrow[/tex] [tex]\tt{3×2^2-1 }[/tex] ⠀

[tex]\rightsquigarrow[/tex] [tex]\tt{ 3×4-1 }[/tex] ⠀

[tex]\rightsquigarrow[/tex] [tex]\tt{ 12-1 }[/tex] ⠀

[tex]\rightsquigarrow[/tex] [tex]\tt{ 11 }[/tex] ⠀

so,2nd term is 11.

If n=5

so,

5th term =

[tex]\rightsquigarrow[/tex] [tex]\tt{ 3×5^2-1 }[/tex] ⠀

[tex]\rightsquigarrow[/tex] [tex]\tt{ 3×25-1 }[/tex] ⠀

[tex]\rightsquigarrow[/tex] [tex]\tt{75-1 }[/tex] ⠀

[tex]\rightsquigarrow[/tex] [tex]\tt{74 }[/tex]

so 5th term is 74.⠀

Pls help urgently extra points and mark brainlist sorry it’s reading but easy

Answers

Answer:

Gather

Step-by-step explanation:

Answer: Gather

Hope this helps!

. What will be the coordinates of point T after a 180° rotation about the origin? ​

Answers

Step-by-step explanation:

180 Degree Rotation

When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y)

What is 1.2 divided by 25?

A. 0.48
B. 0.0048
C. 48.0
D. 00.48

Answers

Answer:

D 0.048

Step-by-step explanation:

Answer:

0.048

Step-by-step explanation:

0.048 is the correct answer but I don't see that choice.

A certain population increases at a rate proportional to the square root of the population. If the population goes from 2500 to 3600 in five years, what is the population at the end of t years

Answers

Answer:

[tex]P(t) = (2t + 50)^2[/tex]

Step-by-step explanation:

A certain population increases at a rate proportional to the square root of the population.

This means that the population can be described by the following differential equation:

[tex]\frac{dP}{dt} = r\sqrt{P}[/tex]

In which r is the growth rate.

Solving by separation of variables, we have that:

[tex]\frac{dP}{\sqrt{P}} = r dt[/tex]

Integrating both sides:

[tex]2\sqrt{P} = rt + K[/tex]

In which K is a random constant

[tex]\sqrt{P} = 0.5rt + K[/tex]

Finding the squares of both sides:

[tex]P(t) = (0.5rt + K)^2[/tex]

Finding the value of K

The initial population is of 2500. That is, when [tex]t = 0, P = 2500[/tex]. So

[tex]P(t) = (0.5rt + K)^2[/tex]

[tex]2500 = (0.5r(0) + K)^2[/tex]

[tex]K^2 = 2500[/tex]

[tex]K = \sqrt{2500}[/tex]

[tex]K = 50[/tex]

So

[tex]P(t) = (0.5rt + 50)^2[/tex]

Finding the value of r

Population of 3600 in 5 years(when t = 5). So

[tex]P(t) = (0.5rt + 50)^2[/tex]

[tex]3600 = (0.5r(5) + 50)^2[/tex]

[tex](2.5r + 50)^2 = 3600[/tex]

Taking the square root of both sides

[tex]\sqrt{(2.5r + 50)^2} = \sqrt{3600}[/tex]

[tex]2.5r + 50 = 60[/tex]

[tex]2.5r = 10[/tex]

[tex]r = 4[/tex]

So, the equation for the population at the end of t years is given by:

[tex]P(t) = (0.5rt + 50)^2[/tex]

[tex]P(t) = (0.5(4)t + 50)^2[/tex]

[tex]P(t) = (2t + 50)^2[/tex]

Which shape do you use to set up the proportion for similar shape?​

Answers

Answer:

a smaller version of the shape think :)

HELP I NEED HELP ON THIS ASSIGNMENT

Jeff invested 3000 dollars into an account that gives 6.5% interest, compounded annually. The formula of the compound interest is A(t)=P(1+i)^t.


How much did Jeff have after three years?

Answers

Answer:

he will have $3623.85 after 3 years.

welp this is me with my instrument...i look weird

Answers

Answer:

wow i have never seen that instrument before.

