verify the linear approximation at (0, 0). f(x, y) = y + cos2(x) ≈ 1 + 1 2 y

Answers

Answer 1

Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.

In the given question, we have to verify the linear approximation at (0, 0).

f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y

Let f(x, y) = √(y+cos^{2}x)

f(x, y) ≈ f(a, b)+fx(a, b)(x-a)+fy(y-b)

f(x) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex]

f(y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]

f(x, y) ≈ 1+0(x-0)(1/2)(y-0)

f(x, y) ≈ 1+1/2y

Hence, left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.

To learn more about linear approximation link is here

brainly.com/question/6768038

#SPJ4

The complete question is:

Verify the linear approximation at (0, 0). f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y

Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) =.............. and fy(x, y) = ............. Both fx and fy are continuous functions for y >............ , so f is Differentiable at (0, 0) by this theorem. We have fx(0, 0) =........... and fy(0, 0) =............. , so the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)=........


Related Questions

3. Find the balance of a savings account at the end of 15 years if the interest
earned each year is 6.3%. The principal is $700.

Answers

Answer:

The balance of the savings account in 15 years will be $1,750.24.

PPPPPPPPPPPPPPPPPLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLZZZZZZZZZZZZZZZZZZZZZ Help its due by end of day i relay need a good grade

Answers

Answer:

first question

AB=CD=15cm

BD=AC=8cm

AB=CD=15cm

BD=AC=8cm

First equation ^

Urgent please help..

Answers

108 !! ye i’m sorry mate i suck at maths

Answer: I’m pretty sure it’s 15 cm

Step-by-step explanation:

Ana participated in a charity walk. She
raised $0.25 for each 1/2
mile that she
walked. The first day, Ana walked 11 miles.
The second day, she walked 14 miles.
How much money did Ana raise?

Answers

Answer:

if $0.25 for each mile, then $1.00 =1 mile.

so the first day would be = $1=1mile

$n=11 miles

= 1n= 11×1=$ 11

Step-by-step explanation:

and the 2nd day is = 14×1= $14.

So the answer is 14+11=$25.00

Mario walked 250 ft south then 430 ft west. How far is he from the starting point? Round off answers to the nearest hundredths place.

Answers

Answer:

497.39 FEET

Step-by-step explanation:

Please check the attached image for a diagram of the bearings

This question can be solved using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

we want to determine the value of c

250² + 430² = 247400

c = √247400 = 497.39 feet

An urn contains 8 green and 9 white balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 6 balls drawn from the urn are white? Round your answer to three decimal places.

Answers

Answer:

The probability is 0.022

Step-by-step explanation:

Firstly, we need to get the total number of balls in the urn

mathematically, we have this as ;

8 + 9 = 17

now, the probability of selecting a white ball will be the number of white balls divided by the total number of balls

Mathematically, we have this as 9/17

Now, since the event is carried out with replacement, the probability for the six times is the same

So, we have the probability as;

(9/17)^6 = 0.022

Mark correct answer for wrong ones.
Except one needs to answers I haven't gotten to yet. Correct answer gets brainliest!

Answers

Answer: Can I see a better pic?

Step-by-step explanation:

Answer: D and C

Step-by-step explanation:

A girl successfully made 12 free throws yesterday today she made 150% as a nanny how many successful Fritos did she make today

Answers

Answer:

18 throws

Step-by-step explanation:

Given data

Number of throws= 12

Let us 150% if 12

=150/100*12

=1.5*12

=18 throws

Hence she made 18 throws today

Please help me with this

Answers

2)

Okay so because the right side is two times the length and width of the left side, we need to divide 20 and 14 by 2 which gives us 10 and 7. That means x+2 = 10 so we need to subtract 2 from each side which gives you 8. Therefore, x = 8.

20/2 = 10

10 - 2 = 8

x = 8

3.71 × 1,000 pls need answer

Answers

Answer: 3,710

Step-by-step explanation:

Practice Triangle Ratios (Sides) Find the value of c. Round to the nearest tenth!

Answers

Answer:

30.6688

Step-by-step explanation:

We usually use the formula SOHCAHTOA meaning Sine = opposite side/hypotenuse Cosine = opposite side /hypotenuse then Tangent = Opposite side/Adjacent side. We then say Tan61°= x/17 to get the height as 30.6688 PS/ Hypotenuse is the slanting side of the triangle


When 'x' is multiplied by a number inside the parentheses, it causes what type of
transformation:

Answers

i am just answering for points

find c
A. square root of 7 and 2
B. 14
C. 7
D. square root of 7 and 3


can you please help.​​

Answers

Answer:

3.74-a

7

2.64

4.58

Step-by-step explanation:

hope it helps please mark me as brainlist

Simplify the following expression: (2x2+3x−4)−(4x2−7x+1)

A
−2x2+10x−5

B
2x2−4x−3

C
−8x2+21x+4

D
−2x−4x−5

Answers

The answer for this problem is B

A ball is dropped from a height of 180 meters. The height of the ball can be represented by
-5t2 + 180, in meters, when t represents the time in seconds since the ball was dropped.
Which expression represents the height of the ball In factored form?

