If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 10 cm. (Round your answer to three decimal places.)

Answers

Answer 1

Answer:

The diameter decreases at a rate of 0.143cm/min when it is of 10 cm.

Step-by-step explanation:

Surface area of an snowball:

An snowball has spherical format. The surface area of an sphere is given by:

[tex]S = d^2\pi[/tex]

In which d is the diameter of the sphere.

In this question:

We need to differentiate S implicitly in function of time. So

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

Surface area decreases at a rate of 9 cm2/min

This means that [tex]\frac{dS}{dt} = -9[/tex]

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

[tex]-9 = 2(10)\pi\frac{dd}{dt}[/tex]

[tex]\frac{dd}{dt} = -\frac{9}{20\pi}[/tex]

[tex]\frac{dd}{dt} = -0.143[/tex]

Area in cm², so diameter in cm.

The diameter decreases at a rate of 0.143cm/min when it is of 10 cm.


Related Questions

Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 81st percentile.

Answers

Answer:

[tex]P(81)=56.16[/tex]

Step-by-step explanation:

From the question we are told that:

Mean [tex]\mu=50[/tex]

Standard Deviation [tex]\sigma=7[/tex]

Percentile 81st

Generally Probability of 81st Percentile

 [tex]P(Z<x)=81\%[/tex]

Using Standard normal Table

 [tex]P(Z<0.88)=81\%[/tex]

Therefore the 81st percentile is given as

 [tex]P(81)=z*\sigma *\mu[/tex]

 [tex]P(81)=0.88*7*50[/tex]

 [tex]P(81)=56.16[/tex]

A toy manufacturer wants to know how many new toys children buy each year. A sample of 686686 children was taken to study their purchasing habits. Construct the 85%85% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 6.86.8. Assume that the population standard deviation is 2.12.1. Round your answers to one decimal place.

Answers

Answer:

The 85% confidence interval for the mean number of toys purchased each year is (6.7, 6.9).

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.85}{2} = 0.075[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.075 = 0.925[/tex], so Z = 1.44.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.44\frac{2.1}{\sqrt{686}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 6.8 - 0.1 = 6.7

The upper end of the interval is the sample mean added to M. So it is 6.8 + 0.1 = 6.9

The 85% confidence interval for the mean number of toys purchased each year is (6.7, 6.9).

Instructor Vallejo is trying to figure out the percentage of students that still listen to The Doors. Instructor Vallejo
is pretty out of touch, so he doesn't have a prior percentage of students who listen to The Doors that he can use.
How many students should instructor Vallejo sample if he wants to be within 11% of the actual percentage of
students who listen to The Doors with a 82% confidence level.

Answers

Answer:

N=115

Step-by-step explanation:

n=.25(2.5715/.12)^2 =114.8 so round up to 115. Hope that help you

Which graph best represents an exponential function?
O A.
O B.
C.
D.

Answers

Answer:

B

Step-by-step explanation:

that's how exponential functions are shaped

Calculate the gradient of the line 2y =8x+4

Answers

Answer:

m=4

2y/2=y

8x/2=4x

4/2=2

so

y=4x+4

y= mx+c
y= 2/8x+4
y=4x+2

The rate of change in sales for Garmin from 2008 through 2013 can be modeled by
dS/dT = -0.0972t^2 + 2.136t -11.9
where S is the sales (in billions of dollars) and is the time in years, with t = 8 corresponding to 2008. In 2009, the sales for Garmin were $2.9 billion.
A. Find the model for the sales of Garmin.
B. What were the average sales of Garmin from 2008 through 2013?

Answers

Answer:

a) The model for the sales of Garmin is represented by [tex]S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112[/tex].

b) The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.

Step-by-step explanation:

a) The model for the sales of Garmin is obtained by integration:

[tex]S(t) = -0.0972\int {t^{2}} \, dt + 2.136\int {t}\,dt -11.9 \int\,dt[/tex]

[tex]S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + C[/tex] (1)

Where [tex]C[/tex] is the integration constant.

