A circular garden has a circumference of 21 pi yards. Lars is digging a straight line along across the garden at a rate of 7 yards per hour. How many hours will it take to dig across
the garden?

He took 3 hours to dig across the garden

Step-by-step explanation: First of all, we calculate the radius of the circular garden. Digging across the garden simply means drawing a line from end to end along the middle of the garden (in other words, the diameter).

The circumference has been given as 21pi. If the circumference is calculated as

Circumference = 2Pi x r, then

21Pi = 2Pi x r

By cross multiplication we now have

(21Pi/2Pi) = r

21/2 = r

10.5 = r

If the radius has been identified as 10.5 yards, then the diameter can be derived as radius times 2

Diameter = 10.5 x 2

Diameter = 21 yards

However, he is digging at a rate of 7 yards per hour, which means by the time he has dug 21 yards he has spent;

7 yds = 1 hr

(7 x 3 = 21 yds) = 1 x 3 hrs

21 yds = 1 x 3 hrs

21 yds = 3 hrs

Therefore he took 3 hours to dig across the garden.

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the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is