A beach ball is inflated so its diameter increases from 12 inches to 12.5 inches. Given that the formula for the volume of a sphere is V=4/3π,r^3 the change in the volume of the beach ball using differentials is approximately.

a. 367π cubic inches.
b. 727π cubic inches.
c. 1447π cubic inches.
d. 288.7π cubic inches.

Answers

Answer 1

Answer:

V = 36π cubic inches.

Step-by-step explanation:

Given that:

The volume of the sphere is [tex]V = \dfrac{4}{3} \pi r^3[/tex]

If the diameter is represented by P.

Then P = 2r

and r = P/2

[tex]V = \dfrac{4}{3} \pi ( \dfrac{P}{2})^3[/tex]

By differentiating both sides;

[tex]dV = \dfrac{4}{3} \pi \times 3 ( \dfrac{P}{2})^2 \times \dfrac{1}{2} \times dP[/tex]

[tex]dV = \dfrac{1}{2} \pi P^2 \ dP[/tex]

where;

P = 12

dP = 12.5 - 12

dP = 0.5

Then;

[tex]\dfrac{1}{2} \pi ( 12)^2 \times 0.5[/tex]

= 36π

Thus, the volume is V = 36π cubic inches.


Related Questions

Identify the y-intercept for y=0.5x−3.

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Answer:

the y-intercept is -3 because the equation is in y=mx+b where m is the slope and b is the y-intercept

Step-by-step explanation:

(4x+8)+(7x+3) help me!!!!

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Answer:

Step-by-step explanation:

11x+11

a
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What is b in the terms of a and x

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Step-by-step explanation:

i think its

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hope it help u...

Quaddlateral CART is dilated with the center at the origin and a scale
factor of 6/5
Describe Quaddlateral CART and Quadrilateral C’A’R’T’by completing the
table below with the BEST answer

Answers

Answer:

Step-by-step explanation:

Rule for the dilation of a point by a scale factor 'k' about the origin is,

(x, y) → (kx, ky)

If the scale factor for the dilation is [tex]k=\frac{6}{5}[/tex],

Rule for the dilation,

A(x, y) → A'[tex](\frac{6}{5}x,\frac{6}{5}y)[/tex]

If the coordinates of point A' (Image) is given and we have to find the coordinates of point A (Preimage),

Rule for the dilation,

A'(x, y) → [tex]A(\frac{5}{6}x,\frac{5}{6}y)[/tex]

             Quadrilateral CART                   Quadrilateral C'A'R'T'

                          (x, y)                                           [tex](\frac{6}{5}x,\frac{6}{5}y)[/tex]

                       C(-5, 15)                                       C'(-6, 18)

                       A(10, 5)                                         A'(12, 6)

                       R(-20, -10)                                    R'(-24, -12)                          

                       T(-25, 0)                                       T'(-30, 0)

STEAM: The boiling pint of water is affected by changes in elevation. Use the expression of -2A/1000 where a represents the altitude in feet to find the number of degrees Farenhite at which the boiling point of water changes at altitude 5,000 feet

A) -10°F B) 20°F C) 10°F D) -20°F

Answers

Answer:

A) -10°F

Step-by-step explanation:

Given that:

Boiling point of water gets affected when there is a change in the elevation.

Expression to represent the temperature i.e. boiling point w.r.to altitude [tex]A[/tex] is given by the equation:

Temperature in [tex]^\circ F[/tex] = [tex]\frac{-2A}{1000}[/tex]

Given that, the altitude, [tex]A[/tex] = 5,000 feet

To find:

The number of degrees Farenhite at which the boiling point of water will change.

Solution:

Here, we are given the expression:

Temperature in [tex]^\circ F[/tex] = [tex]\frac{-2A}{1000}[/tex]

And value of altitude, [tex]A[/tex] = 5,000 feet

Let us put the value of [tex]A[/tex] in the equation and let us find the value of temperature in [tex]^\circ F[/tex].

Temperature in [tex]^\circ F[/tex] =

[tex]\frac{-2\times 5000}{1000}\\\Rightarrow -2\times 5\\\Rightarrow \bold{-10^\circ F}[/tex]

Therefore, the answer is:

A) -10°F

PLZZZ WILLL GIVEEEE BRAINLEASTTTT The record low for Florida is 2 degrees below zero Fahrenheit and was set on February 13, 1899. The record high is 109 degrees Fahrenheit and was set on June 29, 1931. Which pair of numbers shows these temperatures, in degrees Fahrenheit, written as integers?
2 and 109
2 and -109
-2 and 109
-2 and -109

Answers

Third answer: -2 and 109

please help please i need help​

Answers

Answer:

d + 85

Step-by-step explanation:

Look at it like this,

suppose you have 1 DVD, and the mother buys 85 DVDs then you have 1 + 85 = 86 DVDS

or when you have 2 DVDs, then you have 2 + 85 = 87 DVDs afterwards.

notice that you always take the number of DVDs you already have, and add 85 to it.

d is just a number, but you just don't know it yet. you can change d by any number, and you know d+85 is the number of DVDs afterwards

please help!! i need this badly please!!

