Three neighbors plan to complete fencing projects this spring. as shown in the diagrams below, neighbor a plans to fence in his rectangular backyard with a 6-foot tall wooden privacy fence. neighbor b plans to construct a circular chain link fence around his pool. and, neighbor c is putting a vinyl fence around three side of his front yard. note: diagrams are not drawn to scale. intended fences are marked with a dashed line.
neighbor a can put up three 8 foot sections of wood fencing in two hours.
neighbor b can put up 15 feet of chain link fencing each hour.
neighbor c can put up 1 yard of vinyl fencing in half an hour.
which neighbor's fencing project will take the least amount of time to complete?
which neighbor's fencing project will take the most amount of time to complete?

- the neighbor's fencing project that will take the least amount of time to complete is: neighbor's a fencing project.

- the neighbor's fencing project that will take the most amount of time to complete is: neighbor's c fencing project..

step-by-step explanation:

to calculate the amount of fence that neighbor a has to put up, you need to add the following distances:

convert yards to feet (remember that :

you know that neighbor a can put up three 8 foot sections of wood fencing in two hours. for this fence, the number of sections will be:

≈17

then, the time that this neighbor's fencing project will take is:

  to calculate the amount of fence that neighbor b has to put up, you need to use the formula for calculate the circumference of a circle:

where r is the radius.

in this case, the radius is:

substituting, you get:

≈126 feet

you know that neighbor b can put up 15 feet of chain link fencing each hour. then, the time that this neighbor's fencing project will take is:

to calculate the amount of fence that neighbor c has to put up, you need to add the following distances:

  convert feet to yards (remember that :

you know that neighbor c can put up 1 yard of vinyl fencing in half an hour.   then, the time that this neighbor's fencing project will take is:

therefore, the neighbor's fencing project that will take the least amount of time to complete is: neighbor's a fencing project.

the neighbor's fencing project that will take the most amount of time to complete is: neighbor's c fencing project.

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)