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3 years ago

Choose Yes or No to tell whether each rate is a unit rate, 1/ 1/3 , 2/3 / 1 , 2/3 , 3/1

Mathematics

1 answer:

yan [13]3 years ago

5 0

Answer:

Unit rate is literally 1/x.

Step-by-step explanation:

U can figure out the rest!

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Answer:

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Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

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$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

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By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

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Volume of a cylinder,

$V=\pi r^2 h$

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$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

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Choose Yes or No to tell whether each rate is a unit rate, 1/ 1/3 , 2/3 / 1 , 2/3 , 3/1​

Choose Yes or No to tell whether each rate is a unit rate, 1/ 1/3 , 2/3 / 1 , 2/3 , 3/1