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Answer:

a) dA/dt = 125,42 mm/min

b) dh/dt = - 1,78 mm/min

Step-by-step explanation:

The volume of the cylinder is:

V(c) = π*r²*h         ( r and h radius of the base and heigh respectively )

Then the surface area is: Area of the base : π*r²

Plus lateral area :  h*2*π*r

A(c) =  π*r² + 2*π*r*h

With the help of differentials we obtain:

dA/dt = 2*π*r*dr/dt + 2*π*h*dr/dt + 2*π*r*dh/dt        (1)

In this equation and at time t we know:

r = 18 mm        dr/dt = 2 mm/min      h = 8 mm    dh/dt = ??  

dA/dt = increasing rate of the surface area ( with respect to time)

To find dh/dt we know:

V(c) is constant, then

V(c) = π*r²*h     then   h = V(c) / π*r²

dh/dt = - [V(c)*2*π*r*dr/dt ] / π²*r⁴

By subtitution of V(c)

dh/dt = - [ π*r²*h *2*π*r*dr/dt ] / π²*r⁴

dh/dt = - [2*π²h*r³*dr/dt ] /π²*r⁴

dh/dt = - [2*h* dr/dt ] / r

dh/dt =  -  2*8*2 / 18    mm/min

dh/dt = - 1,78 mm/min

By subtitution in equation (1)

dA/dt = 2*π*r*dr/dt + 2*π*h*dr/dt + 2*π*r*dh/dt

dA/dt = 2*π*18*2 + 2*π*8*2 + (- 2*π*18*1,78 )

dA/dt = 226,20 + 100,53 - 201,31

dA/dt = 125,42 mm/min

Following are solutions to the given points:

Formula:

Cylinder volume [tex]v = \pi r^2 h...............(i)[/tex]

[tex]\to \frac{dr}{dt} = 2 \frac{mm}{min}\\\\ \to \frac{dh}{dt} = -2 \frac{mm}{min}\\\\ \to h=8\\\\ \to r=18 \\\\[/tex]

Part A:  

Calculating the circular area of the surface:

[tex]\to A=\pi r^2\\\\[/tex]

So, [tex]\frac{dA}{dt}=2 \pi r \frac{dr}{dt}.........(ii)[/tex]

Therefore

[tex]\to \frac{dA}{dt}= 2\pi \times 18 \times 2= 72 \pi \ \frac{mm^2}{min}\\\\[/tex]

Part B:

[tex]\to \frac{dh}{dt}= - 2 \frac{mm}{min}[/tex]

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Answer:

zeros of the function are −2 and 3

Step-by-step explanation:

there is no -2 so H.3

Answer:

A. y = arcsinx and y = arccosx

Step-by-step explanation:

edge

The trigonometric functions have a domain of [–1, 1] is sine and cosine function.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f(x) make up this set. A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

From the given identity, the following things can be interpreted:

cos²x = 1- sin² x

cos x = √(1- sin2x)

Since the cosine function is known to be defined for real numbers, the value contained within the root is always positive. Therefore,

1- sin²x ≥ 0

sin²x ≤ 1

sin x ∈ [-1, 1]

Similarly,

1- cos²x ≥ 0

cos²x ≤1

cos x ∈ [-1,1]

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Answer:

The answer is C or 44/12

Step-by-step explanation:

1/2 is equivalent to 3/6

1 4/6 is equivalent to 1 4/6 or 10/6

1 2/4 is equivalent to 1 3/6 or 9/6

When you add all of these together you get 22/6

Then you multiply 22/6 by 2 to get 44/12

Answer:girl use google

Step-by-step explanation:what

Answer:

C!

Step-by-step explanation:

I Got it correct! I hope you have a wondeful weekend and Day!!!

Answer:

3.2

Step-by-step explanation:

Answer: I think D

Step-by-step explanation: I know slavery and states rights but i don’t know about the b one

Answer: All of the above

Step-by-step explanation: The south wanted slavery, lower or no tariffs, and individualized states writes. On the other hand, the north wanted no slavery, tariffs, and a central government.

Answer:

11:1

Step-by-step explanation:

For every 11 copies, 1 minute passes. Four minutes passed in this case and thus 11*4 would equal 44 and 1*4 would equal 4.

im sorry: In order to solve the inequality -x > 8, which of the following steps must be done?

Answer:

.54

Step-by-step explanation:

The probability is 33%.

The probability is the measure of the likelihood of an event to happen.

Given:

Random student to studies for test is 0.6, and to does not study for test is 0.4.

Studies for test to Gets B or higher is 0.55; does not get B or higher is 0.45.

Does not study for test to Gets B or higher is 0.20; does not get B or higher is 0.80.

P(A) =55%

P(B)= 20%

60% of the students study.

So, the probability that a student studies, and gets B or higher is:

Probability =P(A) * 0.6

P= 55* 0.6

Probability = 33%

Hence, the probability is 33%

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Answer:

25 yds

Step-by-step explanation:

Since it is a square all sides are equal and there are 4 sides so you divide the perimeter, 100, by 4 to get 25 yds.

Answer: no solution

Hope this helps and good luck :)

Step-by-step explanation:

Answer:

only one solution at x=0

Step-by-step explanation:

Answer:

$1.05 Per Pound

Step-by-step explanation:

Answer: $1.05/pound

Step-by-step explanation:

$26.25 / 25 = $1.05

Answer:

42

Step-by-step explanation:

5/7x=30

x=42

Answer:

40

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

-4+7-3=0

-4+7=3

3-3=0

Answer is 0

Answer:

-6

Step-by-step explanation:

-2-3/1-1

0.01/100 = 0.0001 x 1000 = 0.1lb

The answer would be:

8 and -1/8

1 and -1

And could be 0 and undefined, but I'm not 100% sure

Answer:

f(-4)=3(4)^2-5(4)

16*3-20

48-20

f(-4)=28

Answer:

43 ft per minute

Step-by-step explanation:

divide 172 by 4 to get the feet per 1 minute

Answer:

12+# OR 12+x

Step-by-step explanation:

Increased by 12 means plus 12. The word "is" in equations is an equal sign. So far, you have 2n+12. On the other side of the equal sign, you have 31 less than 3 times a number.

Answer:

each person gets 12.35oz

Step-by-step explanation:

74.1

6

=12.35

Answer:

12.35 oz

Step-by-step explanation:

74.1 divided by 6 equals 12.35