Oil from a leaking container radiates outwards in the form of a circular film on the water surfaces.
If the area of the circle increases at rate of 900m²/s, how fast is the radius of the circle
increasing when the area is 1400 z m??
[6 marks)
[Ans:3.83m/s]

Answers

Answer 1

[tex] \frac{dr}{dt} = 6.79 \: \frac{m}{s} [/tex]

Step by Step Explanation:

The area a is defined as

[tex]a = \pi {r}^{2} [/tex]

Now take derivative of the above expression with respect to time:

[tex] \frac{da}{dt} = 2\pi r \frac{dr}{dt} [/tex]

Solving for dr/dt, we then get

[tex] \frac{dr}{dt} = \frac{1}{2\pi r} \frac{da}{dt} [/tex]

Note that da/dt = 900 m^2/s and when the area of the oil slick is 1400 m^2, the radius r is r = √(1400/π) = 21.1 m. Therefore,the rate at which the radius is increasing dr/dt is

[tex] \frac{dr}{dt} = \frac{1}{2\pi(21.1 \: m)}(900 \frac{ {m}^{2} }{s} ) = 6.79 \frac{m}{s} [/tex]


Related Questions

2. Evaluate the expression when x = 7 and y = 4 x * y - 4(2)

Answers

Answer:

20

Step-by-step explanation

7*4=28

28-4=24

4(2)=8

28-8=20

hope that helped!!

Answer:

y = 8/27

Step-by-step explanation:

given

x = 7

y = 4x*y - 4(2)

y = 4*7*y - 8

y = 28y - 8

8 = 28y - y

8 = 27y

8/27 = y

to prove

y = 4x*y - 4(2)

8/27 = 4*7*y - 8

8/27 = 28*8/27 - 8

8/27 = 224/27 - 8

8/27 = 224 - 27*8/27

8/27 = 8/27

hence it is proved that y is 8/27 .

The area of a sector created by a 120° angle is 4 pi in squaredWhat is the area of a sector created by an angle of 30°
in the same circle

Answers

Answer:

π in²

Step-by-step explanation:

We'll begin by calculating the radius of the circle. This can be obtained:

Area of sector (A) = 4π in²

Angle (θ) = 120 °

Radius (r) =?

The radius of the circle can be obtained by using the formula for calculating the area of a sector. This is illustrated below:

A = θ/360 × πr²

4π = 120/360 × πr²

4π = ⅓ × πr²

Cross multiply

3 × 4π = πr²

12π = πr²

Divide both side by π

r² = 12π / π

r² = 12

Take the square root of both side

r = √12 in

Thus, the radius is √12 in.

Finally, we shall determine the area of the sector created by 30 °. This can be obtained as follow:

Radius (r) = √12 in

Angle (θ) = 30 °

Area of sector (A) = ?

A = θ/360 × πr²

A = 30/360 × π(√12)²

A = 1/12 × 12π

A = π in²

Therefore, the area of the sector created by 30 ° us π in².

What is the value of ?

Answers

Answer:

x=3

Step-by-step explanation:

Log base 5 of 125=x

that is equal to 5x5x5 which is 125

5 is multiplied 3 times so x is 3

Answer is 3 so pretty much I’m done

if x=-4 then what is x^2? in an equation for my homework, they have the solution as positive instead of negative and I don’t understand why.

Answers

Since x=-4
X^2 = -4^2
16.

Answer:

see explanation

Step-by-step explanation:

Given

x² , then when x = - 4

x² = - 4 × - 4 = + 16

[ the product of a negative and a negative results in a positive ]

Which of the following is geometric sequence
A. 1,1/2,1/4,1/8
B.2,4,6,8
C.1,1,2,3,5
D.7,4,1,-2

Answers

Answer:

A

Step-by-step explanation:

...................

Answer:

here's the whole unit test

Step-by-step explanation:

ur welcomeeeee ;)

solve
(3431​)−2/3÷(491​)3/2

a. 16807
b.343
c.49
d.2401​

Answers

Try photo math it is very helpful

4th grade math question

Answers

Answer:

1 1/6

Step-by-step explanation:

the problem is asking you to do 1/6 7 times. Lets break it down and make it 1/6 plus 1/6 plus 1/6 plus 1/6 plus 1/6 plus 1/6 plus 1/6

so lets add the all the numerators 1 plus 1 plus 1 plus 1 plus 1 plus 1 plus 1 is 7

the numerator value is 7 and you dont add the denominator so it stays as 6

so the answer is 7/6 or 1 1/6 as a mixed number

Answer:1 1/6

Step-by-step explanation: The answer is one and one sixth because when you imagine that the 7 is over one, when you times it you get 7/6 and that is 1/ 1/6

