The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 mm

Answers

Answer 1

Answer:

[tex]\dfrac{dV}{dt}=502.65\ mm^3/s[/tex]

Step-by-step explanation:

The volume of a sphere is given by :

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

The rate of change of volume means,

[tex]\dfrac{dV}{dt}=\dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r\times \dfrac{dr}{dt}[/tex]

We have, [tex]\dfrac{dr}{dt}=2\ mm/s\ and\ r=40\ mm[/tex]

So,

[tex]\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3\times 20\times 2\\\\=502.65\ mm^3/s[/tex]

So, the volume is increasing at the rate of [tex]502.65\ mm^3/s[/tex].


Related Questions

-12(x - 3) - (2x - 6) = 60

Answers

Answer:

x=-9/7

Step-by-step explanation:

Answer:-12(x - 3) - (2x - 6) = 60

= -12 OJHORZHOEHFOSDHSKDKCDEZIAIFDNSQDKFFFFFFFFFFFFZIDJAZIFJOIJF

Step-by-step explanation:

EFKJNDOIDNOIEFJOAIZFOUJFNJBVJFNVJNZJCN

what is ( 5 x 1 ) + ( 5 x 1/3)

Answers

Answer:

The answer is 20/3

Step-by-step explanation:

(5 x 1 ) + ( 5 x 1/3)

5 + ( 5 × 1/3 )

5 + 5/3 = 20/3

If Robert buys a candy bar for 78 cents, how much
change does he get back from a one-dollar bill?
32 cents
23 cents
22 cents
33 cents

Answers

The answer will be 22 cents
22 cents.

Explanation:
One dollar is 100 cents.
Your equation would be...
100 - 78 = 22 (your change)
Subtract the amount given by the total cost to get the change.

Answer this correctly I’ll give brainalist + 10 points

Answers

So the answer is going to be b)77

Find the slope of the line that passes through the two points. (0, 0), (3, 2)

Answers

Answer:

the slope is 2/3 bcoz u do 2-0/3-0

SOMEONE, PLEASE HELPP ME!!!
Ten hamburger values meals cost $60.

Answers

Each burger is 6 dollars each and 4 of them would cause 24$
The burgers are $6 bucks each and 4 times 6 is 24 it’s 24

The area for the trapezoid is__in2.

Answers

Answer:

1204 in squared

Step-by-step explanation:

During a guided tour of Sindrow Castle, a group of tourists climbed to the top of Fineview Tower.
At the top, the guide asked the six children in the group to guess how many steps they had
climbed. Their guesses were 155, 157, 167, 168, 179 and 183.
The guide revealed that the closest guess was only 3 more or less than the correct number and
that two of the other guesses were no more than 10 away.
How many steps had they climbed?
A 160
B 164
C 171
D 176

Answers

Answer:

C

Step-by-step explanation:

A company makes fifty-six million, nine hundred two thousand, one hundred twenty six widgets each year. what is this number in stardard form?​

Answers

50,000,000+6,000,000+900,000+2,000+100+20+6

A local anime fan club surveyed its members regarding their viewing habits last weekend, and the following information was obtained: 35 members had watched an episode of Naruto, 48 had watched an episode of Death Note, 24 had watched both an episode of Naruto and an episode of Death Note, and 12 had watched neither Naruto nor Death Note. (Round your answers to three decimal places.)
(a) What percent of the club members had watched Naruto or Death Note?
(b) What percent of the club members had watched only Naruto?
(c) What percent of the club members had watched only Death Note?

Answers

Answer:

a) 83.099% of the club members had watched Naruto or Death Note.

b) 15.493% of the club members had watched only Naruto

c) 33.803% of the club members had watched only Death Note.

Step-by-step explanation:

First we find the number of students which each habit, treating the habits as Venn sets.

I am going to say that:

Set A: Watched an episode of Naruto.

Set B: Watched an episode of Death Note.

24 had watched both an episode of Naruto and an episode of Death Note:

This means that [tex](A \cap B) = 24[/tex]

48 had watched an episode of Death Note

This means that [tex]B = 48[/tex].

We have that:

[tex]B = (B-A) + (A \cap B)[/tex]

In which B - A are those who watched only Death Note. So

[tex]48 = (B-A) + 24[/tex]

[tex](B-A) = 24[/tex]

35 members had watched an episode of Naruto

This means that [tex]A = 35[/tex].

[tex]A = (A-B) + (A \cap B)[/tex]

[tex]35 = (A-B) + 24[/tex]

[tex](A-B) = 11[/tex]

At least one:

This is

[tex](A \cup B) = A + B - (A \cap B)[/tex]

So

[tex](A \cup B) = 35 + 48 - 24[/tex]

[tex](A \cup B) = 59[/tex]

Total number of students:

59 at least one, 12 none, so 71 total.

(a) What percent of the club members had watched Naruto or Death Note?

At least one, so 59 out of 71

59*100/71 = 83.099

83.099% of the club members had watched Naruto or Death Note.

(b) What percent of the club members had watched only Naruto?

11 out of 71. So

11*100/71 = 15.493

15.493% of the club members had watched only Naruto.

(c) What percent of the club members had watched only Death Note?

24 out of 71. So

24*100/71 = 33.803

33.803% of the club members had watched only Death Note.

Answer:

i think it is (b) What percent of the club members had watched only Naruto?

Step-by-step explanation:

Find the length of the diameter of circle O. Round to the nearest tenth.

Answers

Answer:

Diameter = 19.33

Step-by-step explanation:

Imaging a radius line from O to the endpoints of the 7. call this line R.

Label the part of the vertical line from O to the 90 degree intersection y.

Now you have a right triangle.

Using the Pythagorean theorem:

R² = 7² + y²

also

y = R - 3

substitute for y:

R² = 49 + (R-3)²

R² = 49 + R² - 6R + 9

simplify:

0 = 58 - 6R

6R = 58

R = 9.6667

Diameter = 2(9.6667) = 19.33

↓⊂∩⊥ββ⊄⊃БНasdsxЫ
c=9 d=8
6d-2c

Answers

Answer:

im sorry what?

Step-by-step explanation:

Help please, what's the answer?

Answers

Question 7

Exponential functions have a variable degree.

Answer is 3^x + 6.

Question 8

Changing 15.3% to a decimal, we get 0.153.

Answer: Choice (4)

how do you make like terms? thank you ​

Answers

Answer:

Like terms are terms whose variables are the same. In other words, terms that are "like" each other. For example, 2x and 3x are like terms. Furthermore, 3y² and 4y² are also like terms. If two factors are like terms they can be combined.

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

why is angle 3 congruent to angle 7?​

Answers

Answer:

they are congruent because they are corresponding angles

Step-by-step explanation:

hi, if your looking for extra points (50+) and brainiest here is ur chance, answer this question correctly plz

Answers

Answer:

i will take company (a) because they are giving in less rate

Answer:

You would want to go with A

Step-by-step explanation:

If you do plan a it is 180 dollars a year when you spend 15 dollars per GB, B is cheaper on the other hand because it is 75 dollars a month so therefore 900 dollars a year

A is cheaper

If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions for t 0. Do the particles collide? If they collide find t. If not enter NONE.
r1(t) = t^2, 8t − 15, t^2
r2(t) = 11t − 30, t^2, 13t − 40
t=

Answers

Answer:

Step-by-step explanation:

[tex]r_1(t) = < t^2 , 8t-15,t^2> \\ \\ r_2(t) = < 11t-30, \ t^2 , \ 13t-40> \\ \\ at \ r_1 = r_2 \\ \\ t^2 = 11t - 30 , \ \ \ \ \ \ \ \ \ \ \ \ 8t - 15 = t^2 , \ \ \ \ \ \ \ \ \ t^2 = 13t -40 \\ \\ t^2 - 11t + 30\ \ \ \ \ \ \ \ \ \ \ \ t^2 -8t + 15 , \ \ \ \ \ \ \ \ \ \ \ \ t^2 -13t + 40 \\ \\ t^2 -8t-3t + 30=0 \ \ \ \ \ \ t^2 - 2t -4t + 15=0 \ \ \ \ \ \ t^2 - 1t - 13t + 40 =0[/tex]

[tex](t-6)(t-5) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-3) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-8)[/tex]

[tex]\mathbf{The \ common \ value \ of \ t \ = \ 5}[/tex]

Evaluate 150 - ( 2 +x)^ 3 when x - 2

Answers

Answer:

it's 86

Step-by-step explanation:

150-(2+x)^3=150-(2+2)^3

    =150-4^3

    =150-64

    =86

The value of the expression 150 - (2 + x)³, when x = 2 is, 86.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 150 - (2 + x)³, when x = 2.

This can be obtained by replacing x = 2 in the expression.

