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3 years ago

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Mathematics

1 answer:

MrMuchimi3 years ago

6 0

Samamamam eh eh wack wacka eh eh samamamamammaa welcome to Africa

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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

2 years ago

Ben has 50 drinks and paid 2$ for each. What is 67% of the final price ?

Debora [2.8K]

67% of final price is $67.

Step-by-step explanation:

Given,

Number of drinks Ben has = 50

Amount paid for each drink = $2

Amount paid for 50 drinks = 50*2

Amount paid for 50 drinks = final price = $100

67% of final price = $\frac{67}{100}*100$

67% of final price = $\frac{6700}{100}$

67% of final price = $67

67% of final price is $67.

Keywords: multiplication, percentage

Learn more about percentages at:

#LearnwithBrainly

7 0

3 years ago

True or False, In Euclidean geometry, there is only one equilateral triangle

docker41 [41]

True, In Euclidean geometry an equilateral triangle must be a 60-60-60 triangle.

Hope This Helps!!!

5 0

3 years ago

What number must be added to 15,-6, and 12 to have a mean of 5? Explain.

Genrish500 [490]

You need to add a -1

We can find this by setting up the equation like so

x + (-6) + 12 + 15 / 4 = 5

x + 21 = 20

x = 20 -21

x = -1

Now if we insert -1 where x is located in the equation, you will get a means of 5

3 0

2 years ago

PLEASE Please answer ASAP!!! :)

d1i1m1o1n [39]

Answer: No it is not.

Step-by-step explanation: A rational number is a number that can easily be expressed as a fraction or decimal, and square root of 7 cannot be easily expressed.

6 0

2 years ago

Read 2 more answers