A) -5(t+6)^2
B) -5(t-6)^2
C) -5(t+6)(t-6)
D) (5t-3)(80t+3)

Answers

I think it is C but it also could be B as well

9.8 ft
4f
12 ft
Find the Area of this figure

Answers

I think it’s 470.4 ft

...............................

Answers

In numerology, the letter Y can be a vowel or a consonant

help a girl out please

Answers

Answer:4

Step-by-step explanation:ts is = ed

what is the rate of change of y=0.5•x-2

Answers

Answer:

0.5

Step-by-step explanation:

rate of change is just a synonym for slope and the equation for slope is y=mx +b where m is the slope so 0.5=m and if m= slope then 0.5=slope=rate of change :)

Help 15 points!!
A central angle of a circle of diameter 6 cm measures 86°. What is the length of the intercepted arc?
A)
2.8 cm
B)
4.5 cm
C)
5.1 cm
D)
9 cm

Answers

Answer:

B)

4.5 cm

Step-by-step explanation:

The formula for arc length when our central angle is in degrees =

2πr(θ/360)

θ = 86°

Diameter = 6cm Radius = Diameter /2

Radius = 6cm/2 = 3cm

Hence,

Intercepted arc length = 2 × π × 3 (86/360)

= 2 × π × 3 × 0.2388888889

= 4.5029494701 cm

Approximately = 4.5 cm

Option B is the correct answer

PLEASE HELP WILL GIVE BRAINLIEST!
A dart board contains 20 equal sized sectors numbered 1 to 20. A dart is randomly tossed at the board 10 times. what is the probability that the dart lands in sector 20 exactly 5 times?

Answers

Answer:

1/2

Step-by-step explanation:

There are a total of 20 sections on the board. And a dart hit that the section labeled 20 a total of 5 times, throwing a total of 10 darts. So, if you take these two numbers and and put them into the fraction: 5/10 and then simplify it you will get 1/2. Hope this helps.

Answer:

It's 6.09 x 10^-5.

Step-by-step explanation:

These other answers did not pay attention in school.

Classify the triangle based on its sides

Answers

It is an equilateral triangle

If you are helped with my answer pls tag me brianliest

I really want it

THANK YOU........

Suppose y varies directly with x, and y = 14 when x = 2. What direct variation equation relates x and y? What is the value of y when x = 6? Explain. Show your work

A. The equation y = 2x relates x and y. When x = 6, y =2(6) or 12.
B. The equation y = 14x relates x and y. When x = 6, y =14(6) or 84.
C. The equation y = 7x relates x and y. When x = 6, y =7(6) or 42.

Answers

Answer: C. The equation y = 7x relates x and y. When x = 6, y =7(6) or 42.

Step-by-step explanation:

Using direct variation with the formula:

y = kx

Since y =14, when x = 2.

y = kx

14 = 2k

k = 14/2

k = 7

Therefore, y = 7x

The value of y when x = 6 will be:

y = kx

y = 6k

Recall that k = 7

y = 6 × 7

y = 42

Therefore, the equation y = 7x relates x and y. When x = 6, y =7(6) or 42.

The proportional relationship between the distance driven and the amount of time driving is shown in the
following graph.
Which statements about the graph are true ?
A. The y- coordinate of point A represents the distance driven in 4 hours.
B. The distance driven in 1 hour is 80 km
C. None of the above

Answers

The distance driven in 1 hour is 80 km. Therefore, option B is the correct answer.

The given time graph shows the proportional relationship between the distance driven and the amount of time driving.

What is a distance-time graph?

If an object moves along a straight line, the distance travelled can be represented by a distance-time graph. In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.

From the graph, we can see that object A moved 400 km in 5 hours time.

So, in 1 hour the distance travelled by object =400/5=80 km

Therefore, option B is the correct answer.

To learn more about the distance-time graph visit:

https://brainly.com/question/1378025.

#SPJ5

HELP ASAP!! Which of the following will result in an irrational number? Select all that apply.
A. -√3 +2
B. √2*√3
C. √27*√ 3
D. 3√7 + 2√7-5√7

Answers

Answer:

A and B.

Step-by-step explanation:

The irrational number are -√3 +2  and √2 x √3.

What is Irrational Number?

Any number that cannot be stated as a fraction for any integers is considered to be irrational. The decimal expansions of irrational numbers are neither periodic nor do they come to an end. Every number that is transcendental is illogical.

Given:

A) -√3 +2 is an irrational number.

B) √2 x √3 = √6, which is an irrational number.

C) √27 x √ 3

= 3√3 x √3

= 3 x 3

= 9, which is a rational number.

D)  3√7 + 2√7-5√7

= 5√7- 5√7

= 0, which is a rational number.

