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3 years ago

Which ocean has average depth of about 12,000 feet,to the nearest thousands?

1 answer:

7 0

The Atlantic Ocean has an average depth of about 12,000 feet, to the nearest thousands. It is the second largest ocean in the world. The Atlantic Ocean and the Arctic Ocean are separated by a submarine ridge that extends from the south east of Greenland to the North Scotland. The atlantic Ocean can be divided into two parts based on its shape and they are North Atlantic Ocean and South Atlantic Ocean. These two parts have totally different type of water currents. The North Atlantic Ocean has some of the busiest shipping lanes as commercial ships ply through this route.

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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

2 years ago

Help me... I don't really understand and need an explanation

ehidna [41]

Answer:

x=17

Step-by-step explanation:

This should be for a "kite": AD=DC, AB=BC and ∠A=∠C

8x-27 = 3x+58

5x = 85

x = 17

3 0

2 years ago

For what value of x does the function have an output of -7, given that g(x) = -3x + 8

madam [21]

Answer:

X=5

Step-by-step explanation:

-3x+8=-7

-3x=-15

X=5

4 0

3 years ago

Please help me out on this :(( struggling !

Yuki888 [10]

Answer:

answer is B

Step-by-step explanation:

step by step explanation

3 0

2 years ago

Draw two planes that intersect in line ET<br><br> I have no idea how to draw this please help me

lora16 [44]

Please provide more information and the digits of where the points should be coordinated in a graphic

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2 years ago