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

PLS HELP!!
Figure ABCD has vertices A(1, 1), B(1, 4), C(4,4), and D(4,1). What are the coordinates of the vertices of Figure
A'B'C'D' after a reflection across the line x = -2 and a translation 3 units up? Drag numbers to complete the coordinates.
Numbers may be used once, more than once, or not at all.
-
numbers are -8,-7,-6,-5,-4,4,5,6,7,8

Answers

Answer:

A’ (-5,4) B’ (-5,7), C’ (-8,7), D‘ (-8,4)

Step-by-step explanation:

Just had this test lol

If you were to calculate the average rate of change of a function over a variety of intervals and you found that they were all the same, what conclusion could you draw and why

Answers

You could infer that there was the same amount of every interval.

work out the value of angle x 62 degrees​

Answers

Answer:

180- (62*2)= x( angles opposite to equal sides)

180-124= x

x= 56

Step-by-step explanation:

What is the value of k if (1, 1) is a solution of 2x + 7y=k?​

Answers

answer: k=9
reasoning: just plug in 1 for x and 1 for y

3/2 inches snow fell in 3/4 of an hour which two statements are true

Answers

Answer:

I don't see the two statements

Step-by-step explanation:

Answer:

A and E Usa test prep

Step-by-step explanation:

I know it might be late by now but this is for the people who are searching for the answer for the future

What is the total interest paid on an $185,000 loan at 6.25% APR over 15 years (monthly payments)? ​

Answers

Answer:

Total Interest $100,522

Step-by-step explanation:

Answer:

$100,522

Step-by-step explanation:

Please help me I wanna go to sleep

What is true about this sequence?
8000, 4000, 2000, 1000, ...

Answers

Answer:

B

Step-by-step explanation:

each consecutive term is divided by 2

It’s b because it is b

How many cups are in 16 gallons?

64
256
128
2,048

Answers

Answer:

256 cups

Each gallon has 16 cups so 16 gallons would have 16*16 cups. 16*16 = 256

Evaluate the integral. (Use C for the constant of integration.)
cos(x) (8 + 7 sin^2(x)) dx

Answers

Answer: [tex]8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]

Step-by-step explanation:

Consider [tex]\int \cos(x) (8+7 \sin^2(x)) \, dx[/tex]

Substitute  t= sinx

then dt = cos x dx

[tex]\int \cos(x) (8+7 \sin^2(x)) \, dx = \int (8+7t^2)dt\\\\ =8t+7(\dfrac{t^3}{3})+C[/tex]

[tex][\int x^ndx=\dfrac{x^{n+1}}{n+1}+C][/tex]

[tex]=8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]

Hence, [tex]\int \cos(x) (8+7 \sin^2(x)) \, dx=8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]

Dalle note 3 green 1 we ame 7 vel maps on abier med up and make one of the

Answers

Answer:

I have no idea what this means

Ford provides an option of a sunroof and side air bag package for its Windstar model. This package costs$1400. Ford wants todetermine the percentage of Windstar buyers who would pay $1400 extra for the sunroof and side air bags. How many Windstar buyers must be surveyed if we want to be 95% confident that the sample percentage is within four percentage points of the true percentage for all Windstar buyers

Answers

Answer:

601 buyers must be surveyed.

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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

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

95% confidence level

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

How many Windstar buyers must be surveyed if we want to be 95% confident that the sample percentage is within four percentage points of the true percentage for all Windstar buyers?

We need to survey n buyers. n is found when [tex]M = 0.04[/tex]. We dont have an estimate for the proportion, so we use [tex]\pi = 0.5[/tex], which is when the largest sample will be needed.

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

[tex]0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2[/tex]

[tex]n = 600.3[/tex]

Rounding up

601 buyers must be surveyed.

hottest centralisation​

Answers

Answer:

centralisation mean a direction explain that we often  a high how well we cancan predict future actions of others.

Step-by-step explanation:

2 3/4 yards of fabric for $22 express as unit rate. round to nearest cent if necessary

Answers

Answer:

7

Step-by-step explanation:

Answer:

13(rounded) cents per 1/4 yard and 50 cents per yard

Step-by-step explanation:

Step 1:  Convert the mixed fraction into an improper fraction

[tex]2\frac{3}{4} = \frac{4}{4}+\frac{4}{4}+\frac{3}{4}[/tex]

[tex]2\frac{3}{4}=\frac{11}{4}[/tex]

Step 2:  Find the unit price per 1/4 yard

[tex]\frac{11}{4}/22[/tex]

[tex]0.125 = 13 \ cents[/tex]

Step 3:  Find the unit price per 1 yard

[tex]12.5\ cents\ per\ 1/4\ yard=50\ cents\ per\ 1\ yard[/tex]

Answer:  13(rounded) cents per 1/4 yard and 50 cents per yard

There are 12 counters. One third of the counters are yellow. How many counters are yellow?