Learn more about irrational number here:

https://brainly.com/question/17450097

#SPJ2

the heights of the peach trees in an orchard are normally distributed with a mean of 12.5 feet and a standard deviation of 1.8 feet.
what is the height of a peach tree with a z-score of -0.5?

Enter your answer rounded to the nearest tenth, in the box.

Answers

Answer:

i think 1.8 not sure tho

Answer:

Z-score Formula: z = (x - μ)/σ

Plug in: -0.5 = (x - 12.5)/1.8

Solve: -0.5 * 1.8 = x - 12.5

-0.9 = x - 12.5

-0.9 + 12.5

x = 11.6

Therefore, the height of a peach tree with a z-score of -0.5 is 11.6 feet.

ABCD is a trapizoid of bases [AB] and [DC], M and N are the midpoint of [AD] and [BC] if DC=11cm and MN=9cm then AB=

Answers

Answer:

[tex]AB = 7[/tex]

Step-by-step explanation:

Given

[tex]DC = 11[/tex]

[tex]MN = 9[/tex]

Required

Find AB

Since MN is the midpoint, then:

[tex]MN = \frac{1}{2}(AB + DC)[/tex]

[tex]9 = \frac{1}{2}(AB + 11)[/tex]

Multiply by 2

[tex]2 * 9 = \frac{1}{2}(AB + 11)*2[/tex]

[tex]18 = AB + 11[/tex]

[tex]AB = 18 - 11[/tex]

[tex]AB = 7[/tex]

Help please and Thanks :))

Answers

Creating a government based on religious

What value of x makes x - 10 = -5 true?
-5
15
5
-15​

Answers

Answer:

5

Step-by-step explanation:

x - 10 = -5

+ 10. +10

x = 5

hope this helps

He base rate for a state's workers compensation insurance for a service station attendant is $5.12 per $100.00 paid in wages the payroll for scott park service station for march is 5,784.00. What is the monthly premium for workers compensation insurance?

Answers

Answer:

$2961.41

Step-by-step explanation:

Base rate for a state workers compensation insurance = $5,12 per $100 paid in wages

Scott park payroll for march = $5784 ( inclusive of insurance payment )

Determine the monthly premium for insurance

$5.12 = $100

First; calculate how many $100 are in $5784

 = 5784 / 100 = 578.4

Hence the monthly premium for workers compensation insurance

= $5.12 * 578.4

= $2961.41

Other Questions
TRUE/FALSE. a major environmental problem caused by using the agricultural practice of tilling is responses eutrophication from excessive fertilizer use eutrophication from excessive fertilizer use ozone depletion from fossil fuel use ozone depletion from fossil fuel use intercropping by traditional farmers intercropping by traditional farmers compaction of soil from adding compost What does the pig symbolize? Enterprise systems improve management decision making in all the following ways except: Select one: A. determining the profitability of products. B. providing more accurate sales and production forecasts. C. improving forecasts of consumer behavior. D. providing up-to-the-minute data on sales, inventory and production. E. implementing standard definitions and formats worldwide. What is SSS rule in maths? What element is located on the left side of the table? Conjugate the following verbs in the Present Tense1. Hablar2. Ir3. Estar4. Volver5. Regresar6. bailar7. vivir8. comer9. escribir how did spain respond to french interest in extending their lands past the mississippi river valley in the early 1700s?a.by controlling the Gulf of Mexico with missions along the coast b.by building missions in western Louisiana c.by establishing missions in East Texas d.by opening missions closer to the Rio Grande in the u.s., public opinion most strongly favors which of the following in dealing with delinquent juveniles? Match each type of government to its description. Tiles theocracy oligarchy direct democracy autocracy representative democracy democracy Pairs rule by a few people or a small group arrowBoth rule by one person arrowBoth rule by many people arrowBoth rule by religious authorities arrowBoth type of democracy where eligible citizens vote on issues themselves arrowBoth type of democracy where eligible citizens vote for leaders who will rule on their behalf arrowBoth Why did my monthly mortgage payment decrease? Kelly is fond of pebbles, during summer, her favorite past-time is to cellect peblles of the same shape and size A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10.50, and tickets cost $32.50 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park. Negative expectations about the course of illness has no impact on the course of hiv infection and disease.a. Trueb. False how can i run my car heater at maximum setting to cool down the engine if the car is overheated and the engine is stalled and just cranks without starting? What are the coefficients when the following equations are balanced? sb o2 --> sb4o6 h2s cl2 --> s8 hcl What is the process of splitting light called? 1.List the groups of reptiles that are mentioned in the text. Which group is the smallest? a seizure action plan includes only a students seizure type and basic first aid. T/F barry's bbq had sales revenue for the year of $250 million and net income of $90 million. total assets were $70 million at the beginning of the year, and $80 million at the end of the year. calculate barry's return on assets, profit margin, and asset turnover ratios. (do not round intermediate calculations. round your answers to 1 decimal place.) Check that 12g is equivalent to 48%.