Ten people can dig five holes in three hours. if n people digging at the same rate dig m holes in d hours: 1.is n proportional to m when d=3? 2.is n proportional to d when m=5? 3.is m proportional to d when n=10?

First. get the unit rate. That is, transform "Ten people can dig five holes in three hours" into "One person digs one holes in one hour."

We can say that

(that's still for 10 people). For 1 person this rate will be 1/10th of the above, so:

So the unit rate is 5/30. We can now set up an equation expressing the number of holes "m" dug up by "n" people in "d" hours:

which is clearly linear in n and d.

Now we can answer the questions:

(1) Is n proportional to m when d=3? Yes

which shows that n is proportional to m in this case.

(2) Is n proportional to d when m=5? No

There is an inverse proportionality, therefore this is not proportional.

(3) Is m proportional to d when n=10? Yes

There is a proportional relationship between m and d.

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

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.