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3 years ago

Which number line shows the solutions to n > 3?ヽ(°◇° )ノ

Mathematics

2 answers:

professor190 [17]3 years ago

6 0

Answer:

The first number line represents the solution to the inequality n > 3.

Step-by-step explanation:

We are given a inequality in one variable n as:

n > 3

We know that the solution to n>3 is the set of all the values which are strictly greater than 3 i.e. the shaded region in the number line is to the right of ' 3 ' and goes to infinity with open circle at 3 since the inequality is strict.

Also, in interval form the solution is represented by: (3,∞).

balu736 [363]3 years ago

3 0

It is the first number line :)

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A spherical balloon currently has a radius of 19cm. If the radius is still growing at a rate of 5cm or minute, at what rate is a

miv72 [106K]

Answer:

22670.8 cm³/min

Step-by-step explanation:

Given:

Radius of the balloon at a certain time (r) = 19 cm

Rate of growth of radius is, $\frac{dr}{dt}=5\ cm/min$

The rate at which the air is pumped in the balloon can be calculated by finding the rate of increase in the volume of the balloon.

So, first we find the volume of the sphere in terms of 'r'. As the balloon is spherical in shape, the volume of the balloon is equal to the volume of a sphere. Therefore,

Volume of balloon is given as:

$V=\frac{4}{3}\pi r^3$

Now, rate of increase of volume is obtained by differentiating both sides of the equation with respect to time 't'.

Differentiating both sides with respect to time 't', we get:

$\frac{dV}{dt}=\frac{d}{dt}(\frac{4}{3}\pi r^3)\\\\\frac{dV}{dt}=\frac{4\pi}{3}(3r^2)(\frac{dr}{dt})\\\\\frac{dV}{dt}=4\pi r^2(\frac{dr}{dt})$

Now, plug in 19 cm for 'r', 5 cm per minute for $\frac{dr}{dt}$ and solve for $\frac{dV}{dt}$ . This gives,

$\frac{dV}{dt}=4\pi (19 cm)^2(5\ cm/min)\\\\\frac{dV}{dt}=4\times 3.14\times 361\times 5\ cm^3/min\\\\\frac{dV}{dt}=22670.8\ cm^3/min$

Therefore, the rate at which the air is being pumped into the balloon is 22670.8 cm³/min.

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3 years ago

What are three numbers whose products are 9000

Ne4ueva [31]

300*30*1 = 9000
4500*2*1 = 9000
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KengaRu [80]

Answer:

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2x^2(x+3)

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3 years ago

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Korvikt [17]

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