In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all directions. Assuming that the area polluted is a circle and that its radius is increasing at a rate of 3ft/sec, determine how fast the area is increasing when the radius of the circle is 30 feet. Hint: consider that the radius r is a function, and we know the rate of change of r with respect to time.

Answers

Answer 1

Answer:

180π ft/sec

Step-by-step explanation:

Since the area pollute sis assumed to be a circle, we will be using the formula for calculating the area of a circle to solve the problem.

Area of a circle A = πr²

r is the radius of the circle

The rate at which the area is increasing is expressed as dA/dt. According to chain rule, dA/dt = dA/dr*dr/dt where;

dr/dt is the rate at which the area is increasing.

If dA/dr = 2πr (by mere differentiation)

dA/dt = 2πr * dr/dt

Given dr/dt = 3ft/sec and r = 30feet

dA/dt = 2π(30) * 3

dA/dt = 180π ft/sec

Hence, the area is increasing at the rate of 180π ft/sec


Related Questions

A person who takes a 10-minute shower might use between 20 and 25 gallons of water,depending on the speed of the water passing through the showerhead . The lower the speed, the less water that is used.

The equation w=2.5m models the amount of water, w, in gallons that passes through a showerhead in minutes.

Which is the independent variable and which is the dependent variable?

The amount of water in gallons, w, is the independent or dependent variable.

The time in minutes, m, is the independent or dependent variable. ​

Answers

Answer:

The amount of water in gallons, w, is the dependent variable.

The time in minutes, m, is the independent variable.

Step-by-step explanation:

The amount of water in gallons depends on the time in minutes. If the time is higher, the amount of water in gallons will be higher. If the time is lower, the amount of water in gallons will be lower.

Hope that helps.

The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute.

A 2-row table with 10 columns. The first row is labeled time (minutes) with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4, 4.5. The second row is labeled temperature (degrees Celsius) with entries 75, 79, 83, 86, 89, 91, 93, 94, 95, 95.5.
According to the line of best fit, at what time will the temperature reach 100°C, the boiling point of water?

Answers

Answer:

A.) 5

Step-by-step explanation:

the answers for me are 5, 5.5 ,6 ,6.5

A line of best fit will show that the time at which the temperature will reach 100°C, the boiling point of water is 6.5 minutes

What is a line of best fit?

A line of best fit in a line graph is the line that allows for equal amount of outliers to the left and to the right of the line.

The line plot of the data above will have time on the horizontal axis and temperature on the vertical axis.

Plotting the points on the graph and drawing a line of best fit will show that the time at which the temperature will reach 100 °C is 6.5 minutes.

Therefore, the time at which the temperature will reach 100°C, the boiling point of water is 6.5 minutes.

Learn more about line of best fit at: https://brainly.com/question/1441182

If 18% of q is 27 , what is 27% of 2q

Answers

In this problem, there are two parts. We will need to find what q is if 18% of q is 27, and what 27% of 2q is.

First, let's set up and solve the equation for 18% of q is 27.

18 / 100 = 27 / q

100q = 486

q = 4.86

Next, we'll find the value of 2q.

2(4.86) = 9.72

Finally, we'll set up a proportion and solve for 27% of 2q.

27 / 100 = x / 9.72

100x = 262.44

x = 2.6244

If 18% of q is 27, then 27% of 2q is 2.6244 (round to tenths/hundredths place as needed).

Hope this helps!! :)

Answer:

81

Step-by-step explanation: Let's first find the value of q

[tex]18/100 \times q = 27\\\frac{18q}{100} = \frac{27}{1}\\18q = 2700\\\frac{18q}{18} = \frac{2700}{18} \\q= 150.\\[/tex]

Now we can find 27% of 2q

[tex]27 \% \times 2q = \\27 \% \times 2(150)\\\frac{27}{100} \times 300\\\\= \frac{8100}{100} \\= 81[/tex]

If log3=0.4771 and log2=0.3010,Find the value of log12

Answers

Answer:

log 12 = 1.0761

Step-by-step explanation:

log 12

=log(3*2*2)

= log 3 +log 2+ log 2

=0.4771+0.3010+0.3010

=1.0761

Answer:

Log 12 = 1.0791

Step-by-step explanation:

=> log (12)

Prime Factorizing 12

=> log (2×2×3)

Using log rule : [tex]log (a*b) = log a+logb[/tex]

=> Log 2 + log 2 + log 3

Given that log 2 = 0.3010 , log 3 = 0.4771

=> 0.3010 + 0.3010 + 0.4771

=> 1.0791

Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y

Answers

Answer:

135° and 45° respectively

Step-by-step explanation:

x + y = 180° (angles on a straight line)

x = 3y (corresponding angles)

3y + y = 180°

4y = 180°

y = 180/4

y = 45°

x = 180 - y

x = 180 - 45

x = 135°


Stephanie casts a shadow of 1.2 m and she is 1.8 m tall. A wind turbine casts a shadow of 10m at the same time that Stephanie measured her shadow. Draw a diagram of this situation
and then calculate how tall the wind turbine is.​

Answers

Answer:

see below for a diagram15 m

Step-by-step explanation:

Stephanie is 1.8/1.2 = 1.5 times as tall as her shadow is long. We expect the same is true of the wind turbine.

The wind turbine's shadow is 10 m long, so its height is 1.5·(10 m) = 15 m.

The wind turbine is 15 m tall.

Paige launched a ball using a catapult she built. The
height of the ball (in meters above the ground) t seconds
after launch is modeled by
h(t) = -5t2 + 40t
Paige wants to know when the ball will hit the ground.
1) Rewrite the function in a different form (factored
or vertex) where the answer appears as a number in
the equation.
h(t) =
2) How many seconds after launch does the ball hit
the ground?
seconds

Answers

Answer:

5 seconds ma boii

Step-by-step explanation:

i just took tha test

Answer:

1) h(t) = -5t(t - 8)

t - 8 = 0, so

2) t = 8 seconds

Step-by-step explanation:

Help me please I can’t figure it out

Answers

Answer:

2 m

Step-by-step explanation:

The bottom length of the bottom cuboid is equal to the top length of the bottom cuboid.

8 = 3 + c + 3

8 = c + 6

8 - 6 = c

2 = c

Answer:

2 is the missing length

Step-by-step explanation:

3 + x+ 3 =8

6+x =8

x= 8-6

x=2


x + y = 6
X - 4y = 1
Find the solution of the system of equations by using
elimination.

Answers

Answer:

x=5, y=1

Step-by-step explanation:

First, you need to multiply both sides of the second equation by -1 so that you can proceed the elimination process. Like this...

x + y = 6

x - 4y = 1

x + y = 6

-x + 4y =- 1

Now you can eliminate the x variable by addition process. It becomes like this...

x + y = 6

-x + 4y =- 1

5y=5

y = 1

Now, let's proceed substitution process. You can substitute the value of y into any equation that you want. I want to put the value of y into the equation of x + y = 6 .

When y=1, substitute into x + y = 6

x + 1 = 6

x = 6-1

x = 5

Hooray! Now you have the value of x and y.

x= 1 and y=5.

I hope you will understand my explanation. Bye!

|3x+9|= 30

Answer: x=7, -13

Answers

Answer:

[tex]\boxed{x=7, \: x=-13}[/tex]

Step-by-step explanation:

[tex]|3x+9|= 30[/tex]

Solve for absolute value.

There are two possibilities.

One possibility:

[tex]3x+9=30\\3x=21\\x=7[/tex]

Second possibility:

[tex]3x+9=-30\\3x=-39\\x=-13[/tex]

Driving on the highway, you can safely drive 60 miles per hour. “How far can you drive in ‘h’ hours?” What is the range of the function which defines this situation?
A. 60
B.the number of hours you drive
C.the amount of gas you use
D.the distance you drive

Answers

Answer:

D.the distance you drive

Step-by-step explanation:

The range of the function is the values of the output

h is the input

60h is the output

60 = miles driven = distance

Answer:

the answer would be D. the distance you drive

Step-by-step explanation:

because i took the quiz and put this answer and got it right

What is a square root

Answers

Answer:

A square root of a number is a value that, when multiplied by itself, gives the number.

