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olya-2409 [2.1K]

2 years ago

12

Sarah is cutting a ribbon for a pep rally. The length of each ribbon needs to be 3.68 inches. If she needs 1000 ribbons what is

the length of the ribbon she needs

1 answer:

AURORKA [14]2 years ago

3 0

9514 1404 393

Answer:

3680 inches

Step-by-step explanation:

1000 × 3.68 inches = 3680 inches

Sarah needs 3680 inches of ribbon.

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You are situated 300 feet from the base of Tower Glitz Plaza watching an external elevator descend down the side of the building

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Answer:

18.66 ft/s

Step-by-step explanation:

The distance between you and the elevator is given by:

$h=\sqrt{x^2+y^2}$

The rate of change for the distance between you and the elevator is given by:

$\frac{dh}{dt}=\frac{dh}{dy}*\frac{dy}{dt}$

$-16=\frac{dh}{dy}*\frac{dy}{dt}$

$\frac{dh}{dy}=\frac{d}{dy} (\sqrt{x^2+y^2})\\$

Applying the chain rule:

$u=x^2+y^2\\\frac{dh}{dy}=\frac{d\sqrt u}{du} *\frac{du}{dy}\\\frac{dh}{dy}=\frac{1}{2\sqrt u} *2y\\\frac{dh}{dy}=\frac{y}{\sqrt {(x^2+y^2)}}$

Therefore, at x=300 and y = 500, dy/dt is:

$-16=\frac{y}{\sqrt {(x^2+y^2)}}*\frac{dy}{dt}\\-16=\frac{500}{\sqrt {(300^2+500^2)}}*\frac{dy}{dt}\\\frac{dy}{dt}=-18.66\ ft/s$

The elevator is descending at 18.66 ft/s.

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