If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at which the diameter decreases when the diameter is 10 cm.

Answers

Answer 1

Answer:

The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.

Step-by-step explanation:

Surface area of a snowball:

A snowball has a spheric format, which means that it's surface area is given by:

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

In which r is the radius, which is half the diameter. In function of the diameter, the area is given by:

[tex]A = 4\pi(\frac{d}{2})^2 = \pi d^2[/tex]

Solving the question:

To solve this question, we have to implicitly derivate the area in function of t. So

[tex]\frac{dA}{dt} = 2d\pi\frac{dd}{dt}[/tex]

Snowball melts so that its surface area decreases at a rate of 3 cm2/min

This means that [tex]\frac{dA}{dt} = -3[/tex]

Find the rate at which the diameter decreases when the diameter is 10 cm.

This is [tex]\frac{dd}{dt}[/tex] when [tex]d = 10[/tex]. So

[tex]\frac{dA}{dt} = 2d\pi\frac{dd}{dt}[/tex]

[tex]-3 = 20\pi\frac{dd}{dt}[/tex]

[tex]\frac{dd}{dt} = -\frac{3}{20\pi}[/tex]

[tex]\frac{dd}{dt} = -0.0477[/tex]

The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.


Related Questions

A Random survey of 25 students in each grade level of school was conducted to determine whether the students preferred to have less time between classes. The results are shown in the table

Answers

Answer:it is b

Step-by-step explanation:

Because I know

WHO WANTS BRAINLIEST FOR HELPING ME!
also can u explain how to solve ;[

Answers

Answer:

20

Step-by-step explanation:

The equation for area of a triangle is base times height divided by two.


Find the exact trigonometric value:
sin 255

Answers

Answer:

−0.965925826289068

Step-by-step explanation:

sin 255 = −0.965925826289068

What the person said above is correct

a = 3 and c = 12 c/a =

Answers

Answer:

4, because 12/3 is 4 cause 3×4=12

Answer: 4

Step-by-step explanation: you need to divide 12 and 3 to get 4.

The data is shown below:
91, 48, 86, 49, 77, 86, 64, 78
What is the median?

a. 72.37
b. 74
c. 86

Answers

Answer:  72

Step-by-step explanation: Its in the middle

Is it a function yes or no

Answers

Answer:

no

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Solve the equation. 7x = 3x^2 - 1

Answers

Answer:

Step-by-step explanation:

Answer:

If you still need help search up Mathaway it gives u the answer to all your problems and it gives a step by step explination

Step-by-step explanation:

Subtract

3

x

2

from both sides of the equation.

7

x

3

x

2

=

1

Add

1

to both sides of the equation.

7

x

3

x

2

+

1

=

0

Use the quadratic formula to find the solutions.

b

±

b

2

4

(

a

c

)

2

a

Substitute the values

a

=

3

,

b

=

7

, and

c

=

1

into the quadratic formula and solve for

x

.

7

±

7

2

4

(

3

1

)

2

3

Simplify.

Tap for more steps...

x

=

7

±

61

6

The final answer is the combination of both solutions.

x

=

7

+

61

6

,

7

61

6

The result can be shown in multiple forms.

Exact Form:

x

=

7

+

61

6

,

7

61

6

Decimal Form:

x

=

2.46837494

,

0.13504161

3. $595 refrigerator; 22% discount.
Show the work

Answers

Answer:

Discount: $130.90

Total cost after discount: $464.10

Step-by-step explanation:

Since I don't know what the actual question is, I will solve for the discount:

595 × 22%

Convert percentage into decimal

595 × 0.22

130.9

Discount is 130.9

Now I'll solve for how much that will take off from the original price:

595 - 130.9

464.1

Branliest to correct answer no guessing explain how you got your answer

Answers

Answer:

the answer is 1771! good luck!

Step-by-step explanation:

i attached an image with the steps!

What is the probability of flipping a coin 85 times and getting tails 30 times or
fewer?
A. 99.8%
B. 33.2%
C. 95.9%
D. 0.4%

Answers

Answer:

C

Step-by-step explanation:

Answer:

0.4

Step-by-step explanation:

Karim began his day by drinking 1 1/8

cups of milk at breakfast. By the end of the day, he drank a total of 2 2/3

cups of milk.


Which equation and solution correctly represent the amount of milk in cups, m , Karim drank after breakfast?

