Write the equation of the line that is parallel to y = 9x+ 4 and crosses the y-axis at -3.

9514 1404 393

  y = 9x -3

Step-by-step explanation:

The given line is in "slope-intercept form"

  y = mx + b

where m is the slope and b is the y-intercept (where it crosses the y-axis).

In your given line, we have ...

  m = 9, b = 4

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A parallel line will have the same slope, so we know that the line you want has m = 9. You are told to make the line cross the y-axis at -3, so that makes b = -3. Putting these values into the slope-intercept form gives the desired equation:

  y = 9x -3

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The attached graph is intended to show the lines are parallel and the equation given here meets the requirement for a crossing of the y-axis at -3. The vertical and horizontal scales are different in order to better show these things.

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.