A farmer has 4 times as many ducks as chickens. There are 72 more chickens than ducks. How many chickens and ducks does the farmer have altogether?

The farmer has 120 birds altogether

Step-by-step explanation:

Now, since the number of chickens us equal to 4 times the number of ducks, it means that if there are 2 ducks, there are (2 × 4) chickens and if there are 5 ducks in the farm, there are (5 × 4) chickens.

Let's then denote the number of ducks by "b". So, if the number of chickens is equal to 4 times the number of ducks, then the total quantity of birds belonging to the farmer

= 4b + b

If there are 72 more chickens than ducks, the quantity of birds is:

4b - b = 72

3b = 72

b = 72/3

b = 24 ducks

Since 4b represents the quantity of chickens and b is equal to 24, then the actual quantity of chickens = 4 × 24 = 96.

Therefore, if there are 96 chickens and 24 ducks in the farm, then the actual sum of the birds belonging to the farmer is:

96 + 24

= 120 birds

The farmer has 120 birds altogether.

42.4

step-by-step explanation:

convert to decimal

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.