Compute the derivative dy/dx using the power, product, and chain rules. Given
x³ + y³ = 11xy
differentiate both sides with respect to x to get
3x² + 3y² dy/dx = 11y + 11x dy/dx
Solve for dy/dx :
(3y² - 11x) dy/dx = 11y - 3x²
dy/dx = (11y - 3x²)/(3y² - 11x)
The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when
11y - 3x² = 0
or
y = 3/11 x²
(provided that 3y² - 11x ≠ 0)
Substitute y into into the original equation:
x³ + (3/11 x²)³ = 11x (3/11 x²)
x³ + (3/11)³ x⁶ = 3x³
(3/11)³ x⁶ - 2x³ = 0
x³ ((3/11)³ x³ - 2) = 0
One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with
(3/11)³ x³ - 2 = 0
(3/11 x)³ - 2 = 0
(3/11 x)³ = 2
3/11 x = ³√2
x = (11•³√2)/3
Solving for y gives
y = 3/11 x²
y = 3/11 ((11•³√2)/3)²
y = (11•³√4)/3
So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).
Answer:
Rational.
Step-by-step explanation:
1.666... can be expressed as 
.
Hence it is rational.
Answer:
250 is the answers for the question
Step-by-step explanation:
please give me brainlest
The fourth class ends at 12:30 pm
<em><u>Solution:</u></em>
Given that Harold has 4 classes each morning
Each class is 1 hour long, and there are 10 minutes between classes
The first class is at 8 A.M
<em><u>To find: Time at which fourth class ends</u></em>
Since each is 1 hour long and 10 minutes gap between classes
First class = 8 A.M to 9 A.M
Second class = 9:10 A.M to 10 : 10 AM
Third class = 10 : 20 AM to 11 : 20 AM
Fourth class = 11 : 30 AM to 12 : 30 PM
Thus the fourth class ends at 12:30 pm
If the insurance pays $2,000, but the test itself cost $2,750, you simply subtract.
$2,750-$2,000= $750
Therefore Bobby has to pay $750