Which of the following are the domain and range that represent the inverse of the function f(x), given the mapping diagram of f(x) below? 1 AWN O 2. 4 6 8​

Answers

Answer:b

Step-by-step explanation:

Find Z for the following sequence:
210, 209, 213, 186, 202, Z

Answers

Answer:

77

Step-by-step explanation:

as far as I can tell the steps between the given numbers are

-1

+4

-27

+16

1 can be expressed as 1³

4 can be expressed as 2²

27 can be expressed as 3³

16 can be expressed as 4²

my best guess is that next one is minus 5³ = -125

edit: technically the given steps can be expressed as

(-1)³

(-2)²

(-3)³

(-4)²

somewhat nicer pattern there

{3/4 x (3/3/4 ÷ 5/16)} -3/1/3

Answers

I did this online and got this hope this helps

An airplane flying at an altitude of 37,000 feet is still A horizontal distance of 100 miles (100 miles = 5280 ft) from the airport. What angle of depression does the airplane need to use to reach the runway?

Answers

Given :

An airplane flying at an altitude of 37,000 feet is still A horizontal distance of 100 miles (100 miles = 5280 ft) from the airport.

To Find :

What angle of depression does the airplane need to use to reach the runway?

Solution :

Let, angle of depression is [tex]\theta[/tex] .

So,

[tex]tan\ \theta = \dfrac{ Altitude \ in \ which \ plane \ is \ flying}{Horizontal \ Distance}\\\\tan \ \theta = \dfrac{37000}{5280}\\\\tan \ \theta = 7.00\\\\\theta = tan^{-1} 7\\\\\theta = 81.87^o[/tex]

Hence, this is the required solution.

I need help with this with work asap thank you

Answers

Answer:

multiply all sides (5.5 x 6 x 8.5) which results to 261.5 ft squared

Can someone help me? Question attached, 20 points.

Answers

Answer:

6

Step-by-step explanation:

[tex]V = A * b = 5A[/tex]

[tex]5A = 141.3[/tex]

[tex]A = 28.26[/tex]

[tex]\pi r^2 = 28.26[/tex]

[tex]3.14 r^2 = 28.26[/tex]

[tex]r^2 = 9[/tex]

[tex]r = 3[/tex]

[tex]D = 2r = 2 * 3 = 6[/tex]

- Leona Bahr is paid a commission of 12% on all sales above $7,000 for the week. She is also paid a weekly salary of $380. What are her total earnings for a week in which her sales were $9,800?

Answers

Answer:

716

Step-by-step explanation:

9800-7000=2800 sales over 7000

2800 x .12=336 commission

380 (salary) + 336 (commission)=716 Total earnings

accounting equation is what​

Answers

The accounting equation also called the balance sheet equation represents the relationships between the assets,liabilities etc
I agree with what the other person said

Help me...!
!!
!!
!!
!!

Answers

The answer to this question is:

2 ¾ inches.

The answer to question would be 2 3/4.

Can anyone solve this?

Answers

Answer:

They are congruent

Step-by-step explanation:

The reason that WK is congruent to WL is because both come from the same origin of W and they both end up in the same place on their side. Which means if WK and WL are congruent, that means that AK and AL are congruent as well.

Which choice is equivalent to the fraction below when x is an appropriate
value? Hint: Rationalize the denominator and simplify.
4
4 - 6x
A. 8+226x
16 - 6x
B. 8+ 2162
846
C.
2 + V6
4- 6x
D. 8. 216
8 - 3x
UN

Answers

1. 8^3 * 8^2, 8^5, and (2^3)^5

2. 6^9, and 6^5 x 6^4

Answer:

8+2√6x / 8-3x

Step-by-step explanation:

yes

Sarah can do 68 push ups in 4 minutes . At this rate how many push ups can she do each minute?

Answers

Answer:

Sarah can do 17 push-ups each minute.

Step-by-step explanation:

4 minutes = 68 push ups

68  divided by 4 = 17 push ups

1 minute = 17 push ups

- 12. What is the greatest common factor of 120 and 84?
e.
a. 3
b. 6
12
18
d.

Answers

Answer:

12 (the third one is the greatest common factor of 120 and 84)

Answer:

12

Step-by-step explanation:

factors of 120. 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,80,120

factors of 84: 1,2,3, 4,6,7,12,14,28,42,84

greatest common factor=12

The area of A PQR is 15 m², and p = 5 m, q = 10 m.
Find the possible measure of angle R (in degrees)

Answers

i don’t know mannmmnnndjj xjhdjajji

PLEASE HELP i dont know the answer for: Chose an equivalent ratio 15 cats to 20 dogs. choices: A. 4 to 5. B. 3 to 4. C. 3 to 5. D. 10 to 15.

