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 movie theater sells popcorn in bags of different sizes. The table shows the volume of popcorn and the price of the bag

complete one column of the table with prices where popcorn is priced..... and to be continue ​

Answers

Answer:

The price for a 60-ounce bag of popcorn would be $16

Step-by-step explanation:

Answer:

The price for a 60-ounce bag of popcorn would be $16

Step-by-step explanation:

Function Modeling

The behavior of some parameters that depend on a set of variables can be modeled in several ways, like linear, quadratic, exponential, logarithmic, among many others.

The selection of the model is often a complex decision that involves statistics and data analysis.

The question provides us with four points where the volume of popcorn bags and the price in dollars. The easiest function that can be used is the line.

The equation of a line of the volume V and the price p can be found with the expression

We'll use the first two values (6,10) (8,20)

Simplifying and rearranging, we get the model

To test the accuracy of the model, we compute the values of p for V=35 and for V=48

Since the computed values are equal to those of the table, the model is accurate. We can now predict the price for V=60

The price for a 60-ounce bag of popcorn would be $16

You have 26 songs in your MP3 player. After you add some more, you have 39 songs. How many songs did you add?

A. -13
B. 13
C. 65
D. 23

Answers

Answer:

b

Step-by-step explanation:

39-26 = ?

39

-26

____

 13

you added 13 songs.

Write 40673 to the nearest thousand.​

Answers

Answer:

50000

Step-by-step explanation:

Answer:

41000

thank me later have a great day

The ratio of the interior angles of a triangle is 2 : 3 : 4. What are the angle measures? Write the angle measures from least to greatest.

Answers

9514 1404 393

Answer:

  40°, 60°, 80°

Step-by-step explanation:

The total of ratio units is 2+3+4 = 9.

The total of angles in a triangle is 180°, so each ratio unit stands for 180°/9 = 20°.

The angle measures are ...

  20° × 2 = 40°

  20° × 3 = 60°

  20° × 4 = 80°

Is this a complementary, supplementary, vertical, or adjacent

ill give brainly​

Answers

Answer:

its complemtary

Step-by-step explanation:

check this photo

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!

If you are asked to complete 5 sit-ups for every 9 push-ups you complete, answer each of the following questions:
Write the ratio of push-up’s to sit-ups three different ways.

_____________ ____________ ____________


If you complete 36 push-ups, how many sit-ups did you complete?



____________

If you complete 95 sit-ups, how many push-ups did you complete?



_____________

Answers

Answer:

1)5:9 ,5 of 9 5/9 2) 36x5 3) 95x5

Aaron currently earns $1,400 per month working. Each year he will get a $150 per month raise. How much money will Aaron earn per month in 7 years?

Answers

the correct answer is 10290000

Answer:

130,200

Step-by-step explanation:

Earnings for 7yrs= $1,400 × 12 months × 7yrs

= $117,600

Raise for 7 yrs= $150 × 12 months × 7yrs

=$ 12,600

Earnings in 7yrs= $117,600 + $12,600

= 130,200


How many angles do 5 triangles and 3 rectangles have?
(1) 7
(2) 17
(3)
18
(4) 27

Answers

Answer:

27

Explanation:

5 * 3 = 15 (5 triangles with 3 angles each)

3 * 4 = 12 (3 rectangles with 4 angles each)

15 + 12 = 27

Answer:

the answer is 27 because a triangle has 3 sides so multiply 3 tomes 5 because of how many triandles and then the same with the rectangle that has 4 sides then multiply by 3 because of the number of triangles you have

can 8 go into 3? plz answer

Answers

Answer:no

Step-by-step explanation:it would not be possible as 8 is a larger number then 3 unless u would be multiplying by decimals which in which case might be possible

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.

Help please?? Thank you

Answers

Answer:

Isosceles right

Step-by-step explanation:

And isosceles triangle has 2 congruent sides, and since 90° is a right angles, it is a right triangle.

Answer:

isosceles acute I believe, since the two even sides are acute angles, however it could also be right since the top angle is a right angle and therefore the other two equal a right angle sorry if this didn't come in very useful

SOLVE FOR X!!
(will mark brainliest)

Answers

Answer:

19

Step-by-step explanation:

Since it is a 90° angle we can say that 3x-15+2x+10 = 90.

3x-15+2x+10 = 90

5x-5=90

5x=95

x=19

By solving this we find that x is equal to 19.

Answer:

19

Step-by-step explanation:

3*19 = 57

57 - 15 = 42

2*19 = 38

38 + 10 = 48

48 + 42 = 90

(As this is a 90 degree angle)

sin430° x sin490° x sin530° = 1/8​

Answers

Answer: 1/8

Step-by-step explanation:

https://math.stackexchange.com/a/1788346

A candy bag contains 12
green candies and 1
blue candy. Preston will choose 2
candies from the bag without looking.

Which answer describes a possible event?

choosing 2
2
blue candies
choosing 2 blue candies

choosing 1
1
blue and 1
1
red candy
choosing 1 blue and 1 red candy

choosing 2
2
red candies
choosing 2 red candies

choosing 1
1
blue and 1
1
green candy

Answers

Answer:

choosing 1 blue and 1 green candy or choosing 2 green candies

Find the slope of the line that passes through (10, 2) and (1, 6).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

The original answer would be 4 over negative 9 but when divide a positive by a negative your new answer would be negative 4 over 9. The correct format should be negative 4 over 9


How many even numbers less than 1000 can be formed from the given
digits 0,2,3,5 if repetition is not allowed.
(a) 16
(b) 24
(c) 6
(d) none of these

Answers

Answer:

non of them it should be 32 iʻm pretty sure

Step-by-step explanation:

The system shown is
O
inconsistent

equivalent
consistent

Answers

Answer:

This is pogers

Step-by-step explanation:

What is ur minecraft usernaem

Answer:

consistent  

A consistent and independent solution to a system of linear equations is one point

A consistent and dependent solution to a system of linear equations is where they are the same line ( they could also be called equivalent)

An inconsistent solution is where there is no solution, the lines do not cross

Since the lines cross at exactly one point, this is a consistent and dependent solution

The solution is at x = 3  ( 3 units to the right of the origin)

and y = 2 ( 2 units up from the origin)

Step-by-step explanation:

Which function describes the graph below?
X

Answers

La respuesta no está allí a si que cuando puedas no las mandas si!

