Ty has 5 goats and 19 carrots. He gives each goat the same number of carrots, and he uses as many carrots as he can. How many carrots does Ty give each goat? How many carrots are left?

Each goat gets 3 carrots.

After giving 3 carrots to each of the goat, 4 carrots are left with Ty in total.

Step-by-step explanation:

Here, the total number of carrots  = 19

The total number of goats  = 5

So, in the given condition:

19 is the DIVIDEND

5 is the DIVISOR

Now, dividing 19 by 5, we get:

19  = 5 x 3 +  4

Here,  3 = Quotient

4 = Remainder

So, by the given equation. we can say that:

Each goat gets 3 carrots.

After giving 3 carrots to each of the goat, 4 carrots are left with Ty in total.

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.

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step-by-step explanation: