Three friends are cutting a length of rope to put up a tire swing. Bill needs a small piece to connect to the tire. Amy needs a piece half as long as Bill's to secure it when it's not in use. Carmen needs 5 times as much rope as Bill to climb up and connect to the branch. Write and solve an equation to find what length of rope each friend needs.

If 6.5x meters of rope is needed, Bill needs x meters of rope, Amy needs 0.5x meters of rope and Carmen needs 5x meters of rope.

Step-by-step explanation:

Step 1:

Assume Bill needs x meters of rope, Amy needs y meters of rope, and Carmen needs z meters of rope.

Amy needs a piece half as long as Bill's and Carmen needs 5 times as much rope as Bill.

So we have and

Step 2:

So the total rope needed

So if x = 1, x = 1 meter, y = 0.5 meters, z = 5 meters, a total of 6.5 meters of rope.

So if x = 2, x = 2 meter, y = 1 meters, z = 10 meters, a total of 13 meters of rope.

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation: