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Fynjy0 [20]
3 years ago
5

A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon

increasing at the instant the radius is 40 centimeters
Physics
1 answer:
Nookie1986 [14]3 years ago
8 0

Answer:

<h2>0.245cm/min</h2>

Explanation:

The volume of the spherical balloon is expressed as V = 4/3πr³ where r is the radius of the spherical balloon. If the spherical balloon is inflated with gas at the rate of 500 cubic centimetres per minute then dV/dt = 500cm³.

Using chain rule to express dV/dt;

dV/dt = dV/dr*dr/dt

dr/dt is the rate at which the radius of the gallon is increasing.

From the formula, dV/dr = 3(4/3πr^3-1))

dV/dr = 4πr²

dV/dt = 4πr² *dr/dt

500 =  4πr² *dr/dt

If radius r = 40;

500 = 4π(40)² *dr/dt

500 = 6400π*dr/dt

dr/dt = 500/6400π

dr/dt = 5/64π

dr/dt  = 0.245cm/min

Hence, the radius of the balloon is increasing at the rate of 0.245cm/min

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In a large restaurant an average 60% customers ask for water with their meal. A random sample of 10 customers is selected. Find
Gekata [30.6K]

Answer:

a)P(6)=0.25

b)p(x

c)p(x\geq3)=0.9878

d)\sigma=\sqrt{2.4}=1.5492

Explanation:

From the question we are told that:

Population percentage p_\%=\60%

Sample size n=10

Let x =customers ask for water

Let y =customers dose not ask for water with their meal  

Generally the equation for y is mathematically given by

y=1-p_\%\\y=1-0.60\\y=0.40

Generally the equation for pmf p(x) is mathematically given by

P(x)=10C_x (0..6)^x(0.4)^{10-x}

a)

Generally the probability that exactly 6 ask for water is mathematically given by

P(x)6=10C_6 (0..6)^6(0.4)^{10-6}

P(6)=0.25

b)

Generally the probability that  less than 9 ask for water with meal  is mathematically given by

p(xg)

p(x

p(x

p(x

c)

Generally the probability that  at least 3 ask for water with meal  is mathematically given by

p(x\geq3)=1-p(x

p(x\geq3)=1-[p(0)+p(1)+p(2)]

p(x\geq3)=1-[0.00001+0.0015+0.0106]

p(x\geq3)=1-[0.0122]

p(x\geq3)=0.9878

d)

Generally the mean and standard deviation of sample size is mathematically given by

Mean

\=x=np=10(0.6)=6

Standard deviation

v(x)=npq=10(0.6)(0.4)=2.4

\sigma=\sqrt{2.4}=1.5492

4 0
3 years ago
A steam engine absorbs 4 x 105 J and expels 3.5 x 105 J in each cycle. What is its efficiency?
Wewaii [24]
Input heat, Qin = 4 x 10⁵ J
Output heat, Qout = 3.5 x 10⁵ J

From the first Law of thermodynamics, obtain useful work performed as
W = Qin  -  Qout
     = 0.5 x 10⁵ J

By definition, the efficiency is
η = W/Qin
   = 100*(0.5 x 10⁵/4 x 10⁵)
   = 12.5%

Answer: The efficiency is 12.5%
3 0
3 years ago
1. For a reaction to occur, energy must be
amm1812

For a reaction to occur, energy must be absorbed to break chemical bonds

<u>Explanation:</u>

Reactions can be classified as chemical reaction, nuclear reaction, thermal reaction. So in these three reaction types, the nature of energy will only be varying.

But in order to execute a reaction, there should be breaking of existing bonds and then formation of new bonds. So for breaking of the bonds of reactants, energy should be absorbed from the surrounding.

Then the extra energy will be released after forming the products. Thus, the process of absorption of energy will lead to endothermic process and the process of releasing of energy will lead to exothermic reaction. So for a reaction to occur, energy must be absorbed to break the chemical bonds.

8 0
3 years ago
28. Sound can be heard around a corner because of
Lesechka [4]

Answer:

Diffraction of sound wavelengths.

Explanation:

Diffraction-A wave is able to bend around a corner due to the effects of diffraction. sound aves are capable of bending around corners in the same magnitude as it's wavelength making it possible to hear sounds around corners.

5 0
3 years ago
What is characteristic of an opaque object.
stiks02 [169]

Answer:

allows no light to pass

Explanation:

5 0
2 years ago
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