If we know that [tex]t = 9[/tex] and [tex]S(t) = 2.9[/tex], then the model for the sales of Garmin is:

[tex]-\frac{81}{2500} \cdot 9^{3} + \frac{267}{250}\cdot 9^{2}-11.9\cdot (9) + C = 2.9[/tex]

[tex]C = 47.112[/tex]

The model for the sales of Garmin is represented by [tex]S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112[/tex].

b) The average sales of the Garmin from 2008 through 2013 ([tex]\bar{S}[/tex]) is determined by the integral form of the definition of average, this is:

[tex]\bar{S} = \frac{1}{13 - 8} \cdot \int\limits^{13}_{8} {S(t)} \, dt[/tex] (2)

[tex]\bar S = \frac{1}{5}\cdot \int\limits^{13}_{8} {\left[-\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2}-11.9\cdot t + 47.112 \right]} \, dt[/tex]

[tex]\bar S = \frac{1}{5}\cdot \left[-\frac{81}{10000}\cdot (13^{4}-8^{4}) +\frac{89}{250}\cdot (13^{3}-8^{3}) -\frac{119}{20}\cdot (13^{2}-8^{2}) +47.112\cdot (13-8) \right][/tex][tex]\bar{S} = \frac{1}{5}\cdot (-198.167+599.86-624.75+235.56)[/tex]

[tex]\bar{S} = 2.5[/tex]

The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment. Find the margin of error for the 95% confidence interval used to estimate the population proportion.

Answers

Answer:

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment.

This means that [tex]n = 2161, \pi = \frac{1214}{2161} = 0.5618[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Margin of error:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.5618*0.4382}{2161}}[/tex]

[tex]M = 0.0209[/tex]

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

I REALLY NEED HELP PLS I NEED THIS DONE TODAY!!! JUST LOOK AT THE PICTURE!!!

Answers

Answer:

147 sq meters

Step-by-step explanation:

To find the area of a trapezoid, use the formula ( (a+b)/2 ) x h, where a is base value 1 and b is base value 2. Plugging it all in : ( (4+17)/2 ) = 10.5 x 14 = 147 sq meters.

Answer: the answer is 147 square meters.

Step-by-step explanation:

formula: (a+b)/2 * h

bases are a and b: 4 and 17 meters.

h =14 meters

Plug numbers in (4+7)/2*14

solve and you get 147 square  meters as answer

2
3
us
DO
ON
7
45
US
S

Answers

Answer:

9.8 sq. in.

Step-by-step explanation:

A = πr²

Diameter: 10 inches

Radius: 5 inches

A = π · 5²

A = π · 25

A = 78.54

Section 4 is about one eighth of the circle.

78.54 ÷ 8

9.8175

9.8175 ≈ 9.8

For the equation 3(7 + x) = 3x + k, which value of k will create an equation with Infinity many solutions a) 7 b) 21 c) 10 d) 3

Answers

Answer:

21

Step-by-step explanation:

We have to create an identity

3x + 21 = 3x + k

if we substitute k with 21 we have

3x + 21 = 3x + 21

that is an identity so it’s true for every value of x

solve each problem part 2a. NO LINKS!!!!​

Answers

Answers:

Problem 14) There are 1093 different ice creams possible.Problem 15) There are 120 ways to pick the reading list.Problem 16)  We have 1365 combinations.Problem 17) There are 315 different combos of cars possible.Problem 18) You can go on 21,700 different combinations of rides.

==================================================

Explanations:

Problem 14

There are n = 10 toppings to choose from.

If you order r = 0 toppings, then there is nCr = 13C0 = 1 way to do this.

Use the combination formula nCr = (n!)/(r!*(n-r)!)

If you order r = 1 topping, then there are 13C1 = 13 ways to do this.

If r = 2, then we have 13C2 = 78 different combos

If r = 3, then 13C3 = 286

If r = 4, then 13C4 = 715

Add up those subtotals: 1+13+78+286+715 = 1093

Note the use of nCr instead of nPr. The order of toppings doesn't matter.

