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:
<em>Your Interquartile range (IQR) would be 19.</em>
Step-by-step explanation:
-5, 1, 3, 7, 8, 10, 32, 36
Median: 7.5
Lower quartile: 2
Upper quartile: 21
Interquartile range: 21 - 2 = 19
We are given intersecting lines. The measures of a pair of angles forming vertex angles, are 2x+6° and 96°.
The measure of 2 vertex angles is equal, so we solve the equation:
2x+6°=96°, subtract 6° from both sides of the equation
2x=90°, divide both sides of the equation by 2
x=45°
Answer:
v = 6
Step-by-step explanation:
Solve for v:
-8 (8 v + 1) - 2 = -394
-8 (8 v + 1) = -64 v - 8:
-64 v - 8 - 2 = -394
Grouping like terms, -64 v - 8 - 2 = -64 v + (-8 - 2):
-64 v + (-8 - 2) = -394
-8 - 2 = -10:
-10 - 64 v = -394
Add 10 to both sides:
(10 - 10) - 64 v = 10 - 394
10 - 10 = 0:
-64 v = 10 - 394
10 - 394 = -384:
-64 v = -384
Divide both sides of -64 v = -384 by -64:
(-64 v)/(-64) = (-384)/(-64)
(-64)/(-64) = 1:
v = (-384)/(-64)
The gcd of -384 and -64 is -64, so (-384)/(-64) = (-64×6)/(-64×1) = (-64)/(-64)×6 = 6:
Answer: v = 6
Answer:
2w-5 > (with an underline that means more than or equal to) 18
Step-by-step explanation:
