A block of ice in the shape of a cube melts uniformly maintaining its shape. The volume of a cube given a side length is given by the formula V = S^3. At the moment S = 2 inches, the volume of the cube is decreasing at a rate of 5 cubic inches per minute. What is the rate of change of the side length of the cube with respect to time, in inches per minute, at the moment when S = 2 inches?

Answers

Answer 1

Answer:

Ds/dt  = 1,25 in/minute

Step-by-step explanation:

s   is side of the cube

V(c) = s³

Differentiation on both sides of the equation with respect to time.

DV(c) / dt  = 2*s* Ds/dt          (1)

In that equation:

s  = 2

DV(c) /dt  = 5

By subtitution in equation (1)

5  = 2*s*Ds/dt

2*2*Ds/dt   = 5  

Ds/dt   = 5/4      Ds/dt  = 1,25 in/minute

Answer 2

The rate of change of the side length of the cube with respect to time, in inches per minute, at the moment when S = 2 inches is [tex]\dfrac{5}{12} \: \rm in^3/min[/tex]

How to calculate the instantaneous rate of growth of a function?

Suppose that a function is defined as;

[tex]y = f(x)[/tex]

Then, suppose that we want to know the instantaneous rate of the growth of the function with respect to the change in x, then its instantaneous rate is given as:

[tex]\dfrac{dy}{dx} = \dfrac{d(f(x))}{dx}[/tex]

Let the rate of change of volume V with respect to time t is given by:

[tex]\dfrac{dV}{dt}[/tex]

And let the rate of change of volume S with respect to time t is given by:

[tex]\dfrac{dS}{dt}[/tex]

The relation between V and S is [tex]V = S^3[/tex]. Using this value, and the chain rule of differentiation, we get:

[tex]\dfrac{dV}{dt} = \dfrac{dS^3}{dt} = 3S^2\dfrac{dS}{dt} = 3S^2\dfrac{dS}{dt}\\\\\dfrac{dS}{dt} = \dfrac{1}{3S^2} \dfrac{dV}{dt}[/tex]

At S = 2, we are given that:  [tex]\dfrac{dV}{dt} = 5 \: \rm in^3/min[/tex]

Putting these values in the equation for rate of S, we get:

[tex]\dfrac{dS}{dt} = \dfrac{1}{3S^2} \dfrac{dV}{dt}\\\\\dfrac{dS}{dt} = \dfrac{1}{3(2)^2}\times 5 = \dfrac{5}{12} \: \rm in^3/min[/tex]

Thus, the rate of change of the side length of the cube with respect to time, in inches per minute, at the moment when S = 2 inches is [tex]\dfrac{5}{12} \: \rm in^3/min[/tex]

Learn more about instantaneous rate of change here:

https://brainly.com/question/4746888


Related Questions

4. Find the missing angle

PLS I NEEDDDD HELPPP WILL GIVE BRAINLIEST TO WHOEVER ANSWERS.

Answers

Answer:

i’m not 100% sure, but i’m going to say it’s 30 degrees

Step-by-step explanation:

because ik that all triangles equal 180 degrees. if this is wrong, i’m so sorry.

Chad knows that 5 out of every 50 students at his school have blue eyes. There are 660 students at chads school. How many have blue eyes?

Answers

Answer:

66

Step-by-step explanation:

5=10% of 50

1/10 of the kids have blue eyes

660/10=66

Therefore 66 students at Chad's school have blue eyes.

Multiply. Write your answer in simplest form.
√5 √2
o
Submit

Answers

Answer:

1. the Square root of 5 is 2.5

2. There is no square root for 2.

Step-by-step explanation:

Answer:

[tex]\sqrt{10}[/tex]

Step-by-step explanation:

All you have to do for this is multiply the radicands by each other, so in this case 5 and 2. Once you multiply them, you place them back under the root.

Please help!! No like or I will report!​

Answers

Answer:

B . 3600π m²

is the answer

Step-by-step explanation:

i think so

Answer:

hello the answer is B . 3600π m² mark the other guy brainliest!!

Step-by-step explanation:

Kelly had 13 cups of strawerries. She wants to divide the strawberries into small daily servings. How many 1/3 cup servings are in the 13 cups of strawberries?

Answers

Answer:

Number of servings in 13 cups strawberries = 39

Step-by-step explanation:

Total amount of strawberries Kelly has = 13 cups

Amount of strawberries Kelly used in one serving = [tex]\frac{1}{3}[/tex] cups

Number of servings in 13 cups of strawberries = [tex]\frac{\text{Total amount of strawberries with Kelly}}{\text{Strawberries required in one serving}}[/tex]

= [tex]\frac{13}{\frac{1}{3}}[/tex]

= [tex]13\times \frac{13}{1}[/tex]

= 39

Therefore, number of servings in 13 cups strawberries = 39

Please explain this question in some simple language.

no spam answers please.​

Answers

Answer:

Below.

