At time t= 0, a storage tank is empty and begins filling with water. For t > 0 hours, the depth of the water in the tank is increasing at a rate of W (t) feet per hour. Which of the following is the best interpretation of the statement W' (2) > 3?

a. Two hours after the tank begins filling with water, the depth of the water is increasing at a rate greater than 33 feet per hour.
b. Over the first two hours after the tank begins filling with water, the depth of the water is always increasing at a rate greater than 3 feet per hour.
c. Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.
d. Over the first two hours after the tank begins filling with water, the rate at which the depth of the water is rising is always increasing at a rate greater than 33 feet per hour per hour.

Answers

Answer 1

The given function is the rate of change of the water depth. therefore,

W'(t) is the second derivative.

The correct option is; d. Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.

Reasons:

The volume of water in the tank is 0 at time t = 0 (the tank is empty)

The function that gives the rate at which the depth of water in the tank is

increasing at time t > 0 is W(t).

Where;

t = The time in hours

Therefore;

W'(t), the derivative of the function of the rate at which the water in the

tank is increasing in feet per hour is the rate of increase of W(t).

Which gives;

W'(2) = The rate of change of the rate at which the water level is rising (second derivative) two hours after begins to fill with water, per hour per hour.

Therefore;

W'(2) > 3 = Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.

Learn more about second derivative here:

https://brainly.com/question/10305010


Related Questions

the graphs show information about the different journeys of 4 people

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Answer:

sorry id like to help but i need more info.

Step-by-step explanation:

i hope this helps!

Plz help me thx

Simplify pt2:

Answers

Answer:

π - [tex]\sqrt{17}[/tex]

Step-by-step explanation:

note that [tex]\sqrt{x^2}[/tex] = x

Given

[tex]\sqrt{(\pi -\sqrt{17})^2 }[/tex]

= π - [tex]\sqrt{17}[/tex]

decide whether the function is a polynomial function if it is write the function in standard form

f(x)=1/2x²-3x^4-7 ​

Answers

Answer:

yes, it is a polynomial function because all of the exponents are non-negative; standard form is f(x) = -3x⁴ + 1/2x² - 7

Step-by-step explanation:

standard form is placing all terms in decreasing exponent order

Answer:

it is a polynomial because all of the exponents are non-negative

standard form f(x)=-3x^4+1/2^2-7

Step-by-step explanation:

Hope it helps

Have a nice day : )

Given f(x) = 3x^2 + 2x – 1 and g(x) = 4x-5 find ( g of f) (-2)

Answers

Answer:

23

Step-by-step explanation:

Evaluate f(- 2) then substitute the value obtained into g(x)

f(- 2) = 3(- 2)² + 2(- 2) - 1 = 3(4) - 4 - 1 = 12 - 5 = 7 , then

g(7) = 4(7) - 5 = 28 - 5 = 23

[tex]\text{Given that,}\\\\f(x) = 3x^2 +2x -1\\\\f(-2)=3(-2)^2 +2(-2) -1 = 12-4-1=7\\\\g(x) = 4x -5\\\\\text{Now,}\\\\(g \circ f) (-2)\\\\=g(f(-2))\\\\=g(7)\\\\=4(7)-5\\\\=28-5\\\\=23[/tex]

HELP ME PLEASE GUYS!! :)

Answers

If two lines intersect, then there is only one solution - where they cross.

Looking at the graph, we can see the intersection point of these two lines.

The intersection point is (1,1) - one unit to the right of the origin and one unit up.

Hope this helps! :)

solve one step equation

x/-2 = -3

Answers

If we’re solving for x, x=6

Answer:

x=6

Step-by-step explanation:

x/-2=-3

*-2    *-2

x=6

-hope it helps

2. Which identity could be the missing step to verify the identity (cos e )(csce)=cote? (1 point)
1
cose
= cote
seca
1
cos e
= cote
sin
1
sin e = cote
csce
cos e
= cote
tan

Answers

Answer:I hope it helps to you it's so important to you right♡

The identity could be the missing step to verify the identity

(cosФ)(cscФ) = cotФis, (cosФ)(1/sinФ) = cotФ.

What are periodic functions?

A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.

Any function that has a positive real integer p such that f (x + p) = f(x), with all x being real values, is said to be periodic.

We know, sin/cos = tan = 1/cot = cos/sin.

Given, (cosФ)(cscФ) = cotФ.

We know, sin = 1/csc.

Therefore,

(cosФ)(cscФ) = cotФ.

cosФ×1/sinФ = cotФ.

cosФ/sinФ = cotФ.

learn more about trigonometric identities here :

https://brainly.com/question/3785172

#SPJ7

Answer plz I need the answer

Answers

Answer:

D) 3x + 33

Step-by-step explanation:

3(x + 11)

3x + 33

Hope this helps! Pls give brainliest!

