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Serjik [45]
3 years ago
10

Can you solve 4 .b)​

Mathematics
1 answer:
saul85 [17]3 years ago
8 0

Answer:

yhyhyhyh rashford gonna score a hat trick vs spurs

Step-by-step explanation:

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The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi
storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

V = \frac{1}{3}\pi r^{2}h

Differentiate the equation with respect to time t, such that

\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)

\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)

To differentiate the product,

Let r² = u, so that

\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)

Then, using product rule

\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]

Since u = r^{2}

Then, \frac{du}{dr} = 2r

Using the Chain's rule

\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}

∴ \frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]

Then,

\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]

Now,

From the question

\frac{dr}{dt} = 7 m/min

\frac{dV}{dt} = 236 m^{3}/min

At the instant when r = 99 m

and V = 180 m^{3}

We will determine the value of h, using

V = \frac{1}{3}\pi r^{2}h

180 = \frac{1}{3}\pi (99)^{2}h

180 \times 3 = 9801\pi h

h =\frac{540}{9801\pi }

h =\frac{20}{363\pi }

Now, Putting the parameters into the equation

\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]

236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]

236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]

708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}

708 = 30790.75 \frac{dh}{dt} + 76.36

708 - 76.36 = 30790.75\frac{dh}{dt}

631.64 = 30790.75\frac{dh}{dt}

\frac{dh}{dt}= \frac{631.64}{30790.75}

\frac{dh}{dt} = 0.021 m/min

Hence, the rate of change of the height is 0.021 meters per minute.

3 0
3 years ago
Please help ....this is due tomorrow
marshall27 [118]

A) 0.15 times $2,570 = $412.50

B) $122.85 times 2( 12 ) = $2,948.40

C) $2,570

D) All together it's  $2,948.40 + $2,570 = $5,518.40

For D I didn't add the down payment because it's not an additional charge.

I only did the first one because I don't know if you want me to finish the rest.

Hope I helped :)

5 0
3 years ago
Plz help MATH HW<br>explain/answer
Misha Larkins [42]

No because the sum could also be irrational number which for example it could be square root of 9 or 49

       Hope this helps answer your question

6 0
3 years ago
I am having trouble with converges and diverges<br>​
inna [77]

Answer:

d. converges, -25

Step-by-step explanation:

An infinite geometric series converges if the absolute value of the common ratio is less than 1.

Here, the common ratio is 4/5:

| 4/5 | = 4/5 < 1

So the series converges.  The sum of an infinite geometric series is:

S = a₁ / (1 − r)

where a₁ is the first term and r is the common ratio.

Here, a₁ = -5 and r = 4/5:

S = -5 / (1 − 4/5)

S = -25

5 0
3 years ago
Solve for e.<br> 9e + 4 = -5e + 14 + 13e
Snezhnost [94]

Answer:

17e+18

Step-by-step explanation:

9e+4=-5e+14+13e

4e+4+14+13e

17e+4+14

17e+18

4 0
2 years ago
Read 2 more answers
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