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3 years ago

5

Simplify the expression. 6-4[(8z - 8y)+2(-y-z)]–3

1 answer:

forsale [732]3 years ago

5 0

Step-by-step explanation:

6-4(8z-8y)+2(-y-z)-3

=6-32z+32y-2y-2z-3

=6-3-32z-2z+32y-2y

=3-34z+30y

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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

If town A had 35 people, 12 left, 13 joined, 39 joined, 25 got killed, how many people were there left?

Makovka662 [10]

Answer:

50

Step-by-step explanation:

35 - 12 + 13 + 39 - 25 = 50

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3 years ago

How to slove -10 -1 need help

yuradex [85]

Answer:

-10 - 1 = x

Step-by-step explanation:

If you take -10 and subtract one, it makes the number go down lower because it's negative (example, 12 - 2 is -14)

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Cherries cost $5 for 2 pounds and $7.50 for 3 pounds. Question: a. What is the cost per pound? b. Is it constant? c. If you were

Fittoniya [83]

A. 1 pound of cherries costs 2.50

B. Yes it is constant

C. I believe that you would put cost on the y and lbs on the x
E. 5 lbs of cherries = 2.50 x 5 = $12.50

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3 years ago

One elevator is on the 8th floor ( 8 floors above the ground floor) and the other elevator is one floor below the ground floor.

blagie [28]

Answer:

They're 9 floors apart

Step-by-step explanation:

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3 years ago

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