Answers

Answer:

A. 1⅛ + m = 2⅔

[tex] m = 1\frac{13}{24} [/tex]

Step-by-step explanation:

Cups of milk at breakfast = 1⅛

Cups of milk after breakfast = m

Total cups of milk by the end of the day = 2⅔

Thus:

Total cups of milk by the end of the day = cups of milk at breakfast + cups of drink after breakfast

Therefore:

1⅛ + m = 2⅔ (equation)

Solve for m

Subtract 1⅛ from each side

m = 2⅔ - 1⅛

Convert to improper fraction

m = 8/3 - 9/8

m = (64 - 27)/24 = 37/24

[tex] m = 1\frac{13}{24} [/tex]

a lot of points, Show your work to explain how you found your answers?

Answers

Answer:

5500 ml or 5.5 liters

Step-by-step explanation:

First, we should note that there are 1000 milliliters in 1 liter of liquid.

So, in milliliters, Peter filled three containers with 1500 ml, 750ml, and 2250 ml with 1000ml left over.

To find the total amount, we find the sum of all the milliliters:

1500 + 750 + 2250 + 1000 = 5500 ml

Again, we know that there are 1000 milliliters in 1 liter of liquid, so:

[tex]\frac{5500}{1000}[/tex] = 5.5 liters

5500ml I think that is the answer hope this helps

help me plz branniest to whoever is right

Answers

Answer:

x= -7, x=8

Step-by-step explanation:

factoring method..

f (x) = - x² + 12x - 20

= - x² + 10x + 2x - 20

= - x( x - 10 ) + 2( x - 10 )

= ( x - 10 ) ( -x + 2 )

=> x = 10, x = 2

No links please and make sure its correct.

Answers

Answer:

it is B

Step-by-step explanation:

he is putting in by the 3/5

Answer:

C.

Step-by-step explanation:

Why its C...

You can tell that on the top it say that the total is 15 so it can not be a. So now our answer choices are B, C, ad D.

Now it says that there are 3/5 highlighted but since the rest say 3/5 we can not eliminate yet.

Next we would multiply 3 x 3 to get 9 for how many dollars there are. Cross out B.

Between C and D, C is the most reasonable answer because it says how much did he put in the bank while the other one (D) says how much did he spend?

So it would be C

Hope this helps :)

A rectangular poster has an area of 38 square feet. It is 4 3/4 feet wide at its base. What is the height of the poster

Answers

Answer: The height is 8

Step-by-step explanation:

4.75 x 8 = 32

Which answer best describes the shape of this distribution?


uniform

skewed left

bell-shaped

skewed right
An untitled line plot from 35 to 49. The plot displays the following values as dots above the corresponding value on the number line. One dot at 36. One dot at 37. One dot at 38. One dot at 40. Two dots at 41. One dot at 42. Three dots at 43. Four dots at 44. Five dots at 45. Three dots at 46. Two dots at 47. One dot at 48.

Answers

Answer:

huh what am i looking at

Step-by-step explanation:

step-by-step explanation

Answer:

its skewed left if you are in k12

Step-by-step explanation:

A spinner has 3 equal sections that are purple, green, and blue. What is the probability of not landing on blue?

Answers

Answer:

P(not landing on blue section)=2/3

Step-by-step explanation:

Not landing on blue section = landing on one of the other sections

the remaining sections are 2 each one has a P=1/3

2 × 1/3 = 2/3

Answer:

66%

Step-by-step explanation:

2 divided by 3= 0.666666666 which is then converted to percent (66%)

A woman had $200. She went to a meatshop,
a bookstore and a drugstore. She spent four
times as much money at the meatshop as she
did at the drugstore. She spent $15 less at the
bookstore than at the drugstore. She then had
$5 left.
(a) Using $x to represent the amount she spent
at the drugstore, express in algebraic terms
(i) the amount she spent at the meatshop
(ii) the amount she spent at the bookshop
(b) Obtain an equation for the total amount
of money spent and hence calculate the
amount she spent at the drugstore.​

Answers

A, I think



Lmk if im wrong



Please help anyone please

Answers

Answer:

A=(-5,-4)

B=(-5,-1)

C=(-2,-1)

Step-by-step explanation:

If θ is an angle in standard position whose terminal side lies in quadrant III and sin θ=-√3/2, find the exact value of the tan θ

Answers

Answer:

C) √3

tanθ = √3

Step-by-step explanation:

Step:-1

Given that  θ be an angle in standard position whose terminal side

Given that the angle

                 sinθ = [tex]\frac{-\sqrt{3} }{2}[/tex]

Given that the Opposite side  AB = [tex]\sqrt{3}[/tex]