Answers

Answer:

D 10 to 15 is the answer correct

Someone tell me what the answer

Answers

NEED A BETTER PICTURE FRIEND :)

Answer:

can you please put a better picture?

11x+x^2= 2y
Y + x = 19

Answers

Answer:

x = -15,46 thì y ≈ 34,46

x = 2,46 thì y ≈ 16,54

Step-by-step explanation:

x + y = 19 => x = 19 - y (1)

thay x = 19 -y vào phương trình 11x + x^2 = 2y ta có:

11 * (19 - y) + (19 - y)^2 =2y

=> 209 - 11y + 361 - 38y + y^2 = 2y

=> y^2 - 51y + 570 = 0

=> y ≈ 34,46 và y≈16,54

thay y ≈ 34,46 vào phương trình (1) có:

x = 19 - 34,46 = -15,46

thay y ≈ 16,54 vào phương trình (1) có:

x = 19 - 16,54 = 2,46

Answer:

Step-by-step explanation:

11x+x^2= 2y

Y + x = 19

Multiply and re-arrange second equation:

2y = 38 - 2x

Substitute into first equation:

11x + x^2 = 38 - 2x

Re-arrange:

x^2 + 13x - 38 = 0

Solve using quadratic formula:

x = (-13+(13^2-4*(-38))^(1/2))/2 or (-13-(13^2-4*(-38))^(1/2))/2

x = 2.46 or -15.46

Substitute back to solve for y:

y = 19 - 2.46 or 19 + 15..46

y= 16.54 or 34.46

A.3 1/4
B.1 3/4
C.2 1/4
D.3/3

Answers

The answer is A 3 1/4 hope that helped

Answer:

A. 3 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Which is an asymptotic of the graph of the function y=cot [x- 2pi/3]

Answers

Answer:

B

Step-by-step explanation:

The asymptote of the function [tex]y = cot(x - \frac{2\pi}{3})[/tex] is at x = - π/3.

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, tan = sin/cos.

Hence 1/tan = cos/sin = cot.

So, The denominator sin can not be zero, And sin is zero on π and - π.

Given, A function [tex]y = cot(x - \frac{2\pi}{3})[/tex].

At, x = - π/3.

Therefore, [tex]y = cot(\frac{\pi}{3} - \frac{2\pi}{3})[/tex].

[tex]y = cot(-\pi)[/tex], Which is undefined.

learn more about asymptotes here :

https://brainly.com/question/17767511

#SPJ7

Solve for x. Round to the nearest tenth, if necessary. C С B x 25 34° А

Help with this problem please.​

Answers

Answer:

59 or I’m wrong

Step-by-step explanation:

Answer:

x=20.7

Step-by-step explanation:

using cosine...

cos 34=adjacent/hypotenuse

cos 34=x/25

Cross multiply

x=cos 34 ×25

x=20.72593931

x≈20.7(to the nearest tenth)

Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. The local Tupperware dealers earned these commissions last month: $1077.28, $2661.13, $4642.11, $4264.15, $1019.55, $3444.20, $2525.92, $3740.26, $3533.07, $1633.84 What was the mean commission earned? Round your answer to the nearest cent.

Answers

Answer:

the  mean commission earned is 2854.15

Step-by-step explanation:

The computation of the mean commission earned is shown below'

The mean is  

= ($1077.28 + $2661.13 + $4642.11 + $4264.15 + $1019.55 + $3444.20 + $2525.92 + $3740.26 + $3533.07 + $1633.84) ÷ 10

= 2854.15

Hence, the  mean commission earned is 2854.15

The same should be considered and relevant

Student spend 5 minutes of every 60 minutes at school moving from class to class. Which fraction is equivalent to the number of minutes student spend moving from class to class?

Answers

Answer:

10/120

Step-by-step explanation:

Twice a number divided by 5 gives 4

simple equations

Answers

Answer:

x=10

Step-by-step explanation:

Let the number = x

∴ 2x/5=4

∴2x=5*4

∴2x=20

∴x=20/2

∴x=10

Hope it helps you!

Mark as brainliest if you like it  

Answer:

2x / 5 = 4

x = 10

Step-by-step explanation:

Twice a number   divided by 5   gives 4

          2x                     / 5                  = 4

2x / 5 = 4

Multiply both sides by 5

2x = 20

Divide both sides by 2

x = 10

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