What is the answer please

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

4 years ago

Please help brainliest<br> (Algebra 1)

den301095 [7]

Answer:

B - 11 > (w - 4)²

C - y < 3⁴

D - 5 + 9 < 5 · 9

are your correct answers

Step-by-step explanation:

x² - 5x + 6 and z + 11 / 2z - 1 are equalities phrases and rest of them will be inequalities.

HOPE THIS HELPS YOU

Follw me = 10 thanks

Mark as brainliest = 10 thanks

1 thanks to me = 2 thanks

3 0

3 years ago

A grocer sells 30 loaves of bread a day. The cost is $2.50 per loaf. The grocer estimates that for each $0.50 increase in cost,

Viktor [21]

Answer:

none of the above

Step-by-step explanation:

The grocer's revenue will be the product of the number of loaves sold (30-2x) and their price (2.50+0.50x).

Revenue will be positive for values of x between those that make these factors be zero. The number of loaves sold will be zero when ...

... 30 -2x = 0

... 15 -x = 0 . . . . . divide by 2

... x = 15 . . . . . . . add x

The price of each loaf will be zero when ...

... 2.50 +0.50x = 0

... 5 + x = 0 . . . . . . . multiply by 2

... x = -5 . . . . . . . . . . subtract 5

Revenue will be positive for any number of increases greater than -5 and less than 15.

_____

D is the best of the offered choices, but it is incorrect in detail. -5 is a number less than 15, but will give zero revenue.

4 0

4 years ago

Find 93 • 87 using mental math.

bagirrra123 [75]

Okay so start with multiplying 93 * 7

So 3 x 7= 21

9 X 7 +63, carry the 2 = 651

Then 8 x 93
Remember that first is a zero.
8 X 3= 24
8 X 9= 72, carry the 2= 74
So that is 7440
Now
0651
+7440
8091
And that's the answer

7 0

4 years ago

Read 2 more answers

(2x+5)^2<br><br>is it 4x^2+20x+25?

Daniel [21]

Yes that’s your answer!! Good job!!

4 0

3 years ago