This summer, due to some renovations, a sports club has 105 members. The club's records indicate that this is 25% fewer members than it had last summer. How many members were there last summer?

140

Step-by-step explanation:

we know that this year the sports club has 25% less memeber, so if last year the members where 100% this year there are only 75%

and that 75% is equal to 105 members

we can represent the information that we are given in a table:

memebers       percentage

   105         ⇒        75%

since last summer there were the 100% of member we can represent the number of members from last summer with 'x', and the table now is:

memebers       percentage

   105         ⇒        75%

   x           ⇒        100%

and we use rule of three to solve this problem: multiply cross quantities (105 by 100) and divide by the remaining amount:

x = 105*100/75

x = 140

Last summer the sports club had 140 members

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stay and stay proud! " - zalgo

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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.