The radius of a sphere is decreasing at a rate of 2 centimeters per second. At the instant when the radius of the sphere is 3 centimeters, what is the rate of change, in square centimeters per second, of the surface area of the sphere? (The surface area S of a sphere with radius r is S​ = 4πr2.)

Answers

Answer 1

Answer:

The rate of change of the surface area of the sphere is;

-48π cm^2/s

Step-by-step explanation:

Here, we want to calculate dA/dt

Mathematically that will be;

dA/dt = dA/dr * dr/dt

From the question;

dr/dt = -2 cm/s

dA/dr = 8πr

So dA/dt will be;

-2cm/s * 8πr = -16 πr cm/s where r is 3 cm

So;

dA/dt = -48π cm^2/s

Answer 2

Using implicit differentiation, it is found that the rate of change of the surface area of the sphere is of -151 square centimetres per second.

The surface area of an sphere of radius r is given by:

[tex]S = 4\pi r^2[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]S = 8\pi r\frac{dr}{dt}[/tex]

For this problem:

The radius of a sphere is decreasing at a rate of 2 centimetres per second, hence [tex]\frac{dr}{dt} = -2[/tex]It also is of 3 centimetres, hence [tex]r = 3[/tex]

The rate of change is of:

[tex]S = 8\pi(3)(-2) = -48\pi = -151[/tex]

The rate of change of the surface area of the sphere is of -151 square centimetres per second.

A similar problem is given at https://brainly.com/question/11496075


Related Questions

which statement is true?

Answers

B is the correct answer

please help me thanks

Answers

Answer:

C:124

Step-by-step explanation:

10+2=12

30+20=50

10+30=40

2+20=22

12+50+40+22=124

What is the slope of this here line?

Answers

It’s 3/5 usuzjshwiwnshs

Answer:

3/5

Step-by-step explanation:

It rose 3 and ran 5 (rise over run)

Answer please I dont understand

Answers

Answer: 8m

Step-by-step explanation:

Anything raised to 0 is 1.

8m*1

Multiply 8 by 1.

8m

Express this number in scientific notation. 0.15880.1588

Answers

Answer: 1.588×10−1 (The negative one is small on the top right of the 10)

Step-by-step explanation: Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

WHO WANTS BRAINLIESTT ?????? PLEASE answer this question correctly !!!! STEP BY STEP !!!!!!!!!!!!!!!

Answers

Answer:

x = 45

y = 60

Step-by-step explanation:

2x = 90

2x (1/2) = 90 (1/2)

x = 45

3y - 2y = 90

3y - 2(45) = 90

3y - 90 = 90

3y - 90 (+90) = 90 (+90)

3y = 180

3y (1/3) = 180 (1/3)

y = 60

Hope this helps :)

HELP!!!! THIS IS DUE AT 9:30!!!

Answers

Answer:

C) x=8

Step-by-step explanation:

180=40+(8x-24)+(6x+10)

180=26+14x

154=14x

11=x

[tex]11\neq8[/tex]

What is the value of g divided by 4, if g = 20?

Answers

G divided by 4 will be 5.

If g equals 20, and you divided 20 by 4, your quotient will be 5.

Hope this helps and Happy Holidays! :D

Answer:

5

Step-by-step explanation:

I took the test and got a 100%

Help I’m being timed!!!!

Answers

Answer:

C the 3 one is the answer

determine if graph is a function ​

Answers

No it is not a function.

Angelo grows vegetables and sells them at a farmers'
market. The price of 2 cucumbers and I pepper is
$3.15, and the price of 3 cucumbers and 2 peppers is
$5.35. Based on this pricing, what would be the price,
in dollars, of 4 cucumbers and 3 peppers?

Answers

Answer:

$7.55

Step-by-step explanation:

We can solve this by using a system of equations. The equations would be set up like this:

[tex]2c + p = 3.15\\3c + 2p = 5.35\\[/tex]

Let's isolate a variable in the first equation:

[tex]p = -2c + 3.15[/tex]

Now we can plug this in to the second equation:

[tex]3c + 2(-2c + 3.15) = 5.35\\3c - 4c + 6.3 = 5.35\\-c + 6.3 = 5.35 \\-c = -.95\\c = .95[/tex]

Now that we have found c we can find p by plugging c in to an equation

[tex]2(.95) + p = 3.15\\1.9 + p = 3.15\\p = 1.25[/tex]

We have found both variables now we can use the following equation to answer the question:

[tex]4c + 3p = ?\\4(.95) + 3(1.25) = ?\\3.8+3.75 = 7.55[/tex]

Therefore, the price in dollars of 4 cucumbers and 3 peppers is $7.55.

