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MArishka [77]
3 years ago
9

Make b the subject of the formula

Formula1" title="k = \frac{brt}{v - b} " alt="k = \frac{brt}{v - b} " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
balu736 [363]3 years ago
5 0

Answer:

b = \frac{kv}{k+rt}

Step-by-step explanation:

Given

k = \frac{brt}{v-b} ← multiply both sides by (v - b)

k(v - b) = brt ← distribute left side

kv - kb = brt ( subtract brt from both sides )

kv - kb - brt = 0 ( subtract kv from both sides )

- kb - brt = - kv ( multiply through by - 1 to clear the negatives )

kb + brt = kv ← factor out b from each term on the left

b(k + rt ) = kv ← divide both sides by (k + rt )

b = \frac{kv}{k+rt}

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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}

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18 = r^2 + 3r

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

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

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∵ 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}

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Now,

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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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Divide both sides by 15.

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