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forsale [732]
3 years ago
12

An upright cylindrical tank with radius 8 m is being filled with water at a rate of 2 m3/min. How fast is the height of the wate

r increasing? Part 1 of 3. If h is the water's height, the volume of the water is V = πr2h. We must find dV/dt. Differentiating both sides of the equation gives Dv/Dt= πr2 Dh/Dt Subsituting for r , this becomes Dv/Dt ____________ π Dh/Dt What goes in the blank ? Thanks !
Mathematics
1 answer:
Fiesta28 [93]3 years ago
3 0

Answer:

16 goes in the blank

Step-by-step explanation:

V(c) = 2*π*r*h

Differentiating boh sides

DV(c)/Dt   =  2πr Dh/Dt    now radius is 8 m

DV(c)/Dt   =  8π Dh/Dt

That expression gives the relation of changes in V and h

DV(c)/Dt  is the speed of growing of the volume

Dh/Dt  is the speed of increase in height

so if the cylinder is filling at a rate of  2 m³/min   the height will increase at a rate of 16π m/min  

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Exponential Growth problem.
xxMikexx [17]
It will be understood that population 6,000 billion (6*10^12) in 2017.
If this is not the case, follow the logic and the final number can be adjusted easily.

Mathematical answer:
In 2017: 6,000 billion=6000*10^9 =6*10^12
rate of increase = 1.3% per year (assumed constant)
final year = 2100
Population estimate in 2100
=6*10^12*(1.013^(2100-2017))
=6*10^12*(1.013^(83)
=6*10^12*(2.921352509198383)
=17.528*10^12
=17,528 billion.


8 0
3 years ago
A researcher measured the heights of forty high-school students. The measurements are recorded here.
lord [1]
63 inches is her height

7 0
3 years ago
Read 2 more answers
A radio station is giving away a $100 bill to every 30th caller and movie tickets to every 40th caller. Which call will be the f
Ymorist [56]

Answer:

120th caller

Step-by-step explanation:

According to the problem, calculation of the given data are as follows,

$100 bill = 30th caller

Movie tickets = 40th caller

So, to find out first to win both prizes, we will use LCM method,

LCM of 30 and 40 =       10 | 30 , 40

                                            | 3    , 4

LCM of 30 and 40 = 10 × 3 × 4 = 120

Hence, 120th caller will be the first to win both prizes.

3 0
3 years ago
Luisa solves for x in the equation 9(1/3) + 8x = 4( 2x + 3/4)
Maru [420]

Answer:

x = all real numbers because this equation is an identity

Step-by-step explanation:

9 (1/3) = 9*1/3 = 3

3 + 8x = 4(2x + 3/4)

3 + 8x = 8x + 3

x = all real numbers because this equation is an identity

7 0
2 years ago
Read 2 more answers
Help please.<br><br><br><br> Thank you.
Tom [10]

Answer:

A,D,C would be your answers

Step-by-step explanation:

8 0
3 years ago
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