CAT Exam > CAT Questions > For any point, in the first quadrant, on the ...
Start Learning for Free
For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6 ?
- a)39
- b)312
- c)310
- d)311
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
For any point, in the first quadrant, on the line 4x + 9y = 36, what i...
4x + 9y = 36
Both x and y are positive in the first quadrant ⇒ AM ≥ GM inequality holds true.
Both x and y are positive in the first quadrant ⇒ AM ≥ GM inequality holds true.
Free Test
FREE
| Start Free Test |
Community Answer
For any point, in the first quadrant, on the line 4x + 9y = 36, what i...
Problem:
For any point in the first quadrant on the line 4x + 9y = 36, what is the maximum value of x^6 * y^6?
Solution:
To find the maximum value of x^6 * y^6, we need to find the maximum value of x and y on the given line. Let's solve the equation 4x + 9y = 36 for y in terms of x.
4x + 9y = 36
9y = 36 - 4x
y = (36 - 4x)/9
Maximizing x:
To maximize x, we need to find the x-coordinate of the point where the line intersects the x-axis. When y = 0, we have:
y = (36 - 4x)/9
0 = (36 - 4x)/9
36 - 4x = 0
4x = 36
x = 9
So, the maximum value of x on the line is 9.
Maximizing y:
To maximize y, we need to find the y-coordinate of the point where the line intersects the y-axis. When x = 0, we have:
y = (36 - 4x)/9
y = (36 - 4(0))/9
y = 36/9
y = 4
So, the maximum value of y on the line is 4.
Calculating x^6 * y^6:
Now that we have the maximum values of x and y, let's calculate x^6 * y^6:
x^6 = 9^6 = 531441
y^6 = 4^6 = 4096
x^6 * y^6 = 531441 * 4096 = 2176782336
Therefore, the maximum value of x^6 * y^6 is 2176782336, which corresponds to option B.
For any point in the first quadrant on the line 4x + 9y = 36, what is the maximum value of x^6 * y^6?
Solution:
To find the maximum value of x^6 * y^6, we need to find the maximum value of x and y on the given line. Let's solve the equation 4x + 9y = 36 for y in terms of x.
4x + 9y = 36
9y = 36 - 4x
y = (36 - 4x)/9
Maximizing x:
To maximize x, we need to find the x-coordinate of the point where the line intersects the x-axis. When y = 0, we have:
y = (36 - 4x)/9
0 = (36 - 4x)/9
36 - 4x = 0
4x = 36
x = 9
So, the maximum value of x on the line is 9.
Maximizing y:
To maximize y, we need to find the y-coordinate of the point where the line intersects the y-axis. When x = 0, we have:
y = (36 - 4x)/9
y = (36 - 4(0))/9
y = 36/9
y = 4
So, the maximum value of y on the line is 4.
Calculating x^6 * y^6:
Now that we have the maximum values of x and y, let's calculate x^6 * y^6:
x^6 = 9^6 = 531441
y^6 = 4^6 = 4096
x^6 * y^6 = 531441 * 4096 = 2176782336
Therefore, the maximum value of x^6 * y^6 is 2176782336, which corresponds to option B.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer?
Question Description
For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer?.
For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer?.
Solutions for For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer?, a detailed solution for For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice For any point, in the first quadrant, on the line 4x + 9y = 36, what is the maximum value of x6 * y6?a)39b)312c)310d)311Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup