Me with this problem
dasha has 4 times more rose bushes in her garden than anna. after 39 rose bushes were replanted into anna's garden, the number of bushes in both gardens became the same. how many rose bushes did dasha's have originally?

Dasha has 52 roses

Step-by-step explanation:

Rewrite the first sentence in an equation: (D= Dasha) (A= Anna)

D=4A

Rewrite the second sentence in an equation:

A+39=D

1) Substitute A+39 as D in the first equation:

A+39=4A

2) Subtract A from both sides:

3A=39

3) Divide both sides by 3:

A=13

4) Now substitute 13 as A in the second equation:

13+39=D

5) Solve:

D=52

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.