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:
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Find the LCM of 5, 6 and 9.
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.
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
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
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
the graphs show information about the different journeys of 4 people
Answer:
sorry id like to help but i need more info.
Step-by-step explanation:
i hope this helps!
BRAINLIEST
Please answer these
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).
how to solve 15=6+2(n-3) + 3n
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!!!!!
;)
HELP ME PLEASE GUYS!! :)
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! :)
help plzz
2decimal places
165 x 0.38²
Answer:
23.83
Step-by-step explanation:
Calculate the slope of the coordinates (5,10) (10,20)
Answer:
m=2
Step-by-step explanation:
Find the first six terms of a sequence represented by f(n) = 6(n-2)
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
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.
Answer plz I need the answer
Answer:
D) 3x + 33
Step-by-step explanation:
3(x + 11)
3x + 33
Hope this helps! Pls give brainliest!
um. ill give brainliest help please !!!
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 :)
Help me..What is the length of the missing leg? If necessary, round to the nearest tenth.
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
Given f(x) = 3x^2 + 2x – 1 and g(x) = 4x-5 find ( g of f) (-2)
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]
Which of the following solution sets represent the inequality 3-1/2x>10?
[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]
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?
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
Plz help me thx
Simplify pt2:
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]
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.
Answer:
3.02
Step-by-step explanation:
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
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 :
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Please help me!!!! Thank you
[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 ~
solve one step equation
x/-2 = -3
Answer:
x=6
Step-by-step explanation:
x/-2=-3
*-2 *-2
x=6
-hope it helps
34x 10% discount. What the absolute FLIP
is the answer.
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
If f(x) = 9(x - 7)^2 – 8
Find f( – 4)
Answer:
1,081
[tex]f( - 4) = 9( - 4 - 7) {}^{2} - 8 \\ f( - 4) = 9( - 11 {)}^{2} - 8 \\ f( - 4) = 1081[/tex]
-15x = -75 I need HELP!!!!
Answer:
x=5
Step-by-step explanation:
You divide both sides by -15 which gives you a positive 5
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.
Answer:
Cost of 1 = 30
So cost of 8kg apples=8*30
=240
Step-by-step explanation:
Can someone help me
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
Find the inverse of the function 6-5x
decide whether the function is a polynomial function if it is write the function in standard form
f(x)=1/2x²-3x^4-7
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 : )