A triangle pattern is shown below. Three images are shown of a triangle pattern. Three images are shown of a triangle pattern. The first image shows one isosceles triangle. The base is labeled 5 and the other two sides are labeled 7. The second image shows two adjacent isosceles triangles. The original triangle is there, and now another upside down triangle is adjacent to it. Both triangles are the same size, with bases labeled 5 and the other two sides labeled 7. The third image shows three adjacent isosceles triangles. The two triangles from the second image are there, and now another right side up triangle is adjacent to the upside down one. All three triangles are the same size, with bases labeled 5 and the other two sides labeled 7. The perimeter of each figure in the pattern is shown in the table below.

Figure Perimeter
1 triangle | 19
2 triangles | 24
3 triangles | 29

Which equation relates the number of triangles in the figure (n) to the perimeter of the figure (P)?

A. P = 5n + 7

B. P = 5n + 14

C. P = 7n + 10

D. P = 7n + 5

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.

9987

step-by-step explanation:

i think the answer would be c

is there supposed to be a diagram or a graph for this one? ?

step-by-step explanation: