The curve with equation y=8x^2+2/x has one turning point. Find the coordinates of this turning point.

Coordinates of turning point is (½, 6)

Step-by-step explanation:

We are given the equation of the curve as;

y = 8x² + (2/x)

At turning point, dy/dx = 0

Thus;

dy/dx = 16x - 2/x²

At dy/dx = 0, we have;

16x - 2/x² = 0

Rearrange to get;

16x = 2/x²

Multiply both sides by x² to get;

16x³ = 2

x³ = 2/16

x³ = 1/8

x = ∛(⅛)

x = ½

At x = ½, we have;

y = 8(½)² + (2/½) = 2 + 4 = 6

Thus, coordinates of turning point is (½, 6)

his chances of getting a coin of higher value is 4/19

step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .