The edge length of a cube is changing at a rate of 10 in/sec. At what rate is the cube's volume changing when the edge length is 3 inches?

Answers

Answer 1

Given:

The edge length of a cube is changing at a rate of 10 in/sec.

To find:

The rate by which cube's volume changing when the edge length is 3 inches.

Solution:

We have,

[tex]\dfrac{da}{dt}=10\text{ in/sec}[/tex]

We know that, volume of cube is

[tex]V=a^3[/tex]

Differentiate with respect to t.

[tex]\dfrac{dV}{dt}=3a^2\dfrac{da}{dt}[/tex]

Substituting [tex]\dfrac{da}{dt}=10[/tex] and a=3, we get

[tex]\dfrac{dV}{dt}_{a=3}=3(3)^2(10)[/tex]

[tex]\dfrac{dV}{dt}_{a=3}=3(9)(10)[/tex]

[tex]\dfrac{dV}{dt}_{a=3}=270[/tex]

Therefore, the volume increased by 270 cubic inches per sec.


Related Questions

thankyou! the answer was wrong you saved me.

Answers

Answer:

hey

Step-by-step explanation:

Identify the expression which represents the calculation “subtract 3 from 15, then divided by 6

Answers

Answer:

[tex]\frac{15-3}{6}[/tex]

Step-by-step explanation:

You would start by writing the expression for “subtract 3 from 15", which would be [tex]\frac{15-3}{6}[/tex], then you would add on "then divided by 6", which would make it

Answer:

Step-by-step explanation:

15-3/6

15-3 over 6

12/6

2

Danny paid $17.22 for 6 gallons of gasoline. How much did Danny pay for one gallon of gas?

Answers

Answer:

Danny paid 2.87$ per gallon of gasoline

Step-by-step explanation: 17.22 divided by 6

Clara is putting magazines on a shelf. The shelf is 35.5 inches long and Each magazine is about 0.75 inch thick. About how many magazines can Clara place on the shelf?

A. 35
B. 45
C. 25
D. 70

Answers

C bc 35.5 x 0.75 = 26.625 but it is not on there so the closest number to it is 25 hope this helps

find the sum of the interior angle measures of the polygon

Answers

Answer:  1260

Work Shown:

We have 9 sides of this polygon. See the diagram below. So n = 9

Plug that into the formula below to find the sum of the interior angles

S = 180(n-2)

S = 180(9-2)

S = 180*7

S = 1260

hannah and jayna have disponsable camreas. The table and desprition shiw the number of shots left on thier cameras as a function of time.

Answers

Answer:

Okay, so what is the question?

Answer:

   Tornado: clouds, strong wind, rain, hail.

   Hurricane or cyclone: strong wind, heavy rain.

   Blizzard: heavy snow, ice, cold temperatures.

   Dust storm: strong winds, arid conditions.

   Flood: heavy rainfall.

   Hail storm: cold or warm temperatures, rain, ice.

   Ice storm: freezing rain.Step-by-step explanation:

I need answers for both! plz help
Lealani has 24 scoops of high-fiber chimp food.

a. How many scoops of high-protein food should Lealani add to the mix if she wants to give it to baby chimps? Recall that baby chimps need 40% high-fiber food and 60% high-protein food.

b. How many scoops of high-protein food should Lealani add to the mix if she wants to give it to adult chimps? Recall that adult chimps need 60% high-fiber food and 40% high-protein food.​

Answers

Answer: a = 14.4 scoops; b = 9.6 scoops

Step-by-step explanation:

a.) 40% of the high fiber scoops is 9.6. We need to figure out how much of the high protein she needs, so we would subtract the 9.6 from 24 and get 14.4.

b.) Solved the same as the first problem but with different numbers. 60% of her high fiber food is 14.4, so subtract that from 24 and you get 9.6.

Hope this helps! :) Sorry if I made a mistake

Clare ran 4 miles on Monday. Then for the next six days, she ran the same distance each day. She ran a total of 22 miles during the week. Which tape diagram represents this situation?

Answers

Answer:

In a week we have 7 days.

On the first day, Clare runs 4 miles.

On the other six days, she runs the same distance, let's call it D.

In total, she runs 22 miles.

Then:

4mi + 6*D = 22 mi

6*D = 22mi - 4mi = 18mi

D = 18mi/6 = 3mi.

