If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm

Answers

Answer 1

Answer:

0.0221 cm/min

Step-by-step explanation:

Surface area of a snowball:

An snowball has a spherical format.

The surface area of an sphere is given by:

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

In which r is the radius(half the diameter). So in function of the diameter, we have that:

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

Implicit derivative:

To solve this question, we need to find the implicit derivative of A in function of t.

The variables are A and d, so:

[tex]\frac{dA}{dt} = 8\pi d \frac{dd}{dt}[/tex]

Its surface area decreases at a rate of 5 cm2/min

This means that [tex]\frac{dA}{dt} = -5[/tex]

Find the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm

This is [tex]\frac{dd}{dt}[/tex] when [tex]d = 9[/tex]. So

[tex]\frac{dA}{dt} = 8\pi d \frac{dd}{dt}[/tex]

[tex]-5 = 8\pi*9 \frac{dd}{dt}[/tex]

[tex]\frac{dd}{dt} = -\frac{5}{72\pi}[/tex]

[tex]\frac{dd}{dt} = -0.0221[/tex]

This means that the diameter decreases at a rate of 0.0221 cm/min when the diameter is 9 cm.


Related Questions

Your town has seen a steady decrease of job opportunities by the amount of 10% every year. If the number of jobs available at the end of last year was estimated at 350,000, then how many jobs will there be by the end of the following year? a. 45,000 c. 35,000 b. 385,000 d. 315,000 Please select the best answer from the choices provided A B C D

Answers

Answer:

315000 (D)

Step-by-step explanation:

100%-> 350000

90%->315000

Consider the following data. Click on the datafile logo to reference the data.
14 21 23 21 16 19 22 25 16 16 24 24 25 19 16 19 18 19 21 12 16
17 18 23 25
20 23 16 20 19
24 26 15 22 24
20 22 24 22 20
Summarize the data by filling in the frequency (to the nearest whole number), the relative frequency (3 decimals), and the percent frequency (1 decimal) values below.
Class Frequency Relative Frequency Percent Frequency 12-14 % 15-17 % 18-20 % 21-23 % 24-26 % (Total) %

Answers

Answer:

[tex]\begin{array}{cccc}{Class} & {Frequency} & {Relative Frequency} &{Percent\ Frequency}\ \\ {12-14} & {2} & {0.05} & {5\%}& {15-17} & {8} & {0.200}&{20\%}& {18-20} & {11} & {0.275} & {27.5\%}& {21-23} & {10} & {0.250} &{25\%}& {24-26} & {9} & {0.225}&{22.5\%} & {Total} & {40} & {1} & {100\%}\ \end{array}[/tex]

Step-by-step explanation:

Required

Complete the table.

First, group the data according to the class.

So, we have:

12-14:- 14 12 --- Frequency is 2

15 - 17:- 16 16 16 16 16 17 16 15 --- Frequency is 8

18 - 20:- 19 19 19 18 19 18 20 20 19 20 20 --- Frequency is 11

21 - 23:- 21 23 21 22 21 23 23 22 22 22 --- Frequency is 10

24 - 26:- 25 24 24 25  25  24 26  24  24 --- Frequency is 9

Next, fill the class frequency column

[tex]\begin{array}{cc}{Class} & {Frequency} \ \\ {12-14} & {2} & {15-17} & {8} & {18-20} & {11} & {21-23} & {10} & {24-26} & {9}\ \end{array}[/tex]

Relative frequency is calculated by dividing each frequency by the total frequency (40).

So, we have:

[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative Frequency}\ \\ {12-14} & {2} & {0.05} & {15-17} & {8} & {0.200}& {18-20} & {11} & {0.275} & {21-23} & {10} & {0.250} & {24-26} & {9} & {0.225}\ \end{array}[/tex]

The percent frequency is calculated by multiplying the relative frequency by 100%.