Answers

Answer:

The balance is much more precise than it is accurate. All answers are very close to eachother, making it precise, but the weight is off by about 5 grams every time, making it not very accurate.

Step-by-step explanation:

In a logistic regression model, the predictor _________

a. is interval/ratio data.
b. must undergo a logarithmic transformation before undergoing logistic regression.
c. must be in the range of 0 to 1
d. represents ranked scores
e. must be a binary variable

Answers

Answer:

B. must undergo a logarithmic transformation before undergoing logistic regression.

Step-by-step explanation:

A logistic regression model allows us to establish a relationship between a binary outcome variable and a group of predictor variables. It models the logit-transformed probability as a linear relationship with the predictor variables.

Please help fast.
Answer the question below:

Answers

Either SSS or not possible

Mark if correct!

To practice for a competition, Alexia swam 0.54 kilometers in the pool each day for 2 weeks. How many meters did Alexia swim in those 2 weeks?

Answers

Answer:Alexia swam  7,560meters in 2 weeks

Step-by-step explanation:

Step 1

7 days = 1 week

therefore 2 weeks = 7 x 2 = 14 days

Step 2

Each day  Alexia swam =  0.54 kilometres

So in 14 days( 2 weeks) She swam = 14 x 0.54 km= 7.56km

Answer is needed in meters

so 1000 m = 1km

Therefore 7.56 km = 7.56km x 1000=7,560meters

2 rectangles are similar below find legemth in y meters

Answers

Where are the rectangles????

The two lines graphed on the coordinate grid each represent an equation. Which ordered pair represents a solution?

Answers

Answer:

The ordered pair (-3, 3) represents the solution of two lines on the coordinate grid.

Thus, option B is true.

Step-by-step explanation:

As we know that the point of intersection of two lines is the solution of the lines.

Given the graph of the lines, we can see that the two lines intersect at the point (-3, 3).

i.e. at x= -3, y = 3

The point of intersection is (-3, 3)

Thus, the ordered pair (-3, 3) represents the solution of two lines on the coordinate grid.

Thus, option B is true.

Answer:

B

i'm sorry for wasting your time and these points but i don't think anyone is gonna answer the question since someone already did and its correct, i just answered it so the other person can get the Brainiest :)  Have a nice day!

motorcycle cover 210 kilometre distance with 5 l of petrol how many kilometre does it cover with 8 litre of petrol? how much petrol is needed to cover 588 kilometre​

Answers

Answer:

A: 336 km

B: 14 L

Step-by-step explanation:

Use a proportion

210 km / 5 L = x / 8L         Cross multiply

8*210  = 5 x

1680  = 5x

x = 1680 / 5

x = 336 km

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

210 /5 = 588/x                   Cross multiply

210x = 588 * 5

210x = 2940                     Divide by 210

x = 2940/210

x = 14 L

Find the slope of the line that passes through the pair of points.
(2, 6), (7, 0)

A) 6/5
B) 5/6
C) -6/5
D) -5/6

Answers

m = -6 / 5 = -1.2

EXPLANATION

Formula: Slope m= yB- yB/ xb- xb

Solution: 0-6/7-2

= -6/5

M= - 1.2

If Someone Has 2000 Bassball cards And I Have 1 tenth of the fraction as many How Many Cards do I have

Answers

Answer:

200

Step-by-step explanation:

What is 24 quarts divided by 6 pitchers
equals how many pints

Answers

Each pitcher has 4 quarts of lemonade

Louis made 24 quarts of lemonade, and he divided it equally into 6 pitchers.
Then, each pitcher must has a sixt of the total amount of lemonade, this is:
p = (1/6)*24 quarts= (24/6) quarts = 4 quarts
Each pitcher has 4 quarts of lemonade.

Answer:

it would be 8 pints

Step-by-step explanation:

24÷6=4

4×2=8

Write your answer anywhere in the open area of each question
1)
The tape diagram models the lengths of two snowboarding trails. The beginner trail is
200 meters long. How long is the expert trail?
Beginner Trail
Expert Trail
The expert trail is
meters long
2)

Answers

The length of the expert trail is 800 meters. We can find our answer by using given tape diagram and simple mathematical calculations.

What is tape diagram?

A tape diagram is a visual model resembling a piece of tape, that is used to assist with the calculations of ratios and addition, subtraction and commonly multiplication.

Here,

Length of the Beginner trail is 200 meters

And also expert trail is 4 times to Beginner trail.

So, Expert trail = 4 * Length of beginner trail.

     Expert trail = 4* 200

                        = 800 meters.

