4. If water is being drained from a swimming pool and V liters is the volume of the water at the time t minutes after the draining starts, where � = 250 1600 − 80� + � 2 , how fast is the water flowing out of the water pool 5 minutes after the draining starts?

Answers

Answer 1

Answer:

Water is leaving at 17500m^3 per minute

Step-by-step explanation:

Given

[tex]V(t)= 250(1600 - 80t + t^2)[/tex]

Required

The rate when time is 5 minutes

We have:

[tex]V(t)= 250(1600 - 80t + t^2)[/tex]

Open bracket

[tex]V(t)= 400000 - 20000t + 250t^2[/tex]

Differentiate

[tex]V'(t) = 0 - 20000 + 2*250t[/tex]

[tex]V'(t) = 0 - 20000 + 500t[/tex]

[tex]V'(t) = -20000 + 500t[/tex]

At 5 minutes, we have:

[tex]V'(5) = -20000 + 500*5[/tex]

[tex]V'(5) = -20000 + 2500[/tex]

[tex]V'(5) = -17500[/tex]

This means that water is leaving at 17500m^3 per minute


Related Questions

A coin bank for donations for the protection of the reef contained Php 1,570. There were twice as many Php 5-coins as

Php 10-coins and 14 less Php 1-coins as Php 5-coins. How many of each kind were there?

Answers

Answer:

There are 144 Php 5-coins, 72 Php 10-coins and 130 Php-1 coins

Step-by-step explanation:

The amount of the coins in the coin bank = Php 1,570

The number of Php 5-coins = 2 × The number of Php 10-coins

The number of Php 5 coins = The number of Php 1-coins + 14

Let 'x' represent the number of Php-5 coins, let 'y' represent the number of Php 10-coins, and let 'z' represent the number of Php 1-coins, we get;

x = 2 × y...(1)

x = z + 14...(2)

5·x + 10·y + z = 1,570...(3)

From equation (1) equation (2), and equation three, we have;

y = x/2

z = x - 14

5·x + 10·x/2 + x - 14 = 1,570

11·x - 14 = 1,570

x = (1,570 + 14)/11 = 144

The number of Php 5-coins, x = 144

y = x/2

∴ y = 144/2 = 72

The number of Php 10-coins, y = 72

z = x - 14

∴ z = 144 - 14 = 130

The number of Php 1-coins, z = 130

❓❓❓❓❓❓ anyone know this

Answers

The answer is (-1,3) and (-2,6)

Answer: (-1,3) ; (-2,6)

Step-by-step explanation:

The solution would be where the two graphs intersect or touch (where the line and the parabola intersect or touch).

Look at the two dots on the plane, where the line and parabola intersect--those are the answers.

Liberal Arts Total Engineering and Physical Sciences 368 Health and Human Services 882 2142 A B Lower than B Total 1890 2268 432 800 630 588 Write all probabilities in correct notation, rounded to three decimal places. Show your work. If you know the grade was lower than a "B", what is the probability that the class was taught in the School of Liberal Arts?​

Answers

Answer:

huh i dont understand

Step-by-step explanation:

the cell phone bill recorded that Jeremiah sent 532 text messages last week. On average how many text messages did he send each day?​

Answers

Answer:

76 messages

Step-by-step explanation:

532 divided by 7 = 76

Answer:

76 Texts

Step-by-step explanation:

Amount of texts/Days = 532/7 = 76

The Cooper family and the Reynolds family took a
vacation together. The Cooper family spent two-
thirds as much as the Reynolds family spent on the
vacation. If the Cooper family and the Reynolds
family spent $1,650 in all, how much did each family
spend?

Answers

Answer: well 2/3 of 1650 is 1100 so 1650-1100=550, so the cooper family spend $1100 and the reynolds family spent $550

Step-by-step explanation: i think that’s right

A party is held in a large tent with a perimeter between 100 m and 150 m. A robot travels along
the perimeter to serve refreshments to guests. It is
programmed in such a way that it travels 3 metres,
then turns through an angle of x degrees clockwise, travels
another 3 metres, then turns through an angle of x degrees
clockwise, and so on, until it reaches its initial
position where the staff will top up the
refreshments. Given that the robot is only able
to turn through an integer value of x, find two
possible values of x and the corresponding
perimeters of the tent.​

Answers

Step-by-step explanation:

the tent can be :

1. perimeter 120 m.

40 sides polygon with 3 metres length each.

so, x = 360/40 = 9°

2. perimeter 135 m.