Step-by-step explanation:

)) What is the area of this figure?
3 mi
5 mi
8 mi
15 mi
6 mi
18 mi
8 mi
9 mi
Write your answer using decimals, if necessary.
square miles

Answers

Answer:

678182829jijsjsjsjsjskskwkdkw

Area of the given figure is 199.5 square miles.

What is Area?

Area of a two dimensional shape is the total region which is bounded by the object's shape.

The given figure can be divide in to smaller figures to find the area of each smaller figure and add it.

A rectangle with sides 5 miles and 3 miles.

A rectangle with sides 15 miles and 6 miles.

A rectangle with sides (8 - 5) + 6 = 9 miles and 3 miles.

A triangle with base length 9 miles and height 8 + 6 + 3 = 17 miles.

Area = (5 × 3) + (15 × 6) + (9 × 3) + (1/2 × 9 × 17)

        = 15 + 90 + 18 + 76.5

        = 199.5 square miles

Hence the area of the given figure is 199.5 square miles.

Learn more about Area here :

https://brainly.com/question/23718948

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Dan is moving old monitors and printers from an office to a local electronic recycling center. Danhas to move a total number of 60 printers and monitors with a combined weight of 1750 lbs. One monitor weighs 35 pounds, and a printer weighs 25 pounds. Does Dan recycle a greater weight of printers or monitors. Explain using a system of equation. ​

Answers

Answer:

Dan is recycling equal weight of printers and monitors.

Step-by-step explanation:

Let,

x be the number of printers

y be the number of monitors

According to given statement;

x+y=60      Eqn 1

25x+35y=1750   Eqn 2

Multiplying Eqn 1 by 25

25(x+y=60)

25x+25y=1500    Eqn 3

Subtracting Eqn 3 from Eqn 2

(25x+35y)-(25x+25y)=1750-1500

25x+35y-25x-25y=250

10y = 250

Dividing both sides by 10

[tex]\frac{10y}{10}=\frac{250}{10}\\y=25[/tex]

Putting y=25 in Eqn 1

x+25=60

x=60-25

x=35

Weight of printers = 35*25 = 875 lb

Weight of monitors = 25*35 = 875 lb

Therefore,

Dan is recycling equal weight of printers and monitors.

pls give the right answer to this question it is not 0.45662100456

Answers

Answer:

2.19

Step-by-step explanation:

Answer:

2.19

Step-by-step explanation:

A colony of 100,000 ants has been declining in number at a rate of 11.4% per month. If allowed to decline uninhibited, how long will it take the population to decrease to 25,000 ants? Round to the nearest tenth.

a. 17.6 months
b. 12.2 months
c. 5.3 months
d. 24.3 months

Answers

Answer:

b. 12.2 months

A percentage is a way to describe a part of a whole. The correct option is B.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the colony of 100,000 ants has been declining in number at a rate of 11.4% per month. Therefore, the number of months it will take for the ant population to reach 25,000 ants is,

Population = 100,000(1-0.114)ⁿ

25,000 = 100,000(1-0.114)ⁿ

0.25 = 0.886ⁿ

log(0.25) / log(0.886) = n

n = 11.45335

Since the value is close to 12.2 months.

Hence, the correct option is B.

Learn more about Percentages:

https://brainly.com/question/6972121

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[5, 7.9.11.12.14.19}.

Answers

Answer:

sorry I can get what are you asking

is medium, average or something else?

please help it would mean so much to im stressed out​

Answers

5) the line goes diagnol right throuh the zero from the bottom left corner to the top right.

6) straight line across 3 (3,0)

7) straight line across -2 (-2,0)

8) its a open dot on 1 with the line going right

9) ok so they are both intercecting im pretty sure its a no solution tho

Sorry for the bad picture quality, lol trust me I’m not android user... bUt I really am struggling! Help!-

Answers

Answer:

a to u

Step-by-step explanation:

(I really need help on this) FGHIJ ~ YUVWX. Find UY and GH.

Answers

Answer:

UY = 90

GH = 4

Step-by-step explanation:

Since both figures are similar, the ratio of their corresponding side lengths would be the same.

Thus:

✔️UY/GF = XW/IJ

UY/10 = 54/6 (Substitution)

Multiply both side by 10

UY = (54*10)/6

UY = 90

✔️Also,

UV/GH = XW/IJ

36/GH = 54/6

36/GH = 9

GH = 36/9

GH = 4

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