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3 years ago

Which expression is equivalent to the given expression? 5x−2

Mathematics

2 answers:

kompoz [17]3 years ago

8 0

The second one is same !

as 2x-2+3x= 5x-2 .....so answer is B

PtichkaEL [24]3 years ago

6 0

2x-2+3x you add the 2x and 3x together and the -2 is whats left over

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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

Solve the following equation: 28 ÷ 7 + 2 × 3 = ?

viva [34]

The answer is 10 I think :-)

6 0

3 years ago

Read 2 more answers

PLEASE HELP with these math questions (Please don't answer if you don't know all of them)

Leona [35]

Sqrt (53) = 10 * sqrt (0.53)

0.53 = 64/121
sqrt (0.53) = sqrt (64)/ sqrt (121) = 8/11 = 0.7273
Therefore sqrt (53) = 10 * 0.7273 = 7.27

sqrt (108) = 10 * sqrt (1.08)
sqrt (1.08) = sqrt (676/625) = 26/25 = 1.04
Therefore sqrt (108) = 10 * 1.04 = 10.4

sqrt (128) = 10 * sqrt (1.28)
sqrt (1.28) = sqrt (289/225) = 17/15 = 1.133
Therefore sqrt (108) = 10 * 1.133 = 11.33

5 0

3 years ago

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?

Anna [14]

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution then"it is flatter and wider than the normal distribution."

<h3>What is normal distribution?</h3>

The normal distribution explains a symmetrical plot of data around the mean value, with the standard deviation defining the width of the curve. It is represented graphically as "bell curve."

Some key features regarding the normal distribution are-

The normal distribution is officially known as the Gaussian distribution, but the term "normal" was coined after scientific publications in the nineteenth century demonstrated that many natural events emerged to "deviate normally" from the mean.
The naturalist Sir Francis Galton popularized the concept of "normal variability" as the "normal curve" in his 1889 work, Natural Inheritance.
Even though the normal distribution is a crucial statistical concept, the applications in finance are limited because financial phenomena, such as expected stock-market returns, do not fit neatly within a normal distribution.
In fact, prices generally follow a right-skewed log-normal distribution with fatter tails.

As a result, relying as well heavily on the a bell curve when forecasting these events can yield unreliable results.

To know more about the normal distribution, here

brainly.com/question/23418254

#SPJ4

6 0

1 year ago

Please help this is due after 30 minutes!

Tanzania [10]

Step-by-step explanation:

I entered it in and it was .9993319736

6 0

3 years ago

Read 2 more answers