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Ad libitum [116K]

3 years ago

6

Common factors of 56 and 70

1 answer:

Colt1911 [192]3 years ago

7 0

The common factors are 14,7,2,1

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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

Given the lease terms below, what is the total price of this car if you buy it

Deffense [45]

Answer:

Step-by-step explanation

APEX 28,272

3 0

3 years ago

Miguel e nádia trabalham num escritório de contabilidade. A cada 45 minutos miguel vai á sala de café para relaxar um pouco, enq

Kazeer [188]

Responder:

3 horas

Explicação passo a passo:

Dado :

Miguel a cada 45 minutos

Nádia a cada 60 minutos

Número de horas que eles vão se ver no mesmo lugar:

Para fazer isso ;

Obtenha o menor múltiplo comum de 60 e 45

Múltiplos de:

45: 45, 90, 135, 180, 225.

60: 60, 120, 180, 240, 300.

O menor múltiplo comum de 45 e 60 é 180

° Assim, eles se verão no mesmo lugar após 180 minutos;

Número de horas = 180/60 = 3 horas

6 0

3 years ago

Y=2x+4 use in a graph

AlekseyPX

The slope is 2 and the y intercept is 4

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3 years ago

Sal has already finished 5/9 of the 45 math problems he was assigned. If each math problem took him 3/5 of a minute to finish an

Oliga [24]

Step-by-step explanation:

plz refer the attachment

6 0

3 years ago