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zaharov [31]
3 years ago
5

Can somebody help me with this

Mathematics
1 answer:
bekas [8.4K]3 years ago
3 0

Answer:

8) 260 mm

9)? .............

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The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3
Alekssandra [29.7K]

Answer:

9\pi \text{ cubic meters per hour}

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,

If A= 36\pi\text{ square meters}, h = 3\text{ meters}

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

18 = r^2 + 3r

\implies r^2 + 3r - 18=0

r^2 + 6r - 3r - 18 = 0     ( by middle term splitting )

r(r+6)-3(r+6)=0

(r-3)(r+6)=0

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}

9\pi = (12\pi + 6\pi )\frac{dr}{dt}

9\pi = 18\pi \frac{dr}{dt}

\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}

Now,

Volume of a cylinder,

V=\pi r^2 h

Differentiating w. r. t. t,

\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}

6 0
3 years ago
Your work<br> START<br> f(x)=2x² – 12x-5
MrMuchimi

Answer:

range = (− 23 ,  ∞ )

domain = ( − ∞ ,  ∞ )

y-intercept = -5

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WILL GIVE A MEDAL HELP PLEASE FAST<br><br> FIND THE SLOPE
GREYUIT [131]
The slope here is -4
6 0
3 years ago
Read 2 more answers
The answer was 64cm
mamaluj [8]

Answer:

I'm guessing you want a word problem that answers this?

Step-by-step explanation:

The length of a rectangle is 8 cm more than 3 times its width.

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Cheyenne collects movies. She has 435 movies that are either comedy, scary, or sci-fi. She has the same number of videos for eac
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