) As an ice cube melts its surface area is decreasing at a rate of 6cm2/sec. Find the rate at which the length of each side is decreasing at the moment when each side has length 2 cm. [Hint: a cube has 6 sides and each side has area x 2 where x is the side length]

Answers

Answer 1

Answer:

The rate of decreasing of the length is 0.25 cm/s.

Step-by-step explanation:

The surface area of the ice cube is:

[tex]A_{ice}=6x^{2}[/tex]

Where x is the side of the cube.

Let's take the derivative of A with respect to "t" to get the rate of change.

[tex]\frac{dA_{ice}}{dt}=12x\frac{dx}{dt}[/tex]

We know that dA/dt = 6 cm²/s and x is 2 cm, so we just need to solve it for dx/dt which is the rate change of the length.

[tex]6=12(2)\frac{dx}{dt}[/tex]

[tex]\frac{dx}{dt}=\frac{1}{4}\: cm/s[/tex]

Therefore, the rate of decreasing of the length is 0.25 cm/s.

I hope it helps you!


Related Questions

HELP ME WITH THIS PLEASEEEEE? IM STUGGLING

Answers

Answer:

(x-5)(x+5)

Step-by-step explanation:

x^2 -25

We can rewrite this as the difference of squares

x^2 - 5^2

(x-5)(x+5)

Use the graph of the logarithmic function f(x) to answer the question.

What is the x- intercept?

Answers

Answer:

(0,-2)

Step-by-step explanation:

Are these answers all correct?

Answers

Answer:

Yes they are all right

Step-by-step explanation:

Answer:

Step-by-step explanation:

What is the Kinetic Energy of a 15 kg object that is moving with a speed of 30 m/s?

Answers

Answer:

6750J

Step-by-step explanation:

30^2=900 900x15=13500 13500/2=6750

Answer:

K=6750[J]

Step-by-step explanation:

[tex]Kinetic \:Energy=\frac{1}{2} mv^2\\\\K=\frac{1}{2} (15)(30)^2\\\\K=6750[J][/tex]

A cone has a radius of 5 ft and a height of 15 ft. It is empty and is being filled with water at a constant rate of 15 15 ft 3 ft3 / sec sec . Find the rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 2 ft. (You must also include the units)

Answers

Answer:

[tex]\frac{dr}{dt}=0.11062ft/sec[/tex]

Step-by-step explanation:

From the question we are told that:

Radius [tex]r=5ft[/tex]

Height [tex]H=15ft[/tex]

Rate [tex]R=15ft/3sec =5ft/s[/tex]

Surface Radius [tex]R_{surf}=2.2ft[/tex]

Generally the equation for Volume is mathematically given by

 [tex]V=\frac{1}{3}\pi*r^2h[/tex]

Since radius to height ratio gives

 [tex]\frac{r}{h}=\frac{5}{15}[/tex]

 [tex]\frac{r}{h}=\frac{1}{3}[/tex]

 [tex]h=3r[/tex]

Therefore

 [tex]V=\frac{1}{3}\pi*r^2(3r)[/tex]

 [tex]V=\pi r^3[/tex]

Generally the equation for Change of Volume is mathematically given by

 [tex]\frac{dv}{dt}=\pi \frac{d}{dt}(r^3)[/tex]

 [tex]\frac{dv}{dt}=\pi 3*r^2 \frac{dr}{dt}[/tex]

 [tex]\frac{dv}{dt}=\pi 3*(2.2)^2 \frac{dr}{dt}[/tex]

 [tex]\frac{dr}{dt}=\frac{5}{45.62}[/tex]

 [tex]\frac{dr}{dt}=0.11062ft/sec[/tex]

plz plz plz plz help me plz it is due in 1 hour and no links plz and I needed to be a decimal ​

Answers

Answer:

Solution given:

Area of parking space [parallelogram]=290ft²

base*height=290

base=290/29

base:10ft

Area of rectangular dimensions=11*7.4=81.4ft²

yes

The truck can not fit in the space because the length and breadth is less than that of the parallelogram parking area.

Area of truck bid 81.4ft².

What is the product of 2,436 x 5 and show work

Answers

Answer:

12180

Step-by-step explanation:

angle DAC= angle BAD
what is the length of side bd round to one decimal place

Answers

Answer:

BD ≈ 2.8 units

Step-by-step explanation:

By angle bisector theorem,

"If a segment bisects an angle of a triangle, then it divides the opposite side  into the segments which are proportional to the other two sides"

Here, AD is the bisector of the ∠BAC,

[tex]\frac{BD}{CD}=\frac{AB}{AC}[/tex]

[tex]\frac{8.1}{5.9}= \frac{BD}{2}[/tex]

BD = [tex]\frac{2\times 8.1}{5.9}[/tex]

BD = 2.75

BD ≈ 2.8 units

Plz help me well mark brainliest if correct..??

Answers

Answer:

C/5

Step-by-step explanation:

This is because there are 2 people in the 3| part, and 3 people under 6 in the 4| part.

Answer nyo po to...Ang hirap(;-;)....pls. Lang po

Answers

The answer goes here,

a) We have to tell the time and day which simone has to tell her sister, for picking her up from airport.

b) We have given the day (monday), time(7:00 pm) and total time to reach the destination(18 hours).

c) No such formula will be used here, we will just use our mental ability to solve this question.

d) She will leave at 7:00 pm, day has 24 hours. So, she will be in the flight on monday:

= 24 - (12 + 7) ----------- [12 here means the time of rest of the day,(morning to noon)]

= 24 - 19

= 5 hours

So, she will complete 5 hours of her destination on monday,now the time left is:

= 18 - 5

= 13

= (12 + 1 )hours

So, on tuesday, she will be in the flight for 12 hours (noon) and then on 1:00 pm she will reach the airport, as she needs and extra hour to plane so, the final time is 1:30 pm. And finally, the time she should tell her sister is 1.30 pm.

Which expression has the smallest value?

A. -15
B. |24|
C. -31
D. 42

Answers

Answer:

C

Step-by-step explanation:

Plz help me well mark brainliest!!

Answers

Answer:

735 mm³

Step-by-step explanation:

49 x 15 = 735

Answer:

735mm

Step-by-step explanation:

What is the explicit rule for the geometric sequence? 25.5, 5.1, 1.02, 0.204, ... an=25.5(15)n an=25.5(15)n−1 an=25.5(15)n+1 an=25.5(15)n+2

Answers

Given:

The geometric sequence is:

25.5, 5.1, 1.02, 0.204, ...

To find:

The explicit rule for the given geometric sequence.

Solution:

We have,

25.5, 5.1, 1.02, 0.204, ...

Here, the first term is 25.5 and the common ratio is:

[tex]r=\dfrac{a_2}{a_1}[/tex]

[tex]r=\dfrac{5.1}{25.5}[/tex]

[tex]r=\dfrac{1}{5}[/tex]

The explicit rule for a geometric sequence is:

[tex]a_n=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Putting [tex]a=25.5,\ r=\dfrac{1}{5}[/tex] in the above formula, we get

[tex]a_n=25.5(\dfrac{1}{5})^{n-1}[/tex]

Therefore, the correct option is B.

What is the probability that both spinners will land on 2?
1/12. 1/6. 1/4. 1/3

Answers

Answer:

1/4 bczz its not saying about the highest its about average and the average is 1/4

1/12 bc there are two spinners with 6 spots each

Tickets to the theater cost $8.00 for adults and $3.00 for children. A group of 2
total people showed up to the theater. They spent $93.00 total on tickets. How
many adults and children were in the group?

Answers

Answer: 9 adults 7 children

Step-by-step explanation:

what has the same value as 30%, percent of 18?

Answers

Answer:

Answer: 60.

Step-by-step explanation:

30 percent (calculated percentage %) of what number equals 18?

If a population is
a sample of the population could be
O A. ninth-graders at Peak School; all students at Peak School
B. math teachers; the entire school faculty
O C. people who purchased shoes; all customers
O D. all citizens; registered voters

Answers

Answer:

Step-by-step explanation:

D.all citizens; registered voters

Please help me answer the question

Answers

ANSWER-1Both triangles are equal.

Tuan is an artist. He is painting on a large canvas which is 40 inches wide. The height of the canvas is 6 inches less than the width. What is the area of Tuan's canvas?

Answers

Answer:

1360 inches.

Step-by-step explanation:

Equation: 40 × (40-6) Since 40 inches is the width :)

40-6= 34

34*40=1360

Taun's canvas is 1360 inches :)

You answered 85% of the questions on the quiz correctly. What fraction of
the questions did you answer correctly?

Answers

Answer:

A percentage is out of 100.

85/100

in lowest terms this is

17/20

Hope this helps :)

Step-by-step explanation:

15 points
Right triangle trigonometry

Answers

Answer:

Step-by-step explanation:

take theta as reference angle

tan theta=opposite/adjacent

=15/8

Answer:

option B

Step-by-step explanation:

First find opposite side using Pythagoras theorem:

[tex]17^2 = 8^2 + opposite^2 \\\\opposite^2 = 289 - 64 = 225\\\\opposite = 15[/tex]

Therefore,

          [tex]tan \theta = \frac{opposite}{adjacent} = \frac{15}{8}[/tex]

Find the sum of the first five terms of the geometric series 50 + 25 + 12.5 +

Answers

The sequence is geometric with first term  

a

1

=

100

and common ratio  

r

=

0.5

Explanation:

a

1

=

100

,

a

2

=

50

,

a

3

=

25

,

a

4

=

25

2

,

a

5

=

25

4

...

50

100

=

0.5

,

25

50

=

0.5

,

25

2

25

=

0.5

,

25

4

25

2

=

0.5

a

2

a

1

=

a

3

a

2

=

a

4

a

3

=

a

5

a

4

=

0.5

The ratio of successive term and preceeding term is constant

(

r

=

0.5

)

. Therefore the sequence is geometric whose first

term is  

a

1

=

100

and common ratio is  

r

=

0.5

[Ans]

HELP ME PLEASEEEE SOMEONEEE

Answers

probably 48 but i dont know
The answer you’re looking for is 56

A statistical question produces data that varies. Which question below will produce data that varies?
A. how many days are in a leap year
B. How many quarts are in a gallon
C. How many senses are there
D. How many students are in each class

Answers

The Answer is D. How many students are in each class.

Explanation: this is the only statistical question that would have data that varies. The other answer choices are all questions with one answer that are factual. But there can be any amount of students in a class and there are numerous types of classes so there is lots of data to be produced from this one question.

Need help Math Question Multiple Choice!

Answers

Given :

A function f(x) for different range of x.

To Find :

The value of f( -3 ) .

Solution :

We have to find the value of function at x = -3.

Now, in the given figure -3 lies in range x ≤ -2 and definition of function at that range is :

[tex]f(x) = \dfrac{2}{x}[/tex]

So, putting value of x = -3 in above equation, we get :

[tex]f(-3) = \dfrac{2}{-3} \\\\f(-3) = \dfrac{-2}{3}[/tex]

Hence, this is the required solution.

A sociologist develops a test to measure attitudes towards public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Find the Margin of Error (E) for the 95% confidence interval for the mean score of all such subjects.

Answers

Answer:

The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 27 - 1 = 26

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0518

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

In this question:

[tex]n = 27, s = 21.4[/tex]. So

[tex]M = 2.0518\frac{21.4}{\sqrt{27}}[/tex]

[tex]M = 8.45[/tex]

The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.

Write the equation of the line that passes through (-7,-4) and (-6,-2) in slope intercept form

Answers

Answer:

y = mx + b

m =(-2--4)/(-6--7)

m = 2

-2 = 2(-6) +b

b = 10

y= 2x + 10

Can someone help me please?

Answers

Answer:

.08

Step-by-step explanation:

Answer:

Hi, there your answer is 0.08

Step-by-step explanation:

Give m = -1/2 and n = -1/3 which statement is true?

Answers

Answer:

n

Step-by-step explanation:

Work Time Lost due to Accidents At a large company, the Director of Research found that the average work time lost by employees due to accidents was hours per year. She used a random sample of employees. The standard deviation of the sample was hours. Estimate the population mean for the number of hours lost due to accidents for the company, using a confidence interval. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number.

Answers

Answer:

(95.215 ; 100.785)

(95 ; 101) (nearest whole number)

Step-by-step explanation:

To obtain the confidence interval :

Mean ± margin of error

Mean = 98 hours

Margin of Error = Tcritical * (s/√n)

samole standard deviation, s = 5.6 hours

df = n - 1 = 18 - 1 = 17

Tcritical at (0.05, df = 17) = 2.110

Hence ;

Margin of Error = 2.110 * (5.6/√18) = 2.785

Confidence interval :

98 ± 2.785

Lower boundary = 98 - 2.785 = 95.215

Upper boundary = 98 + 2.785 = 100.785

(95.215 ; 100.785)

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