Irina ate some candies on Monday. On Tuesday, she ate twice as many candies as she did on Monday. On Wednesday, she ate a third as many candies as she did on Tuesday. On Thursday, she ate five more candies than she did on Wednesday. On Friday, she ate two fewer candies than she did on Thursday. If she ate the same number of candies on Friday as she did on Monday, how many did she eat on Tuesday?

10 candies on

Step-by-step explanation:

On Monday, Irina ate some candies. ( let it be )

On Tuesday, she ate twice as many as she did on Monday, ( )

On Wednesday, she ate a third as many as she did on Tuesday means,

=

On Thursday, she ate five more than she did on Wednesday means

On Friday, she ate two fewer candies than she did on Thursday means

She ate the same number of candies on Friday as she did on Monday which is given means,

By subtracting both side by

By cross multiplication:

By dividing both sides by 3

On Tuesday, she ate twice as many as she did on Monday, ( ) =

Therefore, Irina ate 10 candies on Tuesday.                    

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.

the weight of the object inside the box!