Therefore, 150 - (2 + x)³.

= 150 - (2 + 2)³.

= 150 - 4³.

= 150 - 64.

= 86.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ5

Can you please help me

Answers

no xdxdxdxdxdxxdxdxdxdxdxdxdxdxddxd

Find the slope of line with the given points (- 6, 2)(3, 7)

Answers

Answer:

m = 5/9

Step-by-step explanation:

rise = 5

run = 9

m = rise/run

m = 5/9

Answer:

m = 5/9

Step-by-step explanation:

Use the slope formula to find the slope m.

[tex]m = \frac{5}{9}[/tex]

Before dividing, decompose 420 to make it easier to divide by 4.

Answers

Answer:

4/420=105

Step-by-step explanation:

decompose 42 and divide by 4 is 10 and is 20 divided by 4 is 5

Use the distributive property to write an equivalent expression. (6+8)⋅x *

Answers

Answer: 14*x

Step-by-step explanation: I am 99% sure

77006
75863

Subtract

Answers

Answer:

1143

Step-by-step explanation:

Please help please please plewse

Answers

the answer is (1,-7) and (-8,2) I believe

Answer:

-1 and -5

Step-by-step explanation:

(1 point)
Find the area enclosed by the curve r=2 sin(0) + 3 sin(90).

Answers

If the 0's are indeed zeroes, then it would appear that you're using degrees, so that the equation

r(θ) = 2 sin(0°) + 3 sin(90°)

describes a circle r = 3 (since sin(0°) = 0 and sin(90°) = 1). In this case, the area would simply be π r ² = 9π.

But I suspect you meant to use θ, so the curve has the far more interesting equation,

r(θ) = 2 sin(θ) + 3 sin(9θ)

Since sin(9θ) has a period of 2π/9 and sin(θ) has a period of 2π, their sum has a period of 2π. (That is, 2π times the LCM of 1 and 1/9, which is 1.) But we observe r(θ) is odd, since

r(-θ) = 2 sin(-θ) + 3 sin(-9θ)

… = -2 sin(θ) - 3 sin(9θ)

… = - r(θ)

which tells us that the curve closes itself over a half-period. So the area bounded by the curve is given by the integral,

[tex]\displaystyle\int_0^\pi\int_0^{r(\theta)}r\,\mathrm dr\,\mathrm d\theta[/tex]

If you're not familiar with double integrals yet, all you need to know is that this reduces to the area formula you may/should be familiar with,

[tex]\displaystyle\frac12\int_0^\pi r(\theta)^2\,\mathrm d\theta[/tex]

Compute the integral:

[tex]=\displaystyle\frac12\int_0^\pi(2\sin(\theta)+3\sin(9\theta))^2\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac12\int_0^\pi(4\sin^2(\theta)+12\sin(\theta)\sin(9\theta)+9\sin^2(9\theta))\,\mathrm d\theta[/tex]

Apply some identities:

sin²(θ) = (1 - cos(2θ)) / 2

sin(θ) sin(9θ) = (cos(9θ - θ) - cos(9θ + θ)) / 2 = (cos(8θ) - cos(10θ)) / 2

sin²(9θ) = (1 - cos(18θ)) / 2

[tex]=\displaystyle\frac14\int_0^\pi(4(1-\cos(2\theta))+12(\cos(8\theta)-\cos(10\theta))+9(1-\cos(18\theta))\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac14\int_0^\pi(13 - 4\cos(2\theta) + 12\cos(8\theta) - 12\cos(10\theta) - 9\cos(18\theta))\,\mathrm d\theta[/tex]

[tex]=\dfrac14 \left(13\theta-2\sin(2\theta)+\dfrac32\sin(8\theta)-\dfrac65\sin(10\theta)-\dfrac12\sin(18\theta)\right)\bigg|_0^\pi[/tex]

[tex]=\dfrac1{40} \left(130\theta-20\sin(2\theta)+15\sin(8\theta)-12\sin(10\theta)-5\sin(18\theta)\right)\bigg|_0^\pi[/tex]

[tex]=\dfrac{130\pi-20\sin(2\pi)+15\sin(8\pi)-12\sin(10\pi)-5\sin(18\pi)}{40}[/tex]

= 13π/4

Floyd Electric is fabricating flanges for a new electrical motor. The flange is to be 25 millimeters in diameter with an upper tolerance limit of 26.5 millimeters and a lower tolerance limit of 23.5 millimeters. Bill Floyd took a sample consisting of ten flanges, measured the diameter and recorded the observations in the table. He has heard discussion of 6 sigma in the business news recently and would like to join the club. What percentage decrease in process standard deviation would be required for Floyd Electric to achieve 6-sigma process capability? Assume that his process mean remains where it is.
A) 36%
B) 40%
C) 46%
D) 58%

Answers

This question is incomplete, the missing table is uploaded along this answer below.

Answer:

percentage of age reduction is 40

Option B) 40% is the correct answer

Step-by-step explanation:

Given the data in the question;

from the table in the image below;

sample x = 25.69 , 25.58 , 24.78 , 24.94 , 24.87 , 24.63 , 25.70 , 25.52 , 24.95 , 24.91

mean = ∑x/n

where n is sample size

= (25.69  + 25.58  +24.78  + 24.94  + 24.87  + 24.63  + 25.70  + 25.52  +24.95 ) / 10

= 251.57 / 10

mean u = 25.157

so;

S/N    Sample (X)       Mean (u)       (X-U)²

1            25.69              25.157      0.284089

2           25.58              25.157      0.178929

3           24.78              25.157       0.142129

4           24.94              25.157       0.047089

5           24.87              25.157       0.082369

6           24.63              25.157       0.277729

7           25.7                 25.157       0.294849

8           25.52              25.157       0.131769

9           24.95              25.157        0.042849

10          24.91               25.157       0.061009

Total     251.57                               1.54281

Mean  25.157

Sample Variance = ∑(x-u)²/n-1 = 1.54281 / (10 - 1) = 1.54281 / 9 = 0.1714

Standard deviation STD1 = √ (variance) = √0.1714 = 0.414

now, for 6-sigma capability, Cpk = 2

Cpk = min of ( USL - mean ) / 3×STD), (Mean - LSL) / 3×STD

since our mean is centered between USL and LSL;

Cpk = ( 26.5 - 25 ) / 3×STD2

we substitute

2 = ( 26.5 - 25 ) / 3×STD2

6STD2 = 1.5

STD2 =  1.5 / 6

STD2 = 0.25

so current standard deviation STD1 = 0.414

required standard deviation for 6-sigma process STD2 = 0.25

so percentage of age reduction will be;

⇒ ( 0.414 - 0.25 ) 0.414 = 0.164 / 0.414 = 0.396 ≈ 0.4

⇒ 0.4 × 100 = 40%

Therefore, percentage of age reduction is 40

Option B) 40% is the correct answer

A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup of 2% milk, steamed, and 0.5 cup of whipped cream. The low-fat latte contains a shot of espresso, 1.25 cups of skim milk, frothed, and no whipped cream. The plane begins its journey with 100 shots of espresso, 60 cups of skim milk, 60 cups of 2% milk, and 30 cups of whipped cream. The airline makes a profit of $1.58 on each regular latte and $1.65 on each low-fat latte. Assuming that all lattes that are made can be sold, what would be the ideal mix of regular and low-fat lattes to maximize the profit for the airline?

Answers

Answer:

To maximize profit, the amount of each type of coffees made are;

The number of regular latte made = 52 cups

The number of low-fat latte made = 48 cups

Step-by-step explanation:

The given parameters are;

The number of espresso in a regular latte = 1 shot

The number of cups of 2% milk in regular latte = 1 cup

The amount of whipped cream in a regular latte = 0.5 cup

The number of cups of skim milk in the low-fat latte = 1.25 cup

The number of espresso in a low-fat latte = 1 shot

The amount of whipped cream in a low-fat latte = 0 cup

The number of cups of espresso in the journey = 100 shots

The number of cups of skim milk in the journey = 60 cups

The number of cups of 2% milk in the journey = 60 cups

The amount of profit the airline makes on each regular latte = $1.58

The amount of profit the airline makes on each low-fat latte = $1.65

Let 'x' represent the number regular lattes made and let 'y' represent the number low-fat lattes made, we have;

x ≤ 30/0.5 = 60

x ≤ 60

y ≤ 60

y ≤ 60/1.25 = 48

∴ y ≤ 48

x + y ≤ 100

Therefore, the given that more profit is made from the sale of low-fat latte than for regular latte, the maximum number of low-fat latte should be made

Therefore, the number of low-fat latte made, y = 48

Therefore, the number of regular latte made, x ≤ 100 - 48 = 52

For maximum profit, the maximum number of low-fat latte, 'x', should be made

Therefore, x = 52

The ideal mix of regular and low-fat lattes to maximize profit is 52 cups of regular latte and 48 cups of low-fat latte

What is the equation of the line that passes through the point (4, -8) and has a
slope of -1/2?