I hope this helps!!

- Kay :)


The price of a cd was decreased by 20% to £7.68. What was the price before the decrease?

Answers

The answer is £10.75

Tyler’s brother works in a shoe store. The store was selling a pair of shoes for $80. They now are on sale for $50. What is the percentage of markdown on the shoes?

Answers

40% Because if the shoe is $80 and went on sail to $50 they would have to raise the original price by 20% there for when they say it’s on sail for 30% off it’s really should just be 20% off

Angle WXY underwent a sequence of two rotations around different centers. The original size of WXY is 82°. what is the size of the angle after the sequence of rotations?

Answers

Given:

[tex]\angle WXY=82^\circ[/tex]

It underwent a sequence of two rotations around different centers.

To find:

The size of the angle WXY after the sequence of rotations.

Solution:

We know that, rotation is a rigid transformation. It means, the size and shape of the figure remains the same after the rotations. It other words, the figure and its image are congruent after rotation.

So, the measure of angle WXY remains same after the sequence of rotations, i.e.,

[tex]\angle W''X''Y''=82^\circ[/tex]

where, [tex]\angle W'X"Y"[/tex] is the image of [tex]\angle WXY[/tex]  after the sequence of rotations.

Therefore, the size of the angle WXY after the sequence of rotations is 82°.

Calculate value of x
A=24.9
B=19.1
C=10.3
D=12.3

Answers

Answer:

C. 10.3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Trigonometry

[Right Triangle Only] cos∅ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use Trig Rations to solve for the missing side

Step 2: Identify Variables

Adjacent leg = x

Hypotenuse = 16

Angle ∅ = 50°

Step 3: Solve for x

Set up equation:                    cos50° = x/16Isolate x:                                 16cos50° = xEvaluate:                                 10.2846 = xRewrite:                                   x = 10.2846

Find the value of x. Give reasons to justify your solution-

Answers

Answer:

x = 34

Step-by-step explanation:

∠ PSR and ∠ TSU are vertical angles and congruent, then

∠ PSR = 4x, thus ∠ PSQ = x

The exterior angle of a triangle is equal to the 2 opposite interior angles.

∠ SQR is an exterior angle of Δ PQS , thus

x + x = 68

2x = 68 ( divide both sides by 2 )

x = 34

Answer:

X = 34°

Step-by-step explanation:

In order to solve this question we will need to know the following, when two lines intersect the opposite angles at that point are equal to each other, that the sum of all angles of a triangle is 180 degrees, and that the angle of a straight line is equal to 180 degrees.

Frist we will have to notice that ∠TSU is equal to ∠PSR, because they are opposite to each other (If you would like to understand this more you can research on a topic call "vertical angels"). Now it is important to understand the following.

∠PSR  = ∠PSQ + QSR

Since ∠PSR = ∠TSU = 4x, ∠QSR = 3x ⇒

⇒ ∠PSR  = ∠PSQ + QSR

   4x = ∠PSQ + 3x

   4x - 3x = ∠PSQ

   x = ∠PSQ

Now, since the sum of all angles in a triangle is equal to 180 we can now say the following:

∠QPS + ∠PSQ + ∠PQS = 180°

In order to find out what PQS is equal to we need to use our knowledge about the angel of a strait line (the angel of a strait line is equal to 180°).

So now we can say the following:

180° = ∠PQS + SQR

∠PQS = 180° - ∠SQR

Since we know that ∠SQR = 68° ⇒

⇒∠PQS = 180° - ∠SQR

  ∠PQS = 180° - 68°

  ∠PQS = 112°

Since ∠QPS = x, PSQ = x, and ∠PQS = 112° ⇒

⇒ ∠QPS + ∠PSQ + ∠PQS = 180°

   x + x + 112° = 180°

  2x = 180° - 112°

  2x = 68°

  x = 34°

Which number line represents the solution to the inequality −7x−13≥8

7
x

13

8
?