Answers

Answer:

I think 4

Step-by-step explanation:

1/3 is how many are yellow. so if u do 12/3=4

Answer:

4

Step-by-step explanation:

1/3 is equivalent to 4×1 and 2/3 is equivalent to 4×2 and 3/3 is equivalent to 4×3 which equals 12 so there are 4 counters that are yellow.

How do you simplify 32/48

Answers

Answer:

2/3

Step-by-step explanation:

divide numerator and denominator by 16

32÷16=2

48÷16=3

answer is 2/3

Thus, 2/3 is the simplified fraction for 32/48 by using the GCD or HCF method. Thus, 2/3 is the simplified fraction for 32/48 by using the prime factorization method.

Nick went canoeing on the river he traveled 1 mile in 17 minutes.at this rate,how far will he travel in an hour and 25 minutes​

Answers

9514 1404 393

Answer:

  5 miles

Step-by-step explanation:

An hour and 25 minutes is 85 minutes. Using the given information we can find the distance d with the proportion ...

  [tex]\dfrac{\text{distance}}{\text{time}}=\dfrac{d}{85\text{ min}}=\dfrac{1\text{ mi}}{17\text{ min}}\\\\d=\dfrac{85\text{ min}}{17\text{ min}}(1\text{ mi)}\qquad\text{multiply by $85$ min}\\\\d=5(1\text{ mi})\qquad\text{simplify}\\\\d=\boxed{5\text{ mi}}[/tex]

In 1 hour and 25 minutes, Nick will travel 5 miles.

How do you find the slope to (3,12),(3,-17)

Answers

Answer:

you plot them together

1. draw a t shape and then plot it like x then y

Answer:

trust your instincts

Step-by-step explanation:

decide on your own destiny i can not interfeir

complete the table by supplying the measure of inscribed angle and its intercepted arc​

Answers

Answer/Step-by-step explanation:

Based on the inscribed angle theorem, any inscribed angle = ½ of its intercepted arc

Thus:

✔️Inscribed angle = 57°

Intercepted arc would be: 2*57 = 114°

✔️Intercepted arc would be: 123°

Inscribed angle = ½(123) = 61.5°

✔️Intercepted arc would be: 46°

Inscribed angle = ½(46) = 23°

✔️Inscribed angle = 69°

Intercepted arc would be: 2*69 = 138°

✔️Intercepted arc would be: 155°

Inscribed angle = ½(155) = 77.5°

Determine the slope of the line whose equation is 2x-3y=5

Answers

The slope would be 2/3 I hope this helps you out!

Please help please please plewse

Answers

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

Answer:

-1 and -5

Step-by-step explanation:

Help me this math problem
Let f(x) be the trigonometric function f(x)=sin(x).
On the interval [0,2π), the maximum value(s) of f(x) occur(s) at what x-value(s)?

Answers

Answer:

im on a chalange

Step-by-step explanation:

please choose someone else i have 1 day to do this

Select all expressions that are equal to 3⋅3⋅3⋅3⋅3.
3^5
3^4 ⋅ 3
5 ⋅ 3
5^3

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3\times3\times3\times3\times3}\\\\\mathsf{3\times3=\bf9}\\\\\mathsf{9\times9\times3}\\\\\mathsf{9\times9=\bf81}\\\\\mathsf{81\times3=\bf result}\\\\\mathsf{= \bf \underline{243}}\large\checkmark[/tex]

[tex]\text{Option A. }\downarrow\\\mathsf{3^5}\\\\\mathsf{3^5= 3\times3\times3\times3\times3}\\\\\mathsf{3\times3\times3\times3\times3}\\\\\mathsf{3\times3 = 9}\\\\\mathsf{9\times9\times3}\\\\\mathsf{9\times9 = 81}\\\\\mathsf{81\times3= 243}\\\\\large\text{\bold{Option A.} could possibly be your \bf ANSWER}\huge\checkmark[/tex]

[tex]\text{Option B. }\downarrow\\\mathsf{3^4\times5}\\\mathsf{3^4 = 3\times3\times3\times3}\\\\\mathsf{3\times3\times3\times3}\\\\\mathsf{3\times3=9}\\\\\mathsf{9\times9= 81}\\\\\mathsf{81\times3=243}\\\\\large\text{Option B. could possibly be your \bf ANSWER}\huge\checkmark[/tex]

[tex]\text{Option C. }\downarrow\\\mathsf{3\times5}\\\\\maths{3+3+3+3+3}\\\\\mathsf{3+3=6}\\\\\mathsf{6+6+3}\\\\\mathsf{6+6=12}\\\\\mathsf{12+3=15}\\\\\mathsf{15\neq243}\\\\\large\text{Option C is NOT your ANSWER}[/tex]

[tex]\text{Option D.}\downarrow\\\mathsf{5^3}\\\\\mathsf{5^3=5\times5\times5}\\\\\mathsf{5\times5\times5}\\\\\mathsf{5\times5=25}\\\\\mathsf{25\times5 = 125}\\\\\mathsf{125\neq243}\\\\\large\text{Option D. is NOT your ANSWER}[/tex]