Then the other 6 days, Clare runs 3 miles, then the tape diagram would look something like:

[tex]\left[\begin{array}{cccccc}Monday&-&-&-&-\\Tuesday&-&-&-\\Wednesday&-&-&-\\Thursday&-&-&-\\Friday&-&-&-\\Saturday&-&-&-\\Sunday&-&-&-\end{array}\right][/tex]

Where each "-" represents one mile.

Answer:

3 miles

Step-by-step explanation:

HELP!!!
Select the correct answer.

Which equation describes the line graphed above?

A. y = 3/2x - 6

B. y = 2/3x - 6

C. y = 3/2x + 4

D. y = 2/3x + 4

Answers

The correct answer is C: y=3/2x+4
Hope that helps
the answer is c hope this helps

57.8 divided by 81, estimate quotient

Answers

Answer:

0.71358024691 But really you can say .7

Which algebraic expression is equivalent to the expression below? 5x + 10x + x


A. 11x

B. 8x

C. 17x

D. 16x

Answers

Answer: D

Step-by-step explanation: Just simplify the whole expression. It’s all the same variable. 5x+10x= 15x. 15x+x=16x.

Answer:It’s D
Explanation:

Please help me with this. If you show your work I will give brainliest if there are 2 answers

Answers

Answer:  22.5

Work Shown:

450 calories = 20 ounces

450/20 calories = 20/20 ounces ..... divide both sides by 20

22.5 calories = 1 ounce

This smoothie has 22.5 calories per ounce.

Rachel and Hugo sorted 236 crayons into boxes for a local arts project. Each boz had 10 crayons. How many crayons were left over?

Answers

If there are 236 dragons which you sorted into boxes of 10 crayons each, you have 6 crayons left over.

If the surface area of a cylinder is 288 picm2 with radius of 8 cm, what is the volume of the cylinder? (in terms of m)
A)
320pi cm3
B)
640pi cm3
9.
720pi cm?
D)
980pi cm3
help me pls hurry thanku

Answers

Answer: The volume of the cylinder is 640π cm³

Step-by-step explanation:

The formula of the surface area of a cylinder is SA = 2πrh + 2πr², where r is the radius of its base and h is its height

The formula of the volume of a cylinder is V = πr²h

Let us use the formula of the surface area to find the height of the cylinder, then use the formula of the volume to find its volume

∵ The surface area of a cylinder is 288π cm²

∵ Its radius is 8 cm

∵ SA = 2πrh + 2πr²

- Substitute the SA by 288π and r by 8 in the formula

∴ 288π = 2π(8)h + 2π(8)²

∴ 288π = 16πh + 128π

- Subtract 128π from both sides

∴ 160π = 16πh

- Divide both sides by 16π

∴ 10 = h

∴ The height of the cylinder is 10 cm

Now let us find the volume of the cylinder

∵ V = πr²h

- Substitute r by 8 and h by 10

∴ V = π(8)²(10)

∴ V = π(64)(10)

∴ V = 640π

The volume of the cylinder is 640π cm³

PLEASE HELP!
x=3 is a factor of x^3+3x^2-7x+19.
A. Never
B. Always
C. Sometimes

Answers

Answer:

I think it is

C. Sometimes

Solve -3(5x-9) please

Answers

Answer:

12

Step-by-step explanation:

The school Library was building a new one-room addition. the architects drawing shown below uses the scale 1/8 in = 1ft

Dimensions: 2 1/4 and 3 3/16

Using the dimensions indicated on the drawing, what is the total area of the new room?

Answers

Answer:

the total are is 459

Step-by-step explanation:

3  3/16 divided by 1/8 = 25 1/2 or 25.5

2  1/4 divided by 1/8 = 18

so 18 x 25.5 = 459

hope this helps

The total area of the new room is 459.

What is the scale factor?

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

WE are given that school Library was building a new one-room addition. the architects drawing shown below uses the scale 1/8 in = 1ft

Dimensions: 2 1/4 and 3 3/16

Therefore,

3  3/16 divided by 1/8 = 51/2 or 25.5

2  1/4 divided by 1/8 = 18

Thus we have the area

= 18 x 25.5

Area = 459

The total area of the new room is 459.

Learn more about scale factor here:

https://brainly.com/question/11178083

#SPJ2

Graph a line with a slope of 4 that contains the point (3,0).

Answers

Hi there!

