Dennis has less than 70 min. to spend on some homework questions. He spent 10 min. on the first two questions. The rest of the questions will take 52 min. each.

Which statement describes the solution to this inequality?

Drag and drop the answer into the box.

Answer:

0

Step-by-step explanation:

-4+7-3=0

-4+7=3

3-3=0

Answer is 0

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:

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

Answer:

185.714285714%

A change from 14 to 40 represents a positive change (increase) of 185.71428571428572%

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:

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.

0.01/100 = 0.0001 x 1000 = 0.1lb

Answer:

3.2

Step-by-step explanation:

Answer:girl use google

Step-by-step explanation:what

Answer:

zeros of the function are −2 and 3

Step-by-step explanation:

there is no -2 so H.3

Answer:

-6

Step-by-step explanation:

-2-3/1-1

Answer:

43 ft per minute

Step-by-step explanation:

divide 172 by 4 to get the feet per 1 minute

Answer:

x = 33

Step-by-step explanation:

Because of the little square we know the total angle is 90

24 + 2x = 90

-24

2x = 66

/2

x = 33

Answer:

1/5 is ur answer

Step-by-step explanation:

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:

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]

Learn more about Domain here:

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Answer:

42

Step-by-step explanation:

5/7x=30

x=42

Answer:

40

Step-by-step explanation:

Answer:

only one solution at x=0

Step-by-step explanation:

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

Answer:

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

16*3-20

48-20

f(-4)=28

Answer: no solution

Hope this helps and good luck :)

Step-by-step explanation:

The answer would be:

8 and -1/8

1 and -1

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

Answer:

C!

Step-by-step explanation:

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

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:

$1.05 Per Pound

Step-by-step explanation:

Answer: $1.05/pound

Step-by-step explanation:

$26.25 / 25 = $1.05