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:
20-gon
Step-by-step explanation:
First we start with the formula to find what the sum of angles will be if we know the number of sides.
S=(n-2)*180 where S is the sum of angles and n is the number of sides.
Normally you'd plug in n to find S, but you can do the opposite too.
3240=(n-2)*180
Let me know if you need help working it from here.
Answer:
Walt has 37 quarters. Hank has 33.
Step-by-step explanation:
Solve the given equation for q:
0.25q + 0.25q - 1.00 = 17.50
Simplify this, obtaining:
0.50q = 18.50
Simplifying this by multiplying both terms of this result by 100:
50 q = 1850
Thus, q = 1850/50 = 37
Walt has 37 quarters. Hank has 33.
Note that 37 + 33 = 70, and that 70($0.25) = $17.50. So our results are correct.
In case of plane, for y intercept, x and z are o .
So we will get
4(0)+5y-0=20
5y=20
Dividing both sides by 5
y = 4
So the y intercept is (0,4,0).
In second question, x intercept is 1, y intercept is -1 and z intercept is 2 .
So the correct option is the third equation , that is x-y+2z=4 .
Answer:
A. The grocery list the user input
Step-by-step explanation:
