Share 720cm in the ratio 3:4:2:9

120 cm, 160 cm, 80 cm, 360 cm

Step-by-step explanation:

The ratio 3:4:2:9 is the same as the ratio 3x:4x:2x:9x

We add all the terms of the second ratio:

3x + 4x + 2x + 9x = 18x

18x = 720

x = 40

3x = 3(40) = 120

4x = 4(40) = 160

2x = 2(40) = 80

9x = 9(40) = 360

120 cm, 160 cm, 80 cm, 360 cm

The parabola has a horizontal tangent line at the point (2,4)

The parabola has a vertical tangent line at the point (1,5)

Step-by-step explanation:

Ir order to perform the implicit differentiation, you have to differentiate with respect to x. Then, you have to use the conditions for horizontal and vertical tangent lines.

-To obtain horizontal tangent lines, the condition is:

(The slope is zero)

--To obtain vertical tangent lines, the condition is:

(The slope is undefined, therefore the denominator is set to zero)

Derivating respect to x:

=

Solving for dy/dx:

Applying the first conditon (slope is zero)

Solving for y (Adding 2x+4, dividing by 2)

y=x+2 (I)

Replacing (I) in the given equation:

Replacing it in (I)

y=(2)+2

y=4

Therefore, the parabola has a horizontal tangent line at the point (2,4)

Applying the second condition (slope is undefined where denominator is zero)

2y-2x-8=0

Adding 2x+8 both sides and dividing by 2:

y=x+4(II)

Replacing (II) in the given equation:

Replacing it in (II)

y=1+4

y=5

The parabola has vertical tangent lines at the point (1,5)