So, we have:

[tex]\begin{array}{cccc}{Class} & {Frequency} & {Relative Frequency} &{Percent\ Frequency}\ \\ {12-14} & {2} & {0.05} & {5\%}& {15-17} & {8} & {0.200}&{20\%}& {18-20} & {11} & {0.275} & {27.5\%}& {21-23} & {10} & {0.250} &{25\%}& {24-26} & {9} & {0.225}&{22.5\%} & {Total} & {40} & {1} & {100\%}\ \end{array}[/tex]

HELPPPP DUEEE IN A FEW MINSSS PLS HELPPP

Answers

1.because it’s a straight line that passes through the origin
2.he make $16
3.$96
4. $240/16 per hour = 15

Intrigued by a 2013 study at the University of Nebraska that suggested marijuana smokers may be thinner than other adults, a group of students did a project to explore the relationship between body mass index (BMI) and amount of time spent under the influence of marijuana (measured in hours per week). Based on a random sample of 33 students at their university, they used BMI as the response variable. The equation of the least-squares regression line is: hours per month under influence = 49.2−1.15 BMI. Also, r2=0.134 .

Answers

this question is incomplete, the complete question is:

1. is this model effective

2. what is the correlation coefficient for this data.

3. for a student with a bmi of 25, what is the predicted number of hours under the influence.

Step-by-step explanation:

1. first of all this model is not effective because we have r² as 0.134. this tells us that only 13.4 percent of the of the variations that exist in this data has been explained by the model

1. we get the correlation coefficient by

[tex]+-\sqrt{r^{2} }[/tex]

the regression slope coefficient has a negative sign. this is what we would use in calculating the correlation coefficient.

[tex]-\sqrt{r^{2} }[/tex]

= -√0.134

= -0.366

therefore the correlation coefficient is -0.366

2. to get the number of hours under the influence with a bmi of 25

the equation is

49.2-1.15bmi

= 49.2-1.15(25)

= 49.2-28.75

= 20.45

the sum of 1/7 + 2/5​

Answers

Answer:

19/35

Step-by-step explanation:

The answer would be 19/35

helppp pleaseee ty! :(

Answers

Answer:

A

Step-by-step explanation:

The answer is A because 12 and four are support to be subtracted and. 1/2 at the end when you are done

PLEASE HELP ME !!!!!!!

Answers

Answer:

Joe and Lulu

Step-by-step explanation:

What is the simplified form of the rational expression below?
3x2 - 48
2x +8x

Answers

Answer:

Can you clarify the syntax?  what goes where the '??' is below?

Step-by-step explanation:

32x^2 -48    ??   2x+8x  

<A and <B are complementary
angles. if m<A =(6x-4)° and <B=(x+17)° then find the measure of <A​

Answers

Answer:

<A = 62

Step-by-step explanation:

<A and <B add up to 90 degrees. Definition of Complementary.

<A + <B = 90

(6x - 4) + (x + 17) = 90

7x + 13 = 90

7x = 77

x = 11

<A = 6x - 4

<A = 6(11) - 4

<A = 66 - 4

<A = 62

What is the quotient of 33.288 and 7.6?

Answers

Answer:

219/50 or 4.38

Step-by-step explanation:

divide

Stephanie's graduation picnic costs $7 for every attendee. Write an equation that shows the relationship between the attendees, a,and the cost, c. Complete the table to represent this scenario. Then graph the function. Be sure to label your table and graph.

Answers

Are you studied on his work

What is the sine ratio for

Answers

The sine ratio is the ratio of the length of the opposite side devised by length of the hypotenuse.

I’m kinda confused? Can you help me ?

Answers

The answer is A. -1 2/3

what is 23 x 33 - 21

Answers

Answer:

738

Step-by-step explanation:

Start by multiplying..

23 x 33 = 759

Next subtract..

759 - 21 = 738

Final answer is 738

mr dela cruz uses 18 yards of cloth for making 5 pants how many pants will he make for 72 yards of cloth​

Answers

Answer:

18÷5= 3.6

3.6 = 4 yards

72 yards of cloth ÷ 4 yards of cloth = 18 pants

Step-by-step explanation:

3.6 yards rounded to the nearest is 4. So it takes 4 yards of cloth to make 1 pants. Since it takes 4 yards of cloth to make 1 pants, we simply divide 4 yards into 72 yards which equals to 18 pants.

(08.06) A student wants to report on the number of meals his friends buy each week. The collected data are below: 4,19,3,3,2,3,2,4. Which measure of center is most appropriate for this situation and what is its value?

Answers

Answer:

median

Step-by-step explanation:

For a group of data with one big outlier, the mean is thrown off.