                        Hypotensue     AC = 2

Step(ii):-

By using Pythagoras theorem

                        AC² = AB² +BC²

                        BC² = AC² - AB²

                       BC²  = 4 - (√3)²

                               = 4-3

                         BC = 1

    Adjacent side(BC)  = 1

Step(iiI):-

Given that 'θ' lies in the third quadrant so tanθ is positive

                     tanθ = [tex]\frac{AB}{BC} = \frac{\sqrt{3} }{1}[/tex]

                       

Answer:

b. -1/2

Step-by-step explanation:

:)

20 POINTS HELP MATH RN SUCSSS

Answers

Answer:

A

Step-by-step explanation:

Given that triangle ABC has angle ABC = 90 degrees, AB = 6 cm and BC = 9 cm. Calculate the length of AC in cm to 1 decimal place

Answers

Answer:

AC = 6.7

Step-by-step explanation:

If this is a 90 degree triangle which I am assuming it is you would the Pythagorean theorem c^2 = a^2 + b^2 since bc seems long I am using that as the hypotenuse.

9^2 = 6^2 + b^2

81 = 36 + b^2

81-36 = b^2

45 = b^2

6.7 = b

so AC = 6.7

A pack of 4 rolls of Charmin cost $3.64. A pack of 32 rolls of Charmin cost $20.80. How much cheaper per roll is it to purchase the bigger pack?

Answers

Answer:

.26 cents cheaper a roll

Step-by-step explanation:

to find this you would do 3.64/4 to get the price a roll which is .91

and then you would do 20.80/32 to get the price per roll which is .65

then to get the difference you would do .91-.65 to get .26

What is the recursive formula for this sequence:
1,-1,-3, -5......

Answers

Answer:

d) A[n] = A[n=1] - 2 (Your selected answer is correct)

Step-by-step explanation:

Think of the formula as:

new number = previous number minus 2

²³√∛·×÷±≈≠≤≥βα∞∨∧∉∈⇔,⇒≅≡ΔπФω↑↓∵∴↔→←⇵∀⊅⊄⊇⊆⊃⊂∑∫⇆⇄⇅°∠∡⊥∪∩∅¬⊕║∦∝㏑㏒∞

What do all of these symbols stand for?

Answers

Answer:

Mathematical symbols used for different calculations?

Hana is putting in a tile floor she needs to determine the angles that should be cut in the tires to fit in the corner that angle in the corner measures 90° one piece of the tire will have a measure of 38 degrees write an equation and use it to determine the measure of the unknown angle​

Answers

Answer:

x = 52°

Step-by-step explanation:

I have attached an image to depict the given angles.

From the attached image, we can see that the unknown angle is x°.

Thus, since that corner is 90°, then;

x + 38 = 90

Subtract 38 from both sides to get;

x = 90 - 38

x = 52°

2. What is the solution to the inequality
--4x > 132? Show your work

Answers

Answer:

x < -33 ( mark me as the brainliest )

Step-by-step explanation:

1) -4x > 132

2) -4x/4 > 132/-4

3) x < -33

Mariel says that a jewelry box that is 3 inches high, 4 1/2 inches wide, and 5 inches long has a volume of 67 1/2 inches. Katie says that answer is not quite correct. What is the error in Mariel's answer?

Answers

Answer: inside width, length and heights may be smaller

Step-by-step explanation. Walls of box have certain thickness, assume 0.1 inches. Then inner measures would be 2.8 in, 4.3 in and 4.8 in. You need to reduce thickness of wall from both sides.

what is the answer to 1\2÷3​

Answers

Answer:

0.16666666666

Step-by-step explanation:

1/2 ÷ 3

1/2/3

0.16666666666

Or

1/2 = 0.5

0.5 ÷ 3

0.16666666666

3/2 or 1.5. You have to multiply by the reciprocal.

I WILL GIVE BRAINLIEST!! PLEASE HURRY


Use the excerpt below taken from the Preamble of the United States Constitution to answer the following question:

"We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America."
—Public Domain

What aspect of Enlightenment influence on the early United States government does this excerpt of the U.S. Constitution illustrate? (5 points)

It gives power to the people rather than God, the Church, or the king.
It rejects the concept of social class in the American system.
It promotes the popular concept of the freedom of speech.
It encourages the development of the separation of church and state.

Answers

Answer:

B. It rejects the concept of social class in the American system.

Explanation:

The Enlightenment of the American Colonies was a period in time where the people were encouraged to become their own nation. This period was represented by many speeches and pieces of writing that boasted freedom of speech, equality, freedom of the press, and religious tolerance.

This specific piece of writing focuses on the aspect of all people in the nation of America having protected freedoms and rights to become their own people.

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