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
11Alexandr11 [23.1K]
3 years ago
10

Find the greatest solution for x+y when x^2+y^2 = 7, x^3+y^3=10

Mathematics
1 answer:
damaskus [11]3 years ago
6 0

Answer:

4

Step-by-step explanation:

set

f(x,y)=x+y\\

constrain:

g(x,y)=x^2+y^2 = 7\\h(x,y)=x^3+y^3=10

Partial derivatives:

f_{x}=1\\f_{y} =1 \\g_{x}=2x \\g_{y}=2y\\h_{x}=3x^2 \\h_{y}=3y^2

Lagrange multiplier:

grad(f)=a*grad(g)+b*grad(h)\\

\left[\begin{array}{ccc}1\\1\end{array}\right]=a\left[\begin{array}{ccc}2x\\2y\end{array}\right]+b\left[\begin{array}{ccc}3x^2\\3y^2\end{array}\right]

4 equations:

1=2ax+3bx^2\\1=2ay+3by^2\\x^2+y^2=7\\x^3+y^3=10

By solving:

a=4/9\\b=-2/27\\x+y=4

Second mathod:

Solve for x^2+y^2 = 7, x^3+y^3=10 first:

x=\frac{1}{2} -\frac{\sqrt{13}}{2} \ or \ y=\frac{1}{2} +\frac{\sqrt{13}}{2} \\x=\frac{1}{2} +\frac{\sqrt{13}}{2} \ or \ y=\frac{1}{2} -\frac{\sqrt{13}}{2} \\x+y=-5\ or\ 1 \or\ 4

The maximum is 4

You might be interested in
.6 is ten times as much as
Triss [41]
.6 divided by 10 is .06 so .6 is 10 times more than .06
5 0
2 years ago
Read 2 more answers
A small bar of gold measure 40 mm by 25 mm. by 2 mm. Find the volume in cubic millimeters.
vladimir2022 [97]

Answer:

2000 mm^3* .0005oz/1mm^3=1oz

Step-by-step explanation:

v=40mm*25mm*2mm=2000mm^3

7 0
3 years ago
Read 2 more answers
I need help with this math problem
Alex17521 [72]

your answer is (1,3) but positive

6 0
2 years ago
What is the domain of the function y=_/x+6-7
bekas [8.4K]

Answer:

I hope this helps you

x+6>=0

x>= -6

please mark me brainliest

5 0
2 years ago
What is the GCF for 84 and 90
vivado [14]

Answer:

The GCF for 84 and 90 is 6.

Step-by-step explanation:

The factors of 84 are: 1, 2, 3, 4, <u>6</u>, 7, 12, 14, 21, 28, 42, 84

The factors of 90 are: 1, 2, 3, 5, <u>6</u>, 9, 10, 15, 18, 30, 45, 90

Then the greatest common factor is 6.

6 0
2 years ago
Read 2 more answers
Other questions:
  • How do you divide fractions?
    13·1 answer
  • Use the drop-down menus to complete the statements about the function p(x) = x(x - 1) + 1.
    7·1 answer
  • Which equation demonstrates the distributive property?
    7·2 answers
  • This is what I meant on my last question. sorry​
    11·1 answer
  • The machine bottled 8,000 bottles in 4 hours. if the rate of the machine were doubled, how long would it take the machine to bot
    14·1 answer
  • To arrive to his appointment on time, Mr. Jones had to drive all the way from his home with the average speed of 60 mph. Due to
    15·1 answer
  • What is the positive difference between the square of the sum of the first five positive integers and the sum of the first five
    12·1 answer
  • The assets division should contain what accounts
    7·1 answer
  • Twice a certain number minus 7 is equal to 5. What is the number.
    11·2 answers
  • Which of the following mixed numbers has the same decimal value as 110 147/168
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!