Like a room of 10 people who each make $50,000 a year except for one person who makes $2 million a year. The mean average for that group would be $245,000 a year but it reflects the actual circumstance of NOBODY in the room.

The median is more refective of the 'average' in these situations.

A large can is 12 inches high the radius of the top is 3.5 inches what is the area of a rectangular label that is wrapped around the can

Answers

Answer:

the aria is what you need to multiply together

Step-by-step explanation:

88=66+7-5x89 this question makes no scence

Answers

Answer:

x = -3/89

Step-by-step explanation:

witch point is best represented by the ordered pair (2,-5.5)



Answers

Answer:

Witch point is best represented by the ordered pair (2,-5.5)

Step-by-step explanation:

Answer:

Point W

Step-by-step explanation:

The following data represent the number of eggs, in ten-thousands, which were sold by various grocery stores in the month of November. Construct a dot plot for the given data.

5 16 13 15 7 7 5 10
14 16 12 12 11 5 11 4

Answers

Answer:

See explanation and attached file

Step-by-step explanation:

A dot plot is a chart that is created using data points. It is one of the easiest ways of plotting the distribution of data and they make it a lot easier to see data. It is like a bar chart but instead of bars, you have dots.

It is created by counting the number of data that a particular variable has and drawing the corresponding number of dots above it.

See attached file

Ken ran 2.5 kilometers, 5,250 meters and 75,650 centimeters. how many meters did Ken run?​

Answers

you just answered your own question. the answer is 5,250

Answer:

8506.5

Step-by-step explanation:

1 km = 1000 meter

2.5 km = 2.5 * 1000 =                                        2500 meters

5250 m does not require any conversion      5250 meters

1 meter = 100 cm

75650 cm   = 75650/100                                   756.5 meters

Total                                                                    8506.5 meters

Does anyone know the answer and could you explain how you got your answer? THANK YOUU​

Answers

Answer:

This would be a 60% increase

Step-by-step explanation:

40-25 and divided by 25 times 100

you should get 15/25 multiply it by 100=60%

hi was wondering if I could get some help on this the person who has the best answer gets brainly​

Answers

Answer:

6/8

Step-by-step explanation:

Please Help Me ASAP.

Answers

Answer:

Parallel lines ALWAYS have the same slope

Step-by-step explanation:

The equations have unequal slopes, meaning they aren't parallel.

Find the measure of the missing angle.

pls help I will give brainliest and 50 points!

Answers

180-98=82 so 82 degrees is the answer

Answer:I think it is 82

Step-by-step explanation: because a straight line is 180° and 180-98=82

g (1 point) Find the angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces, so that the two diagonals have a common vertex. The angle should be measured in radians. (Hint: we may assume that the cube is in the first octant, the origin is one of its vertices, and both diagonals start at the origin.)

Answers

Answer:

Angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces is equal to [tex]0.6155[/tex] radian

Step-by-step explanation:

Please see the attached image for better understanding

Length of OB is equal to

[tex]\sqrt{19^2 + 19^2 }[/tex]

[tex]19\sqrt{2}[/tex]

Now the length of OE is equal to

[tex]\sqrt{19^2 + 19^2 + 19^2 } = 19 \sqrt{3}[/tex]

Now Angle BOE is equal to

[tex]cos^{-1} (\frac{722}{19\sqrt{2}* 19\sqrt{3} }) = 0.6155[/tex] radians

Angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces is equal to [tex]0.6155[/tex] radian

answer please show work

Answers

Answer:

That's too small for me

Step-by-step explanation:

nzwxecrtvbyvtrcexwzqzwxecrtvbynu 7 1/2÷56 nkjnknlnlk

Answers

Answer:

0.1

Step-by-step explanation:

0.13392857142857142857142857142857

If you solve the equation: ax+by/c=d for x, what would you get?

Answers

1. multiply the “c” in the denominator to the other side

2. subtract the “by”

3. divide by “a”

I used to always get super confused when the problems only had variables, but all you have to do is look at it like any other equation. Don’t let the variables confuse you. Hope this helps!

2/3s-4/3=s/6+2/3 solve for s

Answers

Answer:

s = 4

Hope this helps :)

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