[tex]\boxed{\boxed{\large\text{Answers: \boxed{\boxed{\mathsf{\bf{Option\ A.)\ 3^5 \ \& \ Option\ B.)\ 3^4 \times 3}}}}}}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

A) 3^5 B) 3^4*3

Step-by-step explanation:

(ab)(6a^5b)(-ab) simplified please

Answers

Answer:

25b3a+93b+60a=30a2+b2

Step-by-step explanation:

Help and show work please

Answers

Answer:

11111111    111 1 1 1 11

Step-by-step explanation:

Answer:

ok 1+1= 25 and add 3000 and you get 1

Step-by-step explanation:

Please help ..........

Answers

I think the answer is B. Hope this helps!

Please answer !!!! Due in 10 minutes

Answers

1-3=0kwgf8ebeuf iwbrjievtirvr8rvhe

(-4x+4) that’s the answer if I’m correct

2х - 12 = 24
Зу - 15 = 60
Find the product of X and y.
450
325
120
260
144
I don’t know what to do or what the answer is

Answers

Answer:

x=18 y=25

Step-by-step explanation:

1)2x18=36-12=24

2)3x25=75-15-60

The measures of two angles of a triangle are 22 and 85 degrees. Find the measure of the third angle.

Answers

Answer: [tex]73^{\circ}[/tex]

Step-by-step explanation:

Angles in a triangle add to 180 degrees.

A rectangular city park is 6/8 mile long the park has an area of 1/4 Mile2. What is the width of the park?​
I need an answer! Please!

Answers


1/3 miles

Explanation: Area=Length*Width. To find the width divide the area by length. Sub in the fractions for (1/4)/(6/8). You’ll get 1/3 mile.

Answer:

The answer is 1/3

Step-by-step explanation:

divide 6/8 and 1/4 and you will get 1/3

The Property where if the order of addends changes, the sum stays the change

Answers

Property of addiction
Other Questions
What is the vortex of the quadratic function fox (x-8)(x-2)? Choose the best revision for each run on sentence2. Mount Olympus is the highest peak on the island of Cyprus, I would like to visit Cyprus one day.A. Mount Olympus is the highest peak on the island of Cyprus; I would like to visit Cyprus one day.B. Mount Olympus is the highest peak on the island of Cyprus. I would like to visit Cyprus one day C. Mount Olympus is the highest peak on the island of Cyprus, and I would like to visit Cyprusone day. What is the equation of the line in the slope intercept form? Which of the following correctly describes the relationship between speed and velocity? (4 points)Speed is the change in velocity over time; velocity is distance plus direction.Speed is the change in distance over time; velocity is speed plus direction.Speed is distance plus direction; velocity is speed plus time.Speed is the change in acceleration; velocity is distance over tim The amplitude of a wavedetermines the volume of asound.TrueO False The profit for a company this year was $100,000. Each year the profit increases at a rate of 1.2% peryear. Which function shows the company's profit as a function of time in years?a. f(t) = 100,000 0.012^tb. f(t) = 100,000(1 + 1.2)^tc. f(t) = 100,000(1 + 0.012)^td. f(t) = 100,000 - 1.2^t List changes to farm rules or policies that occur in chapter 8. You should list at least 5. Write a rhyming quatrain. Calculate 18% tip on a 6250 dinner bill 2 2/21 +(0.25( 1/4 )1.5( 3/16 ))(4 1/11 )pls answer this is a hundred point question Dr. Lopez is Thomas's doctor. During his appointment, Thomas says he thinkshe has insomnia and wants to be on a specific drug. What should Dr. Lopezdo?O A. Conduct an exam. Thomas might have a drug dependence.O B. Dr. Lopez can't do anything at all. Thomas needs to talk to apharmacist about this.O C. Trust Thomas and prescribe him the medication.O D. Suggest Thomas use a different drug. 33 m44 mWhat is the length of the hypotenuse?C=meters i need help asap pleaseeeeeee All of the following are important environmental problems in Latin American cities, except __________.A.water scarcityB.air pollutionC.transpirationD.waste disposalPlease select the best answer from the choices providedABCD Platinum is a catalyst humans use in fuel cell. Although for green energy humans use some bacteria that releases enzymes such as hydrogenase to perform functions as platinum in fuel cell. This is an example ofa. Biofilmb. Biosensingc. Biomimicry PLEASE HELP ASAP! DO IN 5 MINUTES! WILL MARK BRAINLIEST!!!!!! Please help me !! Pls A line passes through the point (4, -2) and has a slope of -5/4Write an equation in slope-intercept form for this line. How much more than the original $10,000 do you pay in interest? Given the first term and the common ratio of a geometricsequence find the first five terms and the explicit formula. a1= 0.8, r= 5