ANSWER: D. 3x + 33

EXPLANATION

simplify the equation.

When you have an equation with a number on the outside of the parentheses, multiply ever number inside by the number on the outside

So in this case you are multiplying x by 3 and 11 by 3

So you get 3x + 33

Find the inverse of the function 6-5x

Answers

Answer:
-x/5 + 6/5
hope this helps!

20) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test

Answers

Answer:

50-50 chance I suppose (1/2 or 5/10) or 40% to 60% percent chance

Step-by-step explanation:

He can guess all of the questions and get all of them right, and it is a possibility that he can also get all of them wrong. So I say, 50-50. I can't lie, I'm having trouble with probability as we speak.

Please help me!!!! Thank you

Answers

[tex]\huge \rm༆ Answer ༄[/tex]

In the given question, the two sides of the given triangles are parallel, so the the two corresponding angles of the Triangles are equal to one another.

Therefore, the Triangles are similar by AA similarity criteria ~

And since they are similar, the ratio of sides of one Triangle will be equal to ratio of corresponding sides of the other Triangle.

that is ~

[tex] \sf \dfrac{5}{7} = \dfrac{5 + 6}{y} [/tex]

[tex] \sf y = 11 \times \dfrac{7}{5} [/tex]

[tex] \sf y = \dfrac{77}{5} [/tex]

[tex] \sf y = 15.4[/tex]

Hence, value of l = 15.4 units ~

Find the first six terms of a sequence represented by f(n) = 6(n-2)

Answers

The first term is: f(1)=6(1-2) f(1)=6(-1) f(1)=-6
The second term is: f(2)=6(2-2) f(2)=0
The third term is f(3)=6(3-2) f(3)=6
The fourth term is: f(4)=6(4-2) f(4)=12
The fifth term is: f(5)=6(5-2) f(5)=18
The sixth term is: f(6)=6(6-2) f(6)=24

The sequence is: -6, 0, 6, 12, 18, 24

um. ill give brainliest help please !!!

Answers

No, Poppy did not answer the problem correctly.

The mistake I see is that she did not include the exponent on the first 3. She also forgot to keep the -8.

The correct answer would be -7. (see attachment)

Have a nice day :)

How does a domain restriction placed on a non-invertible function affect its inverse? Drag a function or an interval into each box to correctly complete the statement. When the domain of the non-invertible function f(x)=(x+1)^2−3 is [−1,∞), the inverse of the function is Response area, and the domain of the inverse function is

Answers

Using inverse function concepts, it is found that:

The inverse of the function is [tex]y = \sqrt{x + 3} - 1[/tex], and the domain of the inverse function is [tex][-3, \infty][/tex].

A function will have an inverse if for each output, there is only one respective input.The domain of the inverse is the range of the original function.

The function given is:

[tex]f(x) = (x + 1)^2 - 3[/tex]

It's range is [tex][-3, \infty][/tex], which will be the domain of the inverse.

To find the inverse, we exchange x and y, and isolate y, then:

[tex]y = (x + 1)^2 - 3[/tex]

[tex]x = (y + 1)^2 - 3[/tex]

[tex](y + 1)^2 = x + 3[/tex]

[tex]\sqrt{(y + 1)^2} = \sqrt{x + 3}[/tex]

[tex]y + 1 = \sqrt{x + 3}[/tex]

[tex]y = \sqrt{x + 3} - 1[/tex]

The inverse of the function is [tex]y = \sqrt{x + 3} - 1[/tex], and the domain of the inverse function is [tex][-3, \infty][/tex].

A similar problem is given at https://brainly.com/question/13160937

Answer:

Step-by-step explanation:

please help for brainliest ​

Answers

Answer:

84 and 144

Step-by-step explanation:

If the two numbers are  a  and  b  and their LCM is  x  and their HCF is  y  then there is a rule that is  a×b=x×y

in this case:

a×b=x×y

a×b=(504)×(24)

a×b=12096

when finding factors of 12096 that are between 60 and 160, we can see that 84 and 144 is the best pair.

hope this helps! :D

have a miraculous day!! <3

If f(x) = 9(x - 7)^2 – 8
Find f( – 4)

Answers

Answer:

1,081

[tex]f( - 4) = 9( - 4 - 7) {}^{2} - 8 \\ f( - 4) = 9( - 11 {)}^{2} - 8 \\ f( - 4) = 1081[/tex]

Find the LCM of 5, 6 and 9.​

Answers

Step-by-step explanation:

90.......................

Answer:

90.

