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kvv77 [185]
3 years ago
5

Solve : |3x-1/2| < 1 1/2

Mathematics
1 answer:
zysi [14]3 years ago
3 0

Answer:

\:0<x<\frac{1}{3}\:

Step-by-step explanation:

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Find the cordinates of point A.
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A=(1,4) B=(-3,4) C=(-3,-1)

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Find a point on the curve x^3+y^3=11xy other than the origin at which the tangent line is horizontal.
attashe74 [19]

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).

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2 years ago
____ property allows you to regroup terms using parentheses when adding or multiplying, without changing the answer
Alchen [17]
Commutative property
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3 years ago
Read 2 more answers
Solve the equation x³ − 5 = 59
In-s [12.5K]

Answer:

4 = x

Step-by-step explanation:

x³ - 5 = 59     Add five to both sides of the equation.

x³ = 64          Now find the cubed root of 64

∛64 = 4

x = 4

3 0
4 years ago
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