-----------------

Problem 15

Again order doesn't matter. We have n = 10 books to pick from and r = 3 selections to make.

nCr = (n!)/(r!*(n-r)!)

10C3 = (10!)/(3!*(10-3)!)

10C3 = (10*9*8*7!)/(3!*7!)

10C3 = (10*9*8)/(3!)

10C3 = (10*9*8)/(3*2*1)

10C3 = (720)/(6)

10C3 = 120

There are 120 different ways to pick the three books (from a pool of ten).

-----------------

Problem 16

Follow the same steps as problem 15. This time you'll have n = 15 and r = 4. The answer you should get is 1365

Or you could follow these steps below:

We have 15*14*13*12 = 32,760 permutations and 4! = 24 different ways to arrange any group of 4, so we have (32,760)/(24) = 1365 combinations.

nCr = (nPr)/(r!)

-----------------

Problem 17

There are 7C1 = 7 ways to pick the color and 10C2 = 45 ways to pick the two options. Therefore, there are 7*45 = 315 different cars possible.

-----------------

Problem 18

"At least 15" means "15 or more".

If you ride on r = 15 rides, out of n = 20 total, then we have nCr = 20C15 = 15504 different combinations. If you ride on r = 16 rides, out of n = 20 total, then we have nCr = 20C16 = 4845  different combinations. If you ride on r = 17 rides, out of n = 20 total, then we have nCr = 20C17 = 1140  different combinations. If you ride on r = 18 rides, out of n = 20 total, then we have nCr = 20C18 = 190  different combinations. If you ride on r = 19 rides, out of n = 20 total, then we have nCr = 20C19 = 20  different combinations. If you ride on r = 20 rides, out of n = 20 total, then we have nCr = 20C20 = 1  combo only

Add up the subtotals to get

15504+4845+1140+190+20+1 = 21,700

A spinner has three unequal sections: red, yellow, and blue. The table shows the results of Nolan's spins. Find the experimental probability of landing on each color. Enter your answers as simplified fractions.


Red 12
Yellow 18
Blue 5

Answers

Answer:

red: 12/35

yellow: 18/35

blue: 1/7

Step-by-step explanation:

The experimental probability is the total number of each outcome over the total outcomes. The total outcomes would be the sum, 12 + 18 + 5, or 35.

If we are looking for the experimental probability of red, we divide the spins on red by the total:

red - [tex]\frac{12}{35}[/tex]

If we are looking for the experimental probability of yellow, we divide the spins on yellow by the total:

yellow - [tex]\frac{18}{35}[/tex]

If we are looking for the experimental probability of blue, we divide the spins on blue by the total:

blue - [tex]\frac{5}{35}[/tex] = [tex]\frac{1}{7}[/tex]

1. Given f(x) = x2 – X and g(x) = 3x + 2, find f(g(2))

Answers

Answer:

56

Step-by-step explanation:

g(2) = 3(2) + 2

      = 6 + 2

      = 8

f(8) = 8^2 - 8

     = 64 - 8

     = 56

MEAN: 14,12,17,
ASAP!:((

Answers

Answer:

hello there! I am mizuki, and I'll be helping you with this problem.

Mean is the average in numbers by the way!

Anyways, the answer is about 14.3

or...

14 1/3

Step-by-step explanation:

14 + 12 + 17 = 43

43 ÷ 3 = 14.333333...

A cook needs 42 pieces of tomato for salads The cook has 4 tomatoes He cuts each tomato into 6 pieces

Answers

He only has 24 so 18 left

An equilateral triangle has on vertex at the origin, another on the x-axis, and the third in the quadrant. find the slope of each side

Answers

Answer:

0, - 1.732 , 1.732

Step-by-step explanation:

The slope of the line is the angle of the tangent from the positive X axis in counter clock wise direction.

The slope of line AB is

tan 180 = 0

The slope of line BC is

tan 300 = - 1.732

The sloe of line AC is

tan 240 = 1.732

plssss answer no links !!

