Six members of the gymnastics team are going to have their picture taken. The two gymnasts, who are over 5 foot 5 inches, are going to be in the center with the remaining gymnasts on either side of them. How many different pictures can be taken assuming that the two tallest gymnasts will occupy the same position in all the photos

Total number of ways of arranging the total six positions = 18

Step-by-step explanation:

The total members in the team are six.

Six members means six positions. Out of these six positions, two positions are fixed and hence only 4 positions are available for arrangement.

Thus, the total number of ways of arranging the remaining four position are

4 * 4 = 16

Total number of ways of arranging the total six positions are

16 + 2 = 18

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.

positive

step-by-step explanation:

the quadrant is facing upwards