45 sides polygon with 3 metres length each.

so, x = 360/45= 8°

Step-by-step explanation:

the tent can be :

1. perimeter 120 m.

40 sides polygon with 3 metres length each.

so, x = 360/40 = 9°

2. perimeter 135 m.

45 sides polygon with 3 metres length each.

so, x = 360/45= 8°

Factor using the x method


( please do not answer without showing work )

Answers

Answer:

[tex]5(x + 10)(10x - 3)[/tex]

Step-by-step explanation:

We are factoring

[tex]50x^{2} + 485x - 150[/tex]

So:

((2•5^2x^2) +  485x) -  150

Pull like factors :

50x^2 + 485x - 150  =   5 • (10x^2 + 97x - 30)

Factor

 10x^2 + 97x - 30

Step-1: Multiply the coefficient of the first term by the constant   10 • -30 = -300

Step-2: Find two factors of  -300  whose sum equals the coefficient of the middle term, which is 97.

-300    +    1    =    -299

     -150    +    2    =    -148

     -100    +    3    =    -97

     -75    +    4    =    -71

     -60    +    5    =    -55

     -50    +    6    =    -44

     -30    +    10    =    -20

     -25    +    12    =    -13

     -20    +    15    =    -5

     -15    +    20    =    5

     -12    +    25    =    13

     -10    +    30    =    20

     -6    +    50    =    44

     -5    +    60    =    55

     -4    +    75    =    71

     -3    +    100    =    97

Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  100

                    10x^2 - 3x + 100x - 30

Step-4: Add up the first 2 terms, pulling out like factors:

                   x • (10x-3)

             Add up the last 2 terms, pulling out common factors:

                   10 • (10x-3)

Step-5: Add up the four terms of step 4:

                   (x+10)  •  (10x-3)

            Which is the desired factorization

Thus your answer is

[tex]5(x + 10)(10x - 3)[/tex]

Answer:

[tex] \displaystyle \rm 5({x}^{} + 10)( 10x - 3)[/tex]

Step-by-step explanation:

we would like to factor out the following expression:

[tex] \displaystyle {50x}^{2} + 485x - 150[/tex]

notice that, in every term there's a common factor of 5 thus factor it out:

[tex] \displaystyle 5( {10x}^{2} + 97x - 30)[/tex]

now we have to rewrite the middle term as sum or substraction of two different terms in that case 100x-3x can be considered:

[tex] \displaystyle 5( {10x}^{2} + 100 - 3x - 30)[/tex]

factor out 10x:

[tex] \displaystyle 5( 10({x}^{2} + 10)- 3x - 30)[/tex]

factor out -3:

[tex] \displaystyle \rm 5( 10x({x}^{} + 10)- 3(x + 10))[/tex]

group:

[tex] \displaystyle \rm 5({x}^{} + 10)( 10x - 3)[/tex]

and we are done!

hence,

our answer is B)

Colin pays £721.45 a year on his car insurance.
The insurance company reduces the price by 9.2%.
How much does the insurance cost now?
Give your answer rounded to 2 DP.

Answers

Answer:

Id

I forget

Step-by-step explanation:

The answer is 655.08, 9.2% of £721.45=66.3734, 721.45-66.3734=655.0766, when you round it to 2DP the final answer would be 655.08

What 0.257 to the nearest hundredth

Answers

Answer:

0.26

Step-by-step explanation:

0.2 -> tenth

0.25 -> the 5 is the hundred place

0.257 -> the 7 is the thousand place.

Round the 7 and you get 0.26

Answer:

0.26

Step-by-step explanation:

To round 0.257 to the nearest hundreth, you'd have to look at the five and seven. Since seven is a higher number than four, you'd round the 5 up one, and get rid of the seven.

For further help I suggest this website:

https://www.varsitytutors.com/hotmath/hotmath_help/topics/rounding-decimals

YOU WILL BE A LIFE SAVER PLEASE!!!!

Answers

Answer:

A. 92

Step-by-step explanation:

90 × 6 = 540

92 + 84 + 86 + 94 = 356

540 - 356 = 184

184/2 = 92

Y=5x-9
-2x-3y=-7
Please show
work!

Answers

what are the directions

Answer:

im not sure sweetheart <3

Step-by-step explanation:

Can someone help me figure out the best way to do long division? I have trouble with it every time.

Answers

Answer:

follow the steps

divide

times

minus

bring down

Answer:

It can be hard to understand something especially if you comprehend stuff more differently then the person teaching you

Step-by-step explanation:

But I think doing your research and practicing should help.

