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4 years ago

What is the solution to the inequality?

Mathematics

1 answer:

asambeis [7]4 years ago

3 0

Simplify both sides of the inequality, then isolate the variable. That should leave you with x> - 4

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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.

4 0

3 years ago

Plssss helppppppl:((((

Oduvanchick [21]

Answer:

I think it's 1.5 I'm not sure ._.

6 0

3 years ago

Read 2 more answers

for independence day celebration 25000 flags were distributed to 70 schools .if 40 shcool receive 250 each and the remainder dis

aleksandr82 [10.1K]

Answer:

500 flags each

Step-by-step explanation:

If 40 schools receive 250 each, then in total, that's 10,000

25,000 - 10,000 = 15,000. There are 30 schools remaining, so we divide. 15,000 / 30 = 500, so...

40 schools get 250 flags each, and the other 30 schools get 500 flags each.

5 0

3 years ago

James has 6 stamps in his stamp collection. Roy has 12 stamps in his stamp collection. James adds 2 stamps to his stamp collecti

Alina [70]

2:3

it was originally 8:12, but it has to be simplified. 2/3 can also work as an answer.

6 0

4 years ago

Perrys Bikes rents bikes for $17 plus $6 per hour. john paid $59 to rent a bike. For how many hours did he rent the bike?

matrenka [14]

7 hours

Let x represent hours rented
59=17+6x
42=6x
x=7

4 0

3 years ago