Step-by-step explanation:

I can't see the words on your image very well but I can give you an explanation of the remainder theorem.

The theorem allows you to find the remainder of a division without doing the division itself.

You can find the remainder when  a polynomial is divided by a linear expression like 3x - 2, for example,  using this theorem.

An example will explain the method:

What is the remainder when x^3 - x^2 - 2x - 5 is divided by 2x - 1?

Put 2x - 1 = 0, this gives x = 0.5.

Now we plug x = 0.5 into the polynomial:

This = (0.5)^3 - (0.5)^2 -2(0.5) - 5 = -6.125

So the remainder is -6.125.

The formal definition is

The remainder when P(x) is divided by x - a is f(a).

Mary opened a savings account that compounds interest yearly. She deposited money only when she opened her account. The
amount, A (t), in Mary's account t years after it was opened is given by the equation A (t) = 530 (1.002)^t. What is the growth
factor of this function?

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of growth rate.

Answer is D. 1.002

Since, it has power t for the growth rate to increase.

An internet movie rental company charges a yearly membership fee of $50 plus 1.99 per dvd rental

Answers

Answer: y= 1.99x+ 50

Equation: y=mx+b

Trinity asked a random sample of 50 students at her school if they brought lunch from home today. If 30 answered “yes,” about what percent of students at Trinity’s school brought lunch from home today?

a) 15%

b) 50%

c) 30%

d) 60%

Answers

Answer:

D

Step-by-step explanation:

60% of 50 equals 30

30% of 50 equals 15

15% of 50 equals 7.5

7.5% of 50 equals 3.75

3.75% of 50 equals 1.875


1+1+2+3+4+5+6+7+8+9+10

Answers

Answer:

56

Step-by-step explanation:

I need help with lattice.​

Answers

Here is your 4 ft. x 8 ft. Pressure Treated Garden Wood Lattice. Have a good day, good sir.

Link: https://www.homedepot.com/p/4-ft-x-8-ft-Pressure-Treated-Garden-Wood-Lattice-106026/202297464

If there are 2.54 cm in one inch, how many feet do 6096 cm equal? A. 200 ft B. 508 ft C. 2400 ft D. 15,483. 84 ft E. 28,800 ft​

Answers

Answer: A.200 ft

Step-by-step explanation:

You divide 6096 by 2.54. To get the inches. And then you divide that by 12 to get the number of feet

Answer:

200ft

Step-by-step explanation:

The shape of a lateral face of a pyramid is always an isosceles triangle?​

Answers

Answer:

No.

Step-by-step explanation:

Because the lateral faces of a regular pyramid are congruent isosceles triangles. The altitude of any of these triangles is the slant height of the regular pyramid.

what is the height of the triangle?
a.
[tex]5 \sqrt{2} [/tex]
[tex]5 \sqrt{3} [/tex]
[tex]10 \sqrt{2} [/tex]
[tex]10 \sqrt{3} [/tex]

Answers

[tex] \huge\boxed{ \mathfrak {\red{Answer :}}}[/tex]

Area of equilateral triangle :

=》

[tex] \huge{ \mathfrak{ \frac{ \sqrt{3} }{2} a {}^{2} }}[/tex]

where,

a is measure of side

So,

=》

[tex] \dfrac{ \sqrt{3} }{2} \times 10[/tex]

=》

[tex]10 \sqrt{3} [/tex]

[tex]\huge \boxed{\mathfrak{ \red{hope \: it \: helps}}}[/tex]

how many acute angles does an obtuse triangle have​

Answers

Answer:

i think 2

Step-by-step explanation:

ya i think 2

NEED ASAP!!!

Travis read 15 books, 10 magazines, and 25 newspaper articles last year. Based on this data, what percentage of the material that Travis read is a book?

Answers

Answer:

30%

Step-by-step explanation:

15+10+25=50

50x2=100

15x2=30

30/100=30%

Help lol
This is confusing

Answers

Step-by-step explanation:

omg why is this so hard....

Answer:

3. 4/5

4. 4/5

5. 3/4

6. 4/3

Step-by-step explanation:

Write the following in STANDARD FORM:
1. (x + 4) (2x - 6)
2.(x^2-2x-3)-(3x^2+x-6)

Answers

Answer:

1= 2x over 2,+2x-24.

2= -2x over 2 -3x+3

How can you find the constant of
proportionality from the coordinates of
one point on the graph?

Answers

Answer:

To  find the constant of  proportionality from the coordinates of

one point on the graph are as follows :-

1.) Find two easy points.

2.) Start with the leftmost point and count how many squares you need to up to get to your second point.  

3.) Count how many squares you need to go to the right.  

4.) Simplify, and you've found your constant of proportionality.