WILL GIVE 100 POINTS TO WHOEVER ANSWER THIS CORRECTLY. In the similarity transformation of abc to def, abc was dilated by a scale factor of ?, reflected across the , and moved through the translation

Answers

Answer:

Dialated by a scale factor of two, reflected across the x axis, and transformed three units left

Step-by-step explanation:

The triangle was dilated by a scale factor of 2

What is similarity transformation?

One or more stiff transformations (such as reflection, rotation, and translation) followed by a dilation make up a similarity transformation. An image that resembles the original figure is produced when a figure undergoes a similarity transformation.

The following steps are followed while determining the similarities:

Step 1 is to identify the triangles' pairs of corresponding sides and pairs of matching angles. Step 2 Redraft the triangles with the same orientation and space between them. Step 3 Give the triangles names and create a similarity assertion,making sure to maintain the order of corresponding vertices.

Solution:

Given:

AB=2, AC=1, BC=√5

DC=4, DF=2, EF=2√5

So scale factor is 4/2 = 2/1 = 2√5/√5 = 2

hence we get tha scale factor as 2.

Therefore, In the similarity transformation of abc to def, abc was dilated by a scale of 2.

Learn more about " Similarity of transformation" here-

brainly.com/question/26836817

#SPJ2

Please help I’ll give brainliest

Answers

Answer:

it answer would be 50% coz we take out percentage from 100.

Step-by-step explanation:

first add 17% and 33% it would be 50%

then subtract 50%from 100%

answer would be 50%

50%

Add the percentage to get a 100

In ΔHIJ, i = 9.2 cm, j = 1.4 cm and ∠H=84°. Find the length of h, to the nearest 10th of a centimeter.

Answers

Answer:

9.2

Step-by-step explanation:

lol

Please helpppppppppppppppppppppppppppppppppppp

Answers

Step-by-step explanation:

(2×10^8)(2×10^-2)4×10^8+(-2)4×10^6

stay safe healthy and happy.

Answer:

(THIRD/FOURTH QUESTION): 4,000,000/4,096,000,000

Step-by-step explanation:

Third:

10x10x10x10x10= 100,000

100,000x40= 4,000,000

Fourth:

40x40x40x40x40x40= 4,096,000,000

How to work out Pythagoras Theoram​

Answers

The Pythagorean Theorem works only with right angle triangles. There are three sides: Side A, Side B, and the hypotenuse.

The formula for the Pythagorean Theorem is: a^2 + b^2 = c^2

To find the answer (without the exponent), you should find the square root.

Now that we have the formula, let's apply it to a triangle:

90^2 + 95^2 = c^2 =

8100 + 9025 = 17125

Square root = 130.86252328302

130.86252328302 is the exact measure of the hypotenuse.

I hope this helped!

Please mark brainliest :)

Have an amaing day!

Pls help me with this asap

Answers

Step-by-step explanation:

cutie I don't see anything

Help please ?!?!?!!???????!???!???!!????!!??!??!?!?!!??!?!!????

Answers

Answer: B. clusters: yes; outliers: yes (so sorry if it’s incorrect (: )

Please help me! DO NOT SEND LINK!

Answers

Answer:

So option 4; [tex]\frac{35}{100}[/tex] is the correct option

Step-by-step explanation:

First, we need to convert [tex]\frac{2}{10}[/tex] so it's denominator is 100. To do so, we will multiply the numerator and denominator by 10

[tex]\frac{2}{10} *\frac{10}{10} = \frac{20}{100}[/tex]

Second, we need to add the two fractions to get the current total distance walked. Remember, when adding fractions, the denominator does not change.

[tex]\frac{45}{100} + \frac{20}{100} = \frac{65}{100}[/tex]

Now that we have the total distance walked, we need to subtract that to 1 mile. [tex]1mile=\frac{1}{1} = \frac{10}{10} =\frac{100}{100}[/tex]

[tex]\frac{100}{100} -\frac{65}{100} = \frac{35}{100}[/tex]

So option 4; [tex]\frac{35}{100}[/tex] is the correct option

Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.

Answers

The answer to this problem is 6(x+5)(x+9)

Which angles are vertical angles?

Answers

Answer: BCF AND DCA
Explanation:

The perimeter of a square garden is 54 feet. What is the length of one side of the garden?

Answers

Answer: 13.5

Step-by-step explanation:

54/4 = 13.5

13.5 x 4 = 54

Which of the following is closest to the sample standard deviation of the data set shown below?

