On Monday, 279 students went on a trip

A spherical balloon is inflating with helium at a rate of 64 pi StartFraction ft cubed Over min EndFraction . How fast is the b

olga2289 [7]

Answer:

The radius of the balloon is increasing at a rate of 4 feet per minute.

Step-by-step explanation:

We are given the following in the question:

$\dfrac{dV}{dt} = 64\pi \dfrac{\text{ ft}^3}{\text{min}}$

Volume of sphere is given by

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

where r is the radius of the balloon.

Instant radius, r = 2 ft

Rate of change of volume =

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

Putting values, we get,

$64\pi = 4\pi (2)^2\dfrac{dr}{dt}\\\\\Rightarrow \dfrac{dr}{dt} = 4$

Thus, the radius of the balloon is increasing at a rate of 4 feet per minute.

5 0

3 years ago

Skill Sum

Nataly_w [17]

Answer:

I don't know

Step-by-step explanation:

I don't know

3 0

3 years ago

Simplify 616/196<br> thirteen points for whoever answers the best please help!

mixas84 [53]

That’s the equation for pi, but the simplified fraction is 22/3 (please mark brainliest)

3 0

3 years ago

Read 2 more answers

For a certain online store, the distribution of number per hour is approximately normal with mean 1200 purchases and standard de

Advocard [28]

Answer: 16%

Step-by-step explanation:

When we have a normal distribution, the 100% of our sample will be placed in a "gaussian bell".

Where the middle of this bell coincides with the mean.

The mean, in this case, is 1200, and the standard deviation is 200.

In the image below you can see that between the points.

Mean + standard deviation and the end of the graph, we have:

13.5% + 2.35% + 0.15% = 16%

And particularly, if we want to know the percentage that exceed 1400, will be the same percentage above the mean plus the standard deviation.

mean = 1200

SD = 200

mean + standard deviation = 1200 + 200 = 1400.

Then the percentage that exceeds 1400 is equal to the percentage that we found above, then the correct option is C: 16%

5 0

3 years ago

A company makes traffic signs one of those signs can be modeled by an equilateral triangle with the perimeter of 144 inches the

barxatty [35]

Answer:

The height of the larger traffic signs is 51.96 inches

Step-by-step explanation:

Given that initially, A company makes traffic signs of an equilateral triangle with the perimeter of 144 inches

Now, A company makes similar traffic signs of perimeter 1.25 of original

New perimeter will be 1.25x144=180 inches

Let triangle ABC be a larger triangle with 180inches of the perimeter.

It is given that the triangle is an equilateral triangle,

Therefore, Side AB=BC=AC

The perimeter of a triangle ABC is

AB+BC+AC=180

3AB=180

AB=60 inches

Figure show that triangle ABC and AD is the height of the triangle.

Since, the triangle ABC is an equilateral triangle,

AD is the perpendicular bisector of BC

so that,

BD=DC and Angle ADB=90

In right triangle ADB,

Angle D =90 and Angle B =60

Side BD=60/2=30 inches and AB=60 inches

Using Pythagoras theorem,

$AD^{2} +BD^{2} =AC^{2}$

$(AD)^{2} +(30)^{2} =60^{2}$

$(AD)^{2} =60^{2}-(30)^{2}$

AD=51.96 inches

Thus, The height of the larger traffic signs is 51.96 inches

4 0

3 years ago