Fiona solved the equation shown. – StartFraction 5 Over 3 EndFraction v plus 4 equals 8 minus StartFraction 1 Over 3 EndFraction v.(6x – 3) = –
A table titled Fiona's Solution with 3 columns and 5 rows. The first row is, blank, Steps, Resulting equation. The second row has the entries, 1, Use the distributive property to simplify. StartFraction one-half minus 2 x plus 1 equals negative StartFraction 13 Over 2 EndFraction. The third row has the entries, 2, blank, StartFraction 3 Over 2 minus 2 x equals negative StartFraction 13 Over 2 EndFraction. The fourth row has the entries, 3, Isolate the variable expression by using the addition property of equality, negative 2 x equals negative 8. The fifth row has the entries, 4, Isolate the variable by using the division property of equality, x equals 4.
What is the missing step of her solution?

Simplify by combining like terms.
Simplify by using addition property of equality.
Simplify by using the multiplication property of equality.
Simplify by using the division property of equality.

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.

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step-by-step explanation: