A farmer can plow a given field in 11 hours. If his son helps him, they can plow the field together in 6 hours. How many hours would it take his son to plow the field alone? Express your answer as a fraction reduced to lowest terms, if needed.

13 1/5hours

Step-by-step explanation:

If the man can plough a given field in 11hours, this means the man can plough 1/11 of the same field in 1hour.

Let 1/x be the portion of the land the son can plough in 1 hour where x is the number of hours the son can plough the land alone.

If they can plough the field together in 6 hours, it means they can plough 1/6 portion of the field together in 1 hour.

Mathematically,

t/11+t/x = 1

Where t is the total time it takes them to plough the land together

Finding the LCM we have;

xt+11t/11x = 1

xt + 11t = 11x

If t = 6

6x +11(6) = 11x

66 = 11x -6x

66 = 5x

x = 66/5

x = 13 1/5hours

This means it will take the son 13 1/5hours to plough the land alone.

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.

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|