If correct i will make u brainliest

Answers

Exact form= 59049/1048576???
Sorry if I’m wrong

Another answer I got is 225/16

Please answer this question

Answers

Answer:

4.5

Step-by-step explanation:

Do 3x3 as a whole square, do 9 divided by 2 which is 4.5

Find the area of the rectangle and subtract the area of the triangle:

Area rectangle = 9 x 3 = 27 m^2
Area triangle = (3x3) / 2 = 4.5 m^2

Shaded area = 27 - 4.5 = 22.5m^2

A set of data is described as:

The data is around 7. If another measurement were taken it would probably be around 7.

Which group of measures would lead to this conclusion? Think backwards to look at the sets of data that would give the results described above.

Range—4, Mode—6, Median—7, Mean—8
Range—5, Mode—9, Median—9, Mean—7
Range—12, Mode—9, Median—9, Mean—9
Range—10, Mode—7, Median—9, Mean—5

Answers

Answer:

B. Range - 5

Mode - 6

Median - 7

Mean - 8

step by step explaination:

if it's actually around 7, that's means 7 is equal to the median. And then, specifically, the mode & the mean number will side-to-side number of 7..which means number 6 and number 8.

Could you help me with this problem?

Answers

All of them I think since polynomial consists of two or more terms.

year.
Jeevan buys a bike for Rs 200000. At the end of 1 year, the value of the bike has depreciated by 15 percent.How much is the bike now worth?​

Answers

Answer:

Rs.170000

Step-by-step explanation:

Given data

Cost price of bike= Rs 200000

Time= 1 year

Rate of depreciation= 15%

Let us apply the formula for depreciation

A=P(1-r)^t

A= 200000(1-0.15)^1

A= 200000(0.85)^1

A= 200000*(0.85)^1

A= 200000*(0.85)

A=Rs.170000

Hence the value of the bike will be Rs.170000

liza is running at the beach, if she runs 13.25 miles each day, how many miles will she run in seven days?

Answers

Answer:

92.75 miles per 7 days

Step-by-step explanation:

13.25 mi/day times 7 days works out to 92.75 miles per 7 days.

Answer:

92.75

Step-by-step explanation:

do 13.25 times 7

I bought 3 1/4 lbs of apples, 2 2/3 lbs of oranges, 5 3/4 lbs of peaches and 3 1/3 lbs of bananas. How many pounds of fruit did I buy?

Answers

Answer:

[tex]=3\frac{1}{4} + 2\frac{2}{3}+5\frac{3}{4}\\\\[/tex]

=[tex]\frac{13}{4} + \frac{8}{3} + \frac{23}{4}[/tex]

[tex]=\frac{(13*3)+(8*4)+(23*3)}{12} \\\\=\frac{39 + 32 + 69}{12} \\\\=\frac{140}{12}\\\\=\frac{35}{3}\\\\ = 11\frac{2}{3}lbs[/tex]

In a pet adoption center, there were a total of 252 cats and dogs. The number of cats exceeds the number of dogs by 44. Find the number of cats and dogs in the adoption center.

Answers

Answer:

cats = 148

dogs = 104

Step-by-step explanation:

(d + 44) + d = 252

2d + 44 = 252

      -44     -44

2d = 208

divide by 2

d = 104

252 - 104 = 148

Which represents the volume of the cylinder, in cubic
units?
1207
1307
3002
325.7

Answers

Answer: 300π

Step-by-step explanation: Volume=(pi)(radius^2)(height)

Volume=(pi)(5^2)(12)

V=(pi)(25)(12)

V=(pi)(300)

The volume of the given cylinder is equal to 300π.

What is volume?

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write volume as -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is to find the volume of the cylinder shown in the image.

The volume of cylinder is given by -

V = πR²h

Here, the radius of the cylinder base is 5 units. The height of the cylinder

is 12 units. So, we can write the volume as -

V = π x 5 x 5 x 12

V = 300π

Therefore, the volume of the given cylinder is equal to 300π.

To solve more questions on Prisms, visit the link-

https://brainly.com/question/22147194

#SPJ7

PLEASE HELP!! I've been stuck on this question for many days now and haven't found a correct answer! Thanks in advance!!!

Darius makes a shirt for $8. He sells the shirt for $18. By what percentage did Darius increase the cost of the shirt?

Answers

The first time I did the math including 8 but we are increasing it so it will just be how much did the price increase from 8 to 18 well I know 100% of 8 is 8 so thats 100% and 25% of 8 is 2 so I added the two and 8 + 8 = 16 + 2 = 18 I added those percents 100 + 25 = 125%

Answer:

225% seems like the best answer.

Put the following equation of a line into slope-intercept form, simplifying all
fractions.
2x + y = -5

Answers

Answer:

slope intercept form is y=mx + b  so y= -2x - 5

Step-by-step explanation:

subtract 2x from both sides.    

Answer:y=-2x-5

Step-by-step explanation:

slope intercept form is y=mx+b

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