Answers

I recommend using a math app. You can easily get ur answers without waiting
q = 5/3

r = 9/2

s = 21

t = 10

u = -14

v = -3/2

chipo set out from a on a bearing of 130 to town b ,she then boardef a bus from town b another town c on a bearing of 030 directly east of a. calculate the bearing of town a from her new position​

Answers

Answer:

emm who exactly is chipo bcause i literally have no idea

Find the volume of x?
I will mark BRAINLIEST

Answers

Answer:

[tex]x=73[/tex]

180-146=34
-39+x=34
34+39=73
x=73
hope this helped!!

Convert the following angle from degrees to radians. Express your answer in simplest
form.
255°

Answers

Answer:

(17/12)π radians

Step-by-step explanation:

π radians = 180º

255 * (π/180) = (17/12)π

Quadrilateral is shown in the coordinate plane below.
Draw an image of quadrilateral on the coordinate plane reflected over the y-axis.
​​

Answers

Answer:

A'(6, 2), B'(6, 5), C'(3, 6) and D'(2, 1)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is reflected over the y axis, the new point is at A'(-x, y).

From the document attached, the vertices of the quadrilateral is at A(-6, 2), B(-6, 5), C(-3, 6) and D(-2, 1). Hence if quadrilateral ABCD is reflected over the y axis, the new point is at A'(6, 2), B'(6, 5), C'(3, 6) and D'(2, 1).

From her home, Adriana would have to walk due north to get to her friend Gavin's house and due east to get to her friend Zach's house. It is 3 miles from Adriana's house to Zach's house and a straight-line distance of 5 miles from Gavin's house to Zach's house. How far is Adriana's house from Gavin's house?'

Answers

Answer:

4 miles.

Step by step explanation

en un rectnagulo de 17 cm de ancho y su diagonal mide 26 cm ¿cuanto mide el rectangulo de largo?

Answers

Answer:

[tex]x=19.67[/tex]cm

Step-by-step explanation:

Por Pitágoras,

[tex]x^{2} = 26^{2} - 17^{2} \\\\x^{2} = 676 - 289\\\\x^{2} =387\\\\x=\sqrt{387} \\\\x=19.67[/tex]

A 12 ft. ladder is leaning against a house. The ladder makes a 60° angle with the ground. Use special right triangles to find how far up the building the ladder will reach.

Answers

Given:

The length of the ladder  = 12 ft

The angle of ladder with ground = 60 degrees

To find:

How far up the building the ladder will reach.

Solution:

Using the given information draw a figure as shown below.

We need to find the vertical distance between the top of ladder and the ground.

Let x be the required distance.

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

In the below triangle ABC,

[tex]\sin A=\dfrac{BC}{AC}[/tex]

[tex]\sin 60^\circ=\dfrac{x}{12}[/tex]

[tex]\dfrac{\sqrt{3}}{2}=\dfrac{x}{12}[/tex]

Multiply both sides by 12.

[tex]\dfrac{\sqrt{3}}{2}\times 12=x[/tex]

[tex]6\sqrt{3}=x[/tex]

Therefore, the ladder will reach [tex]6\sqrt{3}[/tex] ft far up the building.

How fast would you reach the water if you jump off a cliff using the formula: h(t)= -16t +8t+ 24?

Answers

Answer:

I don’t know if this is correct

Step-by-step explanation:

How to find the value of x round to the nearest tenth for a triangle if one side is 15ft and the other is 13ft

Answers

Answer:

C = 19.9 ft

Step-by-step explanation:

Your question isn't properly constructed. However, I'll attempt in providing a possible way of finding one of the sides of a given triangle.

Generally, the Pythagorean theorem is used to find the side of a triangle when two of its sides are known or provided.

Assuming the following data;

Let the length of sides of the triangle be;

Opposite side = a = 15 ft

Adjacent side = b = 13 ft

Hypotenuse side = c

From Pythagorean theorem;

Mathematically, Pythagorean theorem is given by the formula;

C² = a² + b²

C² = 15² + 13²

C² = 225 + 169

C² = 394

Taking the square root of both sides, we have;

C = √394

C = 19.9 ft

please do both of them THANK YOU

Answers

Answer:

4(3+x)

4x+12

Step-by-step explanation:

Hi there! I am Mizuki, and I'm just answering lol

Anyways, the answer for the first problem is 12 + 4x = 44

The answer for the second problem is 8

Work:

12 + 4x = 44

4x = 32

x = 8

Funny Question :
What is 1 + 1?

