1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Harman [31]
3 years ago
15

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

s of the sphere is 3m?
Mathematics
1 answer:
rjkz [21]3 years ago
4 0

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}

You might be interested in
what is the value of 8/15÷(-0.35) A -75/14 B -32/21 C -21/32 D -14/75 I would really appreciate it if you could also explain how
barxatty [35]
Answer;-1.5238095238
First step; 8/15

8/15 = 0.53 and so on in a repeating form. (0.53333333333)

Divide; 0.53 / -0.35 

= -1.5238095238

5 0
3 years ago
Read 2 more answers
Which of the following inequalities matches the graph?
eimsori [14]

Answer:

Step-by-step explanation:

y=2x+2

4 0
3 years ago
The promising alternative energy sources currently under development are fuel cell technology and large-scale solar energy power
Mumz [18]

Answer:

Step-by-step explanation:

a) Denote the event of commercially availability of f_uel cell technology as F_, commercial availability of solar power technology as S

Write the probability of energy supplied by these energy sources in the next 10 years  

P(energy supplied) = P(S ∪ F) -----(1)

Rewrite eqn (1)

P(energy supplied) = P(S) + P(F) - P(F) P(S) ----(2)

substitute 0.85 for P(S) and 0,7 for P(F) in eqn (2) to find the probability of energy supplied by these energy sources

P(energy supplied) = 0.85 + 0.7 - (0.7 * 0.85)

= 0.85 + 0.7 - (0.595)

= 1.55 - 0.595

= 0.955

Therefore, the probability that there will be energy supplied by these two alternative sources in the next 10 years is 0.955

B) write the probability of only one source of energy available

P(only one source of energy available) = P(\bar F S) ∪ P( \bar S F) ---(3)

Rewrite the equation (3)

P(only one source of energy available) =

=P(\bar F S)+P(\bar S F)\\\\=\{[1-P(F)]P(S)+[1-P(S)]P(F)\}---(4)

=\{[1-0.7]0.85+[1-0.85]0.7\}\\\\=0.255+0.105\\\\=0.36

Therefore,The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years is 0.36

4 0
3 years ago
The linear equation was solved using these steps.
NISA [10]

Answer:

what are the options

Step-by-step explanation:

????????????????????????????????

3 0
3 years ago
13x = 3(X-20) How to solve this algebra equation?
Mashcka [7]
-6x is the correct answer
6 0
2 years ago
Read 2 more answers
Other questions:
  • Calculate the perimeter of each figure <br> How do you find the perimeter of a figure
    12·1 answer
  • Each of the line segments in the word MATH are numbered in the graph below. Find the slope (as a ratio of rise over run) of each
    8·1 answer
  • Suzanne can work 10 math problems in 15 minutes. How many can she work in an hour and a half?
    6·1 answer
  • How far does a train go in 100 minutes
    8·2 answers
  • The Bar Chart shows the weights of 10 dogs entered in a local dog show,
    11·1 answer
  • Polar form of (x+6)^2 +y^2=36
    15·1 answer
  • HELP!!
    9·1 answer
  • 1. Combine the expressions<br>(a) 7x+3+6x +11​
    13·1 answer
  • PLSSS HELP WIL REWARD BRAINLIEST!!
    12·1 answer
  • Mr. Smith is 81 years older than his grandson, Victor. In 3 years, Mr. Smith will be four times as old as Victor. How old is Vic
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!