Recall that slope-intercept form is:

y = mx + b

Where m = slope

In this instance, we are given a slope of 4, therefore:

y = 4x + b

Substitute in the x and y coordinates of the point given:

0 = 4(3) + b

0 = 12 + b

Subtract 12 from both sides:

-12 = b

Therefore, the equation would be:

y = 4x - 12

Graph the equation by finding x and y values or using a calculator:

x = 0, y = 4(0) - 12 = 12            (0, 12)  

x = 1, y = 4(1) - 12 = -8               (1, -8)

x = 2, y = 4(2) - 12 = -4             (2, -4)

x = 3, y = 4(3) - 12 = 0              (3, 0)

And so forth:

To graph a line passing through a point (3, 0) and slope 4, we will find the equation of the line first.

Since, equation of a line passing through a point (h, k) and slope 'm' is given by,

y - k = m(x - h)

Therefore, equation of a line passing through (3, 0) and slope 4 will be,

y - 0 = 4(x - 3)

y = 4x - 12

For y-intercept put x = 0 in the equation,

y = 4(0) - 12

y = -12

For x-intercept put y = 0 in the equation,

0 = 4x - 12

x = 3

Therefore, line will intersect x-axis at (3, 0) and y-axis at (0, -12).

              By joining these points we can find the graph of the line passing through (3, 0) and having slope = 4.

Learn more,

https://brainly.com/question/18817730

what are both square roots of 196

Answers

hi  

square  roots of  196  is  : 14 and  -14   as  14² = 196  and (-14)² = 196

in 2005 a company spent 493,749,335 on advertising. round the advertising figure to the nearest hundred thousand.​

Answers

Answer: 493,700,000

Step-by-step explanation:

Which property justifies drew first step ?



A.commutative property of multiplication

B.associative property of addition

C. subtraction property of equality

D. distributive property of multiplication over addition

Answers

D) Distributive property of multiplication over addition


Which values, in order, will complete the table

Answers

Answer:

A or -1/2, -rad2/2, -rad3/2

Step-by-step explanation:

Right on edge

Answer:

A

Step-by-step explanation:

correct on edge 202222222

Use the figure to find the measure of
the angle. Explain your reasoning.

1. ∠4

2. ∠5

3. ∠8

4. ∠6

Answers

Answer:

1. ∠4 = 152°

2. ∠5 = 152°

3. ∠8 = 152°

4. ∠6 = 28°

Step-by-step explanation:

1. ∠4 and 152° are vertical angles. Therefore, m∠4 = 152°.

2. ∠5 and 152° are corresponding angles. Therefore, m∠5 = 152°

3. ∠8 and 152° are alternate exterior angles, therefore, m∠8 = 152°

4. ∠6 and <8 are a linear pair. Therefore,

m∠6 + m∠8 = 180°

m∠6 = 180° - m∠8

m∠6 = 180° - 152°

m∠6 = 28°

Find the quotient of 60:5

Answers

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

60:5 = 60/5. 60/5=12

Convert 144 pounds to kilograms. Use 1 kg = 2.2 Ib. Round your answer to the nearest tenth. kg​

Answers

Answer:

Since 1 kg is equals to 2.2 lb. You divide 144 by 2.2 :

144/2.2

=65.45

=70 kg

Can anyone help me find parallel segments in this diagram ? It doesn’t matter if it’s just a few or 2

Answers

Answer:

A-F parallel to B-D

B-A parallel to D-F

B-F parallel to C-E

Step-by-step explanation:

Line segment A-F is parallel to B-D

Line segment B-A is parallel to D-F

Line segment B-F is parallel to C-E

How long will it take an investment to double in value if the interest rate is 6% compounded continuously

Answers

Answer:

11.55 years

Step-by-step explanation:

Formula to calculate the final value when the money is compounded continuously is,

Final value = [tex]\text{(Present value)}.e^{rt}[/tex]

Here 'r' = rate of interest

t = duration for the investment

Let the money invested = $x

We have to find the duration in which the present value gets doubled.

Final value = $2x

Rate of interest = 6% per year ≈ 0.06

By substituting these values in the formula,

[tex]2x=x.e^{0.06t}[/tex]

[tex]2=e^{0.06t}[/tex]

ln(2) = [tex]\text{ln}e^{0.06t}[/tex]

0.693147 = 0.06t

t = 11.55 years

Therefore, invested amount will be doubled in 11.55 years.

Need help desperately, I dont want to fail. please answer​

Answers

pretty sure it’s (2, -2)

12x+y when x=3 and y=52

Answers

88 I believe 12(3) = 36 + 52 = 88

Please Help me with this​

Answers

Answer:

16X^2 - 8x

Step-by-step explanation:

A = L x W

L = x + 5 + 3x + 4x - 9 = 8x - 4

W = 2x

(8x - 4) (2x) = 16x^2 - 8x

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