Step-by-step explanation:

We have:

5

6 = 3 * 2

9 = 3 * 3

LCM = 5 * 3 * 2 * 3 = 90

As both 6 and 9 have a 3 in common this 3 is only used once in the calculation.

help plzz
2decimal places
165 x 0.38²

Answers

Answer:

23.83

Step-by-step explanation:

A car is traveling at a rate of kilometers per hour. What is the car's rate in kilometers per minute? How many kilometers will the car travel in minutes? Do not round your answers.

Answers

Answer:

3.02

Step-by-step explanation:

The cost of 3 kg of apples and 6 kg of oranges is Rs 300. If the cost of 1 kg of oranges is Rs 30, find the cost of 8 kg of apples.​

Answers

Answer:

Cost of 1 = 30

So cost of 8kg apples=8*30

=240

Step-by-step explanation:

Help me..What is the length of the missing leg? If necessary, round to the nearest tenth.

Answers

Answer:

27

Step-by-step explanation:

The triangle shown is a right triangle, indicated by the little square at the bottom right. When trying to find the length of a missing leg of a right triangle we can use the Pythagorean theorem.

Pythagorean theorem : a² + b² = c²

Where a and b = legs and c = hypotenuse ( longest side )

We are given the length of the hypotenuse as well as a leg and we need to find the other leg.

Hypotenuse (c) = 45

Leg (a) = 36

To find the length of the other leg we can plug in the given values of the hypotenuse and the leg into the Pythagorean theorem and solve for b

Recall the Pythagorean theorem : a² + b² = c²

a = 36 and c = 45

(36)² + b² = (45)²

simplify exponents : 36² = 1296 and 45² = 2025

1296 + b² = 2025

subtract 1296 from both sides: 1296 - 1296 cancels out and 2025 - 1296 = 729

b² = 729

take the square root of both sides: √(b)² = b and √729 = 27

We're left with b = 27 meaning that the length of the other leg ( or missing side ) is 27

how to solve 15=6+2(n-3) + 3n

Answers

Step-by-step explanation:

15 = 6 + 2(n-3) + 3n

or, 15 = 6 + 2n - 6 + 3n

or, 15 = 6 - 6 + 2n + 3n

or, 15 = 0 + 5n

or, 15 = 5n

or, 15/5 = n

or, 3 = n

;- n = 3.....

I Hope that this will Help you...!!!

Due in 1 min please help!!!!!
;)

Answers

(7^1/5)^5
=(7^5/5)
=(7^1)
=7 therefore C

Which of the following solution sets represent the inequality 3-1/2x>10?​

Answers

[tex]3- \dfrac 12 x >10\\\\\implies - \dfrac x 2> 10 -3\\\\\implies -\dfrac x 2 >7\\\\\implies -x > 14\\\\\implies x<-14\\\\\text{Interval solution,}~ (-\infty,-14)[/tex]

Ok done. Thank to me :>

34x 10% discount. What the absolute FLIP
is the answer.

Answers

Answer:

You would pay $30.6, and the discount would be $3.4

Step-by-step explanation:

Because it is a 10% discount, you will only have to pay 90%. So: 0.9*34=30.6

Another way to solve it would be to calculate 10%, which would be 3.4, so 34-3.4=30.6

BRAINLIEST
Please answer these

Answers

3.14 is used for pi.

6.  r = [tex]\sqrt{\frac{A}{\pi } }[/tex]

14.00

7. d = [tex]\frac{c}{\pi }[/tex]

5.00

8. d = [tex]2 \sqrt{\frac{A}{\pi } }[/tex]

23.01

9. r = [tex]\frac{c}{2\pi }[/tex]

20.01

10. d[tex]\pi[/tex] = [tex]2 \sqrt{{A}[/tex]

31[tex]\pi[/tex]

11. r[tex]\pi[/tex] = [tex]\frac{c}{2}[/tex]

22.5[tex]\pi[/tex]

Hope this helps :)

Answer:

12. 95.03

13. 52π mm or 52 mm

14. 119.38 meters

15. 227 in²

Note: (make sure to double check all of these because it never hurts to).

Calculate the slope of the coordinates (5,10) (10,20)

Answers

Answer:

m=2

Step-by-step explanation:

A plumber charges a $25 flat rate. If he works for 6 hours, how much does he charge per hour if the total is $67?

Answers

Answer:7

Step-by-step explanation:(67-25) divided by 6

mark as brainliest

Subtract the flat rate from the total first:

67-25 = 42

Now divide that by total hours:

42/6 = 7

Answer: $7 per hour

-15x = -75 I need HELP!!!!

Answers

Answer:

x=5

Step-by-step explanation:

You divide both sides by -15 which gives you a positive 5

Can someone help me

Answers

Answer:

i) 0.1056

ii) 0.105

iii) 0.1

iv) 0.1056

Step-by-step explanation:

0.36, to the power of 2 (0.36×0.36) is 0.1296

0.1296-0.03×0.8=0.1056

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