ANSWER ASAP PLZ
Which statement is true based on the diagram?
O PQR - STR
O RST ~ RQP
O QR corresponds to TR.
O PR corresponds to RS.

Answers

Answer: B

O RST ~ RQP

Step-by-step explanation:

The statement that is true based on the diagram is: "QR corresponds to TR."

Based on the given information, we have the following:

1. PQ = 8 cm

2. QR = 12 cm

3. RT = 18 cm

4. ST = x cm (length not specified)

Now, let's analyze the statements:

1. [tex]\( \triangle PQR \sim \triangle STR\)[/tex] - This statement is not necessarily true because we don't have enough information to determine if the two triangles are similar.

2. [tex]\( \triangle RST \sim \triangle RQP\)[/tex] - This statement is not necessarily true because we don't have enough information to determine if the two triangles are similar.

3. QR corresponds to TR - This statement is true based on the fact that QR and TR are corresponding sides of the triangles [tex]\(\triangle PQR\)[/tex] and [tex]\(\triangle STR\)[/tex] that are intersected by transversal QRST.

4. PR corresponds to RS - This statement is not necessarily true because we don't have enough information to determine if PR and RS are corresponding sides of the triangles [tex]\(\triangle PQR\)[/tex] and [tex]\(\triangle STR\)[/tex].

So, the correct answer is: QR corresponds to TR.

To know more about diagram, refer here:

https://brainly.com/question/29251917

#SPJ6

WILL MARK BRAINLIEST
Hannah jumps rope 300 times. Sharon jumps rope 179 times. How many more times does Hannah jump rope than Sharon? Click on the numbers to enter the answers in the boxes​

Answers

Answer:

121

Step-by-step explanation:

300

-179

-------

121


The average number of televisions per family is numbered in the tens.
A. True
B. False

Answers

Answer:

False!

~The Average number of TVs in a house is 2 - 3

Hope this helps!

Answer:

False.

The average number of televisions per family would have to be more than ten for it to be true, and I find this very hard to believe.

Hope I helped!

What is the equation of the line that is perpendicular to y=-3x+1 that passes through the point (9,0)?
y=1/3x-3
y=-1/3x+3
y=3x+9
y=-3x+3

Answers

Answer:

Step-by-step explanation:

the correct answer of the question is y=x/3-3 b.c

m1.m2 = -1 But m1=-3

so -3.m2=-1

-3.m2/-3=-1/-3

m2=1/3 therefore

Y=1/3x-3

PLEASE HELP ME ANYONE ???????????!!!

Answers

Answer:

A x>9

Step-by-step explanation:

add 4 to both sides and ta da

Answer:

x>9

Step-by-step explanation:

you move the negative 4 to the other side to get it away from x so then you can find the answer.

Hope this helps:)

Does anyone know????????

Answers

Answer:

1) -3/2

Step-by-step explanation:

The common ratio is the amount you multiply by to get to the next number in the sequence. To calculate this you will need to divide the term by its preceding term.

For example (3/4) / (-1/2)

When dividing by fractions you should apply KCF (Keep Change Flip), so you will end up with (3/4) x (-2/1) = -3/2

Check this by doing the next term (-9/8) / (3/4)

When dividing by fractions you should apply KCF (Keep Change Flip), so you will end up with (-9/8) x (4/3) = -3/2

a researcher read a 12 page article in 30 mintues. on average, how much time did the researcher spend reading each page of the article? (1 minute = 60 seconds)

Answers

total minute(one year) = 15 X 365 no of pages read in one year = 12 x 200 = 1200

number of page read in one minute = no of pages read in one year/total minute(one year) = 2400/5475= .4383

ie 1 minute - .4383 page

ie 60 sec - .4383 page

time for 1 page 60/.4383 = 136.89

Part 2

Time needed to read a page 30 sec less

ie 136.89 -30 = 106.89.

so number of pages read in 1 sec = 1/106.89

number of pages read in 1 min = 1/106.89 * 60

number of pages read in a day = 1/106.89 * 60 * 20

number of pages read in a year = 1/106.89 * 60 * 20 * 365 = 4097.67 ( ie 1/106.89 * 7300)

number of books = number of pages read in a year/200 = 20.49

Classify the solid figure.
O A. rectangular prism
O B. rectangular pyramid
O C. cylinder
O D. quadrilateral
HELP MEEE

Answers

That looks like a rectangular prism
It’s A.
..................

I need help on this asap

Answers

Answer: 13.7ft (1 decimal place)

Step-by-step explanation:

For this question you will have to use Pythagoras theorem.

The formula for the short side is x²=c²-b² and when you put the numbers from this question into it you get x²=15²-6²

15²=225

6²=36

x²=225-36

x²=189

Then, as you want to find x on its own, you would have to square root 189 which is 13.7 (1 decimal place).

Hope this helps :)

1. What is the value of x?
40
х
9

A.41
B.26
C.17
D.39

Answers

Answer:

B

Step-by-step explanation:

Find the surface area of this cube Be sure to include the correct unit in your answer
i dont really understand this pls help me ill give you brainly and 5 stars and a heart

Answers

Answer:

Which cube?

Step-by-step explanation:

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

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