1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aleks04 [339]
2 years ago
5

If x^2+y^2=1, what is the largest possible value of |x|+|y|?

Mathematics
1 answer:
Marianna [84]2 years ago
6 0

If <em>x</em>² + <em>y</em>² = 1, then <em>y</em> = ±√(1 - <em>x</em>²).

Let <em>f(x)</em> = |<em>x</em>| + |±√(1 - <em>x</em>²)| = |<em>x</em>| + √(1 - <em>x</em>²).

If <em>x</em> < 0, we have |<em>x</em>| = -<em>x</em> ; otherwise, if <em>x</em> ≥ 0, then |<em>x</em>| = <em>x</em>.

• Case 1: suppose <em>x</em> < 0. Then

<em>f(x)</em> = -<em>x</em> + √(1 - <em>x</em>²)

<em>f'(x)</em> = -1 - <em>x</em>/√(1 - <em>x</em>²) = 0   →   <em>x</em> = -1/√2   →   <em>y</em> = ±1/√2

• Case 2: suppose <em>x</em> ≥ 0. Then

<em>f(x)</em> = <em>x</em> + √(1 - <em>x</em>²)

<em>f'(x)</em> = 1 - <em>x</em>/√(1 - <em>x</em>²) = 0   →   <em>x</em> = 1/√2   →   <em>y</em> = ±1/√2

In either case, |<em>x</em>| = |<em>y</em>| = 1/√2, so the maximum value of their sum is 2/√2 = √2.

You might be interested in
I need help plz will give brainliest!!!
Leokris [45]

Answer:

18 red marbles

Step-by-step explanation:

Because the ratio of yellow marbles to red marbles is 1:6 in the population, the expected number of red marbles is 6 times the number of yellow marbles in the representative sample. there should be 18 red marbles.

7 0
3 years ago
Which answer choice shows the correct way to write the phrase?
timurjin [86]

Answer:

y + 1

Step-by-step explanation:

if y = the total balls

then y + 1 = total balls plus 1

8 0
2 years ago
What is the total area of the figure below?
Gnesinka [82]

Answer:

141 square inches

Step-by-step explanation:

Area of a triangle: Base*Height*1/2

Area of a trapezoid: Height * (Base1 +Base2) / 2

Triangle Base = 6

Triangle Height = 8

6*8*1/2 = 24 square inches

Trapezoid Height = 9

Trapezoid Base1 = 16

Trapezoid Base2 = 10

9*(16+10) / 2 = 117 square inches

Total = Area of triangle + Area of trapezoid

Total = 24 + 117 = 141 square inches

3 0
2 years ago
What is the formulaa to fund % of selling overheads(Tender sheet)​
Lina20 [59]
I might not know the answer to this question but I hope you find one
4 0
3 years ago
What is 23579 in word form?<br> Please helppppp
lions [1.4K]

Answer:

Twenty-three thousand five hundred seventy-nine

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • I need to know how to set up the problem on number 8.
    13·1 answer
  • Find the distance between -10.5 and 7 on a number line (geometry)
    8·2 answers
  • Each of the four sides of a swimming pool measures 12 meters. The pool is 6 meters deep. How much water will be needed to fill i
    6·2 answers
  • Explain the error Tina says that 6:8 is equivalent to 36:64 what did tina do wrong
    12·2 answers
  • Can someone help me with this plz I don’t know how to complete the ratio chart
    10·1 answer
  • What is the average rate of change over the interval (-1, 5)​
    14·1 answer
  • Find an angle between 0 and 2π that is coterminal with 10pi/3
    6·1 answer
  • Someone works in a grocery store and earns $7.20 per hour. The store will pay them an extra 5% per hour if she works on Saturday
    10·1 answer
  • Jenny wants to build a concrete patio that will be 8 meters by 11 meters
    9·2 answers
  • Given that
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!