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3 years ago

Find the median and mean of the data set below: 21,44,21,41

Mathematics

1 answer:

Alexeev081 [22]3 years ago

3 0

Median is 41.5 and the mean is 31.75

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The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu

rjkz [21]

The balloon has a volume $V$ dependent on its radius $r$ :

$V(r)=\dfrac43\pi r^3$

Differentiating with respect to time $t$ gives

$\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2\dfrac{\mathrm dr}{\mathrm dt}$

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

$10\dfrac{\mathrm m^3}{\mathrm s}=4\pi (3\,\mathrm m)^2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=\dfrac5{18\pi}\dfrac{\rm m}{\rm s}$

The surface area of the balloon is

$S(r)=4\pi r^2$

and differentiating gives

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi r\dfrac{\mathrm dr}{\mathrm dt}$

so that at the moment the radius is 3 m, its area is increasing at a rate of

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi(3\,\mathrm m)\left(\dfrac5{18\pi}\dfrac{\rm m}{\rm s}\right)=\dfrac{20}3\dfrac{\mathrm m^2}{\rm s}$

4 0

3 years ago

Janae has 280 dimes in her piggy bank she has 10 times as many pennies how many pennies does Janae have

Natalija [7]

Answer:

She has 28 pennies

Step-by-step explanation:

Janae has 280 dimes in her piggy bank she has 10 times as many pennies .

If she has 280 dimes in piggy bank

And has 10 times as many pennies

Let dimes= x

Let pennies= y

X= 10y

But x= 280

280= 10y

280/10 = y

28 = y

She has 28 pennies

8 0

4 years ago

Use the Order of Operations to simplify: 3(8 - 4*5)

aleksklad [387]

Answer:

Step-by-step explanation:

$3\left(8-4\cdot \:5\right)\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(8-4\cdot \:5\right)\::\quad -12\\=3\left(-12\right)\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:3\left(-12\right)\:\\:\quad -36$