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NemiM [27]
3 years ago
14

Write 2050000 in scientific notation( with exponents)

Mathematics
2 answers:
storchak [24]3 years ago
5 0
So,

We have to write 2,050,000 in scientific notation, which means that the first number must be between 1 and 10 and the second number must be an exponent with a base of 10.

In order to get a number between 1 and 10, we will need to move the decimal point 6 places to the left.

2,050,000 ⇒ 2.05 x 10^{6}

2,050,000 in scientific notation is 2.05 *  10^{6}
ICE Princess25 [194]3 years ago
3 0
Since notations have to be under 10, it would start off as 2.05. then count the places to the right until u reach the place after the last 0 which would make it: 2.05 X 10^6
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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
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Answer:

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

Step-by-step explanation:

From the formula

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Differentiate the equation with respect to time t, such that

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

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

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Using the Chain's rule

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

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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.

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