What is the slope of a line perpendicular to the line whose equation is 10x - 12y = -24. Fully reduce your answer.

The slope of the line perpendicular to the line whose equation is

10x - 12y = -24 is - 6 / 5

The slope intercept form is represented as follows;

y = mx + b

where

m = slope

b = y-intercept

Therefore,

10x  - 12y = -24

10x + 24 = 12y

12y = 10x + 24

divide through by 12

12y / 12 = 10 / 12 x + 24 / 12

y = 5 / 6 x + 2

The slope of this equation is 5/6.

For a line perpendicular to another line the product of there slope is negative 1. Therefore,

m₁m₂ = -1

m₁ 5/6 = -1

m₁ = - 6 / 5

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The slope of the perpendicular line is

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

∵ The equation of the given line is 10x - 12y = -24

→ We need to form this equation as the form above to find m

→ Subtract 10x from both sides

∵ 10x - 10x - 12y = -24 - 10x

∴ - 12y = -24 - 10x

→ Divide both sides by -12

∴

∴ y = 2 - () x

→ Remember that (-)(-) = (+)

∴ y = 2 + x

∵ y = m x + b

∴ m =  

∴ The slope of the given line is  

→ To find the slope of the perpendicular line reciprocal it and change

  its sign

∵ The reciprocal of    is  

→ Change its sign from + to -

∴ The slope of the perpendicular line is  

42

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.