Answers

Answer:

2

Step-by-step explanation add 1+1

2? 1+1 is 2, so your answer would be 2 if it’s a genuine question but if you don’t mind me asking what “funny” about the question? (Not in a rude way just curious!)

I think it’s 99 but I’m not sure. Can anyone confirm or deny or explain so I can be sure? thank you!

Answers

Answer:

Yeah its B or 99

Step-by-step explanation:

This problem is easy to solve even without a calculator. Simply 10 times 10 would be 100 (since its asking for square root) and the closest number to 100 would be 99 and the square root of 99 is around 9.94.

I’m confused. Can someone help? Please and thank you so much!

Answers

Answer:

Root of 65

Step-by-step explanation:

8^2 is equal to 64, so the sqrt of 64 would equal 8 exactly. The question is asking for which of the sqrts would be closest to 8, so sqrt of 65 is the number that is closest to 64, so it is the answer.

Answer:

[tex] \sqrt{65} [/tex]

as

[tex] \sqrt{64} = 8[/tex]

so it's the closest value to 8

and also

[tex] \sqrt{65} = 8.06[/tex]

via calculator

Other Questions
Help pleaeee?!,!,!,?,?,! what was the main purpose of establishing Fort Coffee mention any three merits and demerit of federalism? What would happen to the distance between the bright fringes produced by a diffraction grating if the entire interference apparatus (light source, grating, and screen) were immersed in water A train leaves a station at 10.15am andgets to another one at 1.15pm. Theaverage speed between the stationsis 76km/hr. What is the distance? fuerza que ejerce el planeta tierra sobre los cuerpos que en ella se encuentran. Fuerza de distancia Fuerza de Contacto please mark all that apply! HELP ILL GIVE BRAINLIEST The electric field of a negative infinite line of charge: Group of answer choices Points perpendicularly away from the line of charge and decreases in strength at larger distances from the line charge Points parallel to the line of charge and decreases in strength at larger distances from the line charge Points parallel to the line of charge and increases in strength at larger distances from the line charge Points perpendicularly away from the line of charge and increases in strength at larger distances from the line charge Points perpendicularly toward the line of charge and increases in strength at larger distances from the line charge Points perpendicularly toward the line of charge and decreases in strength at larger distances from the line charge Select one:A- 25%B- 15%C- 20%D- 30% Select the sentence that uses academic writing to convey the message. The survey is probably the most interesting to me because I like to study it. As a scholar, I am most interested in the academic uses of the survey findings. Because I study this stuff, I often wonder how I could use it to help others learn. I consider myself a scholar in this area, so I'm really excited to see this particular survey. A discount supermarket, such as Aldi, is most likely to place an emphasis upon which of the following elements of the marketing mix? Part BHow does the section "Supply-Side Strategies for Water Suppliers" contribute to the structure and organization identified in Part A? A It explains how accounting for water and water loss control are methods to achieve sustainability.B It debates whether water loss control or accounting for water is more effective to achieve efficiency.C It describes how and when water meters were first used to measure water usage. D It provides detailed instructions for using a water meter and locating where leaks are most likely to occur.ANSWER REAALLLY FAST I WILL MARK BRAINLIEST Europe was going through a turbulent and difficult time in the mediaeval period in *600-1500500-1200 2w^2-9w+3=-4w solve the equation for all real solutions a round asteroid has a surface gravity of 0.0288 If the mass of the asteroid is 1.10x10^18 kg, what is its radius?? BRAINLIEST PLZ HELP! Which of the following is an example of cultural diffusion?A.the spread of soccer as a sport across countriesB.the use of acupuncture in the United StatesC.releasing old traditions after moving to a new countryD.participating in the pop culture of one country while maintaining personal beliefs Help please............. please After 6 years how much money will she have?