Answers

Answer:

x≥−  

7

13

Step-by-step explanation:

-7x<=13

Anybody know how to do this? Solve for RT.

Answers

Answer:

78

Step-by-step explanation:

x + 21 = 3x - 15

- x          - x

21 = 2x - 15

+ 15       + 15

36 = 2x

/ 2     / 2

18 = x

2 (x + 21)

2 (18 + 21)

36 + 42

78

What is the area of the triangle?
A. 8.64 ft2
B. 10.8 ft2
C. 14.4 ft2
D. 17.28 ft2

Answers

Answer: 8.64

Step-by-step explanation:

3.6 * 4.8 = 17.28

17.82/2 = 8.64

Answer:

A. 8.64 ft²

Step-by-step explanation:

The equation for the area of a triangle is A = 1/2bh

b is base and in this case 4.8

h is height and in this case 3.6

A = 1/2 (3.6)(4.8)

A = 8.64

Hope this helped :)

Lamar planted 56 flowers in his garden. The ratio or orange to yellow flowers planted was 25
2
5
. How many yellow flowers did Lamar plant?

Answers

Answer:

I think its 31

Step-by-step explanation:

because the ratio was 25/56 of orange flowers,

so the rest of them are yellow

What are the measures of the angles in the triangle?
(6x + 10°
(x + 17)
(4x - 34)
O 34; 112; 112
078; 51; 51
O 112; 34; 34
O 60; 60; 60
Help it’s times

Answers

Answer:

it is either A or D

Step-by-step explanation:

Select the correct answer.
Write an expression to represent the product of -3 and the square of a number decreased by 8.
How many terms are in your expression?
4
2
3
1

Answers

Answer:2

Step-by-step explanation:

plss answer it is so important ​

Answers

Answer:

1. (100-5) × (100+3) = 10000 + 300 - 500 - 15

=> 10300 - 515 = 9785

2. (500+1) × (500+2) = 250000 + 1000 + 500 + 2

=> 251502

Help me and I’ll give BRAINLEST

Answers

Answer:

The expression I got is (12d+12m+3a+6c)

MATH PLEASE HELP TwT

Answers

Answer:

The first and the third answer!

Step-by-step explanation:

The slope is NOT -6, it is -3/2 !!

The y intercept is 0

and the last one isn't right bc the slope and intercept is wrong!!!

I hope this helps, tho!! Have an awesome day :D

Ian bought a cup of coffee. At first, he sipped slowly. As it cooled down, he drank more quickly. The last bit was cold, and he dumped it out

Answers

Answer:

ian just wasted the last bit of coffee.

Step-by-step explanation:

how much is 4.189 as a fraction?​

Answers

Answer:

4 189/1000 or you if you want to simplify it you can do that also

4 / 1.21 what’s the answer?

Answers

Answer:

3.30

Step-by-step explanation:

bj...

Suppose that you own a compact car

that you bought new for 18,000 dollars.

The value of this particular make of car is

known to depreciate at a rate of 20%

per year.

Define a unit for each quantity in the

worksheet. Then enter a variable for

the time since you bought the car new

Answers

Answer:

Depreciation and Written Down Value for first 5 years of purchase is explained.

Step-by-step explanation:

The Car was purchased for $18000 this will be depreciated at a rate of 20% per year.

Declining Method

Year 1

$18,000 * 20% = $3,600 Depreciation

$18,000 - $3,600 = $14,400 Written Down Value WDV

Year 2

$14,400 * 20% = $2,880 Depreciation

$14,400 - $2,880 = $11,520 WDV

Year 3

$11,520 * 20% = $2,304 Depreciation

$11,520 - $2,304 = $9,216 WDV

Year 4

$9,216 * 20% = $1,843 Depreciation

$9,216 - $1,843 = $7,373 WDV

Year 5

$7,373 * 20% = $1,475 Depreciation

$7,373 - $1,475 = 5,898 WDV

Evaluate the expression when m= -6.
m^2 + 7m+8

Answers

mhmmm maybe it’s uh mhm

Answer:

2

Step-by-step explanation:

(-6)^2+7(-6)+8

36-42+8

=2

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