Aheptagon has unequal sides that are in a pattern. each side is 2 more than twice the side of the smaller one before it. write the expression of the perimeter.

Heptagon has unequal sides and each side is 2 more than twice the side of the smaller one before it.

Heptagon is a 2 dimensional geometric shape that has got 7 sides.

Lets say the length of smallest side is 'x' units.

Length of the second side will be 2 more than twice the smaller side so the side length will be:

Now the length of the third side will be 2 more than twice the second side that is:

Similarly, length of the fourth side will be:

Similarly, length of the fifth side will be:

Again, length of the sixth side will be

And the length of the seventh side will be

Now, perimeter of any geometric shape is the sum of the lengths of the sides:

Adding all the sides we get:

Therefore, the expression for the perimeter of the required heptagon is .

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.