{13, 14, 17, 22, 26, 30, 31}


(1) 5.2
(3) 7.4
(2) 6.1
(4) 8.3

Answers

(3) 7.4 is the standard deviation for this data set.

Please help me PLEASE PLEASE PLEASE PLEASE PLEASE

Answers

Step-by-step explanation:

rocket : 26 mpg

Glimmer : 484/18 = 26.89 mpg

cambria : 392/16 = 24.5 mpg

Avenger : 60/2 = 30 mpg

a. Avenger, has the highest mileage

b. cambria, has the lowest mileage

c. Avenger,Glimmer, rocket, cambria

A local rectangular patio that originally measured 5 feet by 10 feet was extended on one side each by x feet. The area of the new, larger, L-shaped extension is 126 square feet.

Write an equation that could be used to solve for x.

Explain how you arrived at your equation, i.e. how does it model the situation stated.

Find the value of x by solving your equation. Show your work.

Answers

Answer:

x=4

Step-by-step explanation:

(5+x)(10+x)=126

50+5x+10x+x^2 = 126

x^2 + 15x +50=126

x^2 + 15x - 76 = 0

(x+19)(x-4) = 0

X=-19, 4

X=-19 is not possible

x=4

Please help. I will give brainliest!

Describe the outlier boundaries for the data set.

34, 38, 41, 40, 36, 36, 38, 40

This is due today...

Answers

Answer:

Step-by-step explanation:

How to Find Outliers Using the Interquartile Range(IQR)

Step 1: Find the IQR, Q1(25th percentile) and Q3(75th percentile). ...

Step 2: Multiply the IQR you found in Step 1 by 1.5: ...

Step 3: Add the amount you found in Step 2 to Q3 from Step 1: ...

Step 3: Subtract the amount you found in Step 2 from Q1 from Step 1:

Is the triangle a right triangle?
4 6 7
Is this a right triangle?

Answers

Answer:

No

Step-by-step explanation:

Given :-

A triangle with some side measure .The sides are 4 ,6,7.

And we need to tell whether it is a right angled triangle or not . It will be a right angled triangle if it follows the Pythagoras Theorem.

Pythagoras Theorem :-

In right angle triangle the sum of squares of the two smallest sides is equal to the square of the largest side .

Here the two smallest sides are 4 & 6 .

Sum of Squares of 4 and 6 :-

[tex]:\implies[/tex] 4² + 6²

[tex]:\implies[/tex] 24 + 36

[tex]:\implies[/tex] 60

Square of 7 :-

[tex]:\implies[/tex] 7²

[tex]:\implies[/tex] 49

And :-

They aren't equal. So the triangle is not a right angled triangle .

Hence the triangle is not a right angle triangle.

Answer:

No, this triangle is not a right triangle.

Step-by-step explanation:

Step 1: Definition(s)/explanations

This is a right triangle, so the Pythagorean Theorem applies.The Pythagorean Theorem states that the legs of the triangle, squared, must equal the hypotenuse, squared.The legs of the triangle are the sides that make the right angle.The hypotenuse is the longest side.

Formula:

[tex]pt-a^2+b^2=c^2[/tex]

[tex]legs=a,b[/tex]

[tex]hypotenuse=c[/tex]

Step 2: Solve.

Now, I just plug the numbers into the formula.

[tex]a^2+b^2=c^2[/tex]

[tex]4^2+6^2=7^2[/tex]

[tex]16+36\neq 49[/tex]

If the legs of the triangle do not equal the hypotenuse, then the triangle cannot be a right triangle.

Step 3: Conclude.

Therefore, the triangle cannot be a right triangle.

which term can be used to describe the relationship between <A and <B

A.Complementary
B.Supplementary
C.Vertical
D.Acute

(look at the picture)

Answers

Answer:

D. Acute

Step-by-step explanation:

Acute because both <A and <B are less then 90 degrees

Hope this helps :).

Answer:

Option A

Step-by-step explanation:

Given :-

A line is given which has three angles a , b and 90° .

We need to find the relationship between a and b. Also we know that the measure of angle of straight line is 180 ° .

According to Question :-

[tex]:\implies[/tex] a + b + 90° = 180°

[tex]:\implies[/tex] a + b = 180° - 90°

[tex]:\implies[/tex] a + b = 90°

Hence the angles a and b are complementary.

Use the compound interest formula to determine the final value of the given amount.
​$900 at 7​% compounded annually for 6 years

The final value is $ ?

Answers

Answer:

1,931.99$ is the answer

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