Hence, we get the answer.

Learn more about tape diagram using the link:

https://brainly.com/question/26372029

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A store sells new video games for $60 each. Used video games sell for $12 each. Jacob is buying 3 video games and x used video games which equation can be used to find y, the total price Jacob must pay in dollars?

Answers

It's C or A
Step-by-step explanation
this is because of the Commutative Property.

please tell me answer! i’ll give brainliest

Answers

Answer:

Answer: B. It is a perfect square

Step-by-step explanation:

Radical Expressions

Melissa multiplied [tex]\sqrt{a}[/tex] and [tex]\sqrt{b}[/tex] and got a rational number.

We are also given that a and b are both natural numbers. It means their product must be not only rational but also a natural number.

We can write that product like:

[tex]\sqrt{a} \cdot \sqrt{b}=\sqrt{a\cdot b}[/tex]

If the result is a natural number, then the product of a and b must be a perfect square. so the radical disappears.

Answer: B. It is a perfect square

I think of a number multiply by 3 and add 4 I get 22​

Answers

Answer:

your thinking of 6

Step-by-step explanation:

subtract 4 from 22

you get 18

divide 18 by 3

you get 6

which value is a solution to the inequality 9 - y >12?

Answers

Answer:

(A) -6

Step-by-step explanation: hope this helps!

Answer:

answer is -3 did like 5 days ago

In a dance contest in which 53,000 votes were cast, the winner received 3/5 of votes. How many votes did the winner not receive? (Incorrect solution: 3/5 x 53,000 = 3/5 x 53,000/1 = 3x53,000/ 5 x 1 = 31,800) ( explain error please and add correct work/solution and if you could share a strategy you used? Thanks!!)

Answers

Answer:

21,200

Step-by-step explanation:

Votes casted = 53000

Votes received = 3/5

Votes did not receive = 1- 3/5 = (5-3)/5 = 2/5

Total votes not received by winner

= 53000 *2/5

= 10,600 * 2

= 21,200

Ehhh what is 2+2+9+9+0+2x0+2 dvided by 8 and 234898529 x 2340 i need a full explanation

Answers

Answer:

2+2=4

9+9+4=22

22+0=22

2×0=0

22+2=24÷8=3

Answer:

1. 0

2. 549662557860

Step-by-step explanation:

Well 2+2+9+9+0+2x0+2 is 0 because anything time 0 is 0 so then you do 0 divided by 8 which is 0. Then 234898529 x 2340 is 549662557860 is you add the commas then... 234,898,529 x 2,340 is 549,662,557,860  

1) You are taking a Tae Kwon Do class that costs $15 a month. In addition, you needed to
purchase a uniform. You paid a total of $108 after 6 months. Write an equation that glves
the total cost (in dollars) as a function of the length of time you have been taking classes
(in months). Find the total cost after 9 months.

Answers

Answer:

$162

Step-by-step explanation:

you divide 6 months by 2 then you divide 108 by 2 then you add the half of 108 and plus it to 108 then you get your total.

The function of the length of time you have been taking classes is f(x) = 15x and cost for 9 months is $135

What is unit rate?

A unit rate means a rate for one of something.

Given that, You are taking a TAE Kwan Do class that costs $15 a month. In addition, you needed to purchase a uniform. You paid a total of $108 after 6 months.

We have unit rate = $15 per month

Since, one month cost is $15 therefore, for 6 months = 15×6 = $90

Therefore, cost of uniform = $108 - $90 = $18

Let you are taking classes for x months, the function of the length of time you have been taking classes,

f(x) = 15x

For 9 month cost =

f(9) = 15×9 = 135

Hence, the function of the length of time you have been taking classes is f(x) = 15x and cost for 9 months is $135

Learn more about unit rates, click;

https://brainly.com/question/29781084

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Brainliest for right answer

Answers

Answer:

Yes

Step-by-step explanation:

If you notice, X goes up 1/4 or 0.25 every time and Y goes up 3 everytime.

So they are proportional. H

Hope this helps plz hit the crown :D

Answer:

No it doesn't

Step-by-step explanation:

The proportional relationship in x is not the same as y for there to be a relationship it could be like 2, 4, 6, 8 etc

Find the slope of each line using tables . try using the slope formula

Answers

Answer:

2

Step-by-step explanation:

2х + Зу = 4
у + 3x = 6

Answers

The answer is
(x,y)= (2,0)

What is 26555 x 3? Brainliest will be given!!!!!

Answers

Answer:

79665

Step-by-step explanation:

26555 + 26555 is 53110 then add 26555 again at it equals 79665

Answer:

79665

Step-by-step explanation:

26555 multiply by 3 is equal to 79665

what is 3/4 divided by 1/6
0 3
0 4
0 4 1/12
0 4 1/2​

Answers

The answer should be 4 1/2!

Answer:

c

because i just did the test

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