Answer is y=-1/2x-6
:)

Answers

Answer:

yo sorry I'm dum need points

A directed line segment AB with A (1,3) and B (8,4) is partitioned by point C such that AC and CB form a 4:1 ratio. Find C
Write your answer as a coordinate point.
Do not include spaces in your answer.
Write your answer as a decimal if necessary.

Answers

Answer:

[tex]C = (\frac{33}{5},\frac{19}{5})[/tex]

Step-by-step explanation:

Given

[tex]A = (1,3)[/tex]

[tex]B = (8,4)[/tex]

[tex]AC : BC = 4 : 1[/tex]

Required

Determine the coordinates of C

To do this, we make use of:

[tex]C = (\frac{nx_1 + mx_2}{n+m},\frac{ny_1 + my_2}{n+m})[/tex]

Where:

[tex]A = (1,3)[/tex] ---- [tex](x_1,y_1)[/tex]

[tex]B = (8,4)[/tex] ---- [tex](x_2,y_2)[/tex]

[tex]m:n = 4 : 1[/tex]

So:

[tex]C = (\frac{1 * 1 + 4*8}{1+4},\frac{1*3 + 4*4}{1+4})[/tex]

[tex]C = (\frac{33}{5},\frac{19}{5})[/tex]

-2p-4=2 pls help me.

Answers

Answer:

p= -3

Step-by-step explanation:

-2p-4=2

    +4  +4

-2p=6

/-2    /-2

p=-3

Other Questions
A cuntos grados equivalen rad What text structure is used in this passage? Your tomato plants are turning brown. The leaves are wilting. Theyre being attacked by aphids! Luckily, theres a way to get rid of these unpleasant insects. Its a much friendlier insectthe ladybug! Ladybugs will eat up to a thousand aphids a day. Just release a bag of ladybugs in your garden and your plants will thank you for it. cause and effect comparison-contrast problem-solution chronological order In this next paragraph, I will describe the differences between fruits and vegetables.Strong: ClaimWeak: Not a Claim essay on indiscipline in our secondary school In this activity, you will record a few sentences, in Spanish, describing your future aspirations when you were a child. Use the preterite and imperfect tenses as appropriate. Use comparatives to note how your aspirations changed over the years and why. You can use any audio recording software. Submit the audio file to your teacher. Read these lines from "If" by Rudyard Kipling.If you can dream and not make dreams your master;If you can think and not make thoughts your aim;If you can meet with Triumph and DisasterAnd treat those two impostors just the same;The first three lines are an example ofdialogue.repetition.stanzas.onomatopoeia. Why did the geography of the Americas and Eurasia produce such different results? FOR BRAINIEST PLEASE HELPP!!! I need help plz this is hard The rats of nimh in the cage Questions on The Many Faces of Nigerian Food. 1. How does the author use the title of the selection to introduce us to Nigeria's diversity? 2. Besides the food, what else about Nigeria is very diverse? What types of supporting details does the author use to support the main idea of the 1st paragraph: facts, examples, reasons, cause/effect, other information. Explain you answer 4. How does the author explain the different ingredients used to make jolof rice? 5. What is a common practice in Nigeria about leftover foods? 6. What are the primary ingredients in the soup/stew Nigerians make? 7. How may the ingredients of a popular dish in Nigeria change from one area to another? HELP ME PLEASE I need the answer now and I will give all my brain lists . How does the narrators point of view influence how the story or event is described? *a. The story is not influenced by who tells the story.b. The story is only influenced by who tells the story if it's told in third person omniscient point of view.c. The story can be influenced by the narrator's experiences and emotions.d. The story is always influenced by all character's emotion If the dimensions of a cylinder are doubled he suface area will what is a example of acceleration? pleaseee help me ill press the heart Expressions can be written using a combination of numbers and letters. Those values can also be described using words. Choose ALL expressions that are correctly described in words. which is it Was the bombing of Tokyo a war crime? Why/why not? Fernando is 6 feet tall.if 1 inch is approximately 2.54 cm,what is fernandos height in cm. Please select the word from the list that best fits the definition theorized plans moved in oval path around the sun