Examples:

4 multiplied by itself is 16. Therefore, the square root of 16 is 4.

(4 x 4 = 16)

The same goes for every number.

(3 x 3 = 9) square root of 9 is 3

(5 x 5 = 25) square root of 25 is 5

finding the number which was multiplied to itself giving the given product of question

Help, I need an answer ASAP

Answers

Answer::

SSS: When all three sides are equal to each other on both triangles, the triangle is congruent. AAS: If two angles and a non-included (you can think of it as outside) side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Therefore let's solve according to the statement..

1) yes..all three sides are equal

2)no..all sides aren't equal

3)yes..all sides are equal

4)no..all sides aren't equal

Hope this helped u..

Answer:

1) No 2) No 3) Yes; SAS 4) Yes; AAS

Step-by-step explanation:

In the first triangle, you see two sides are congruent to each other, and there is an angle but it is not in between. An Angle-Side-Side-Postulate doesn't exist, so this will be a no. For number 2, you see one angle and two sides are congruent. The angle isn't between the triangles, so this is not congruent. Again, an Angle-Side-Side Postulate doesn't exist. For number three, we see two sides are given, and the two triangles intersect. This gives us a vertical angle, and vertical angles are congruent. We can conclude these triangles are congruent by the Side-Angle-Side Postulate. Lastly, we're given one side and one angle. We can also infer that the vertical angles are congruent, so this will be the result of Angle-Angle-Side.

Julie gathered data about the numbers of pages and chapters in several books by her favorite author.The equation of the line of best fit is y = 15.261x + 8.83. Based on the line of best fit, approximately how many pages are predicted to be in a book with 8 chapters? A. 113 B. 122 C. 131 D. 193

Answers

Answer:

C

Step-by-step explanation:

To get the approximate number of pages in the chapters, what we need to do is to substitute for the value of x in the line of best fit equation.

Thus, we have;

y = 15.261(8) + 8.83 = 122.088 + 8.83 = 130.918

This is approximately equal to 131

A taste test asks people from Texas and California which pasta they preferred brand a or brand b this table shows the results. A person is randomly selected for those tested. What is the probability that the person is from Texas given that the person prefers Brand b? Round your answer to two decimal places.

Answers

Answer: I just did it and the answer is 0.43

Step-by-step explanation:

Using it's concept, it is found that the probability that the person is from Texas given that the person prefers Brand b is given by:

A. 0.43.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 105 people prefer brand B, and of those, 45 are from Texas, hence:

p = 45/105 = 0.43.

Which means that option A is correct.

More can be learned about probabilities at https://brainly.com/question/14398287

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The distance from Parrot Point Airport to the Ivy Cliffs is 291 miles at and angle of 9.1 degrees northeast. There is a wind blowing southeast at 25 miles per hour. You want to make this trip in 3 hours by flying straight there. At what speed* and heading should you fly?

Answers

Answer:

The speed V = 194.03 mph

Direction = 3.6° northeast

Step-by-step explanation:

The distance of the trip = 291 miles

The direction of flight = 9.1 degrees northeast

Speed of the prevailing wind = 25 mph

Direction of wing = southeast = 45 degrees South of East

The speed heading to Ivy Cliffs = V₁

V×(sin(9.1) + cos(9.1)) + 25×(-sin(45) + cos(45))  × t₁ = 291 miles

V×(sin(9.1) + cos(9.1)) + 25×(sin(45) + -cos(45))  × t₂ = 291 miles

t₁ + t₂ = 3 hours

(V×(sin(9.1)-25×(sin(45))j + (V×cos(9.1) + 25×cos(45))i

The magnitude V² = V²+29.32·V +625= 291²/t₁²......(1)

Also on the return trip we have;

V²-29.32·V +625= 291²/(3-t₁)²..........................................(2)

Subtracting equation (2) from (1) gives;

58.64·V = 291²/t₁² - 291²/(3-t₁)² = 291²×(6·t-9)/(t²·(t-3)²)

V = 291²×(6·t-9)/(t²·(t-3)²)/58.64

Substituting the value of V in (2) with a graphing calculator gives;

t₁= 1.612 or 1.387

Given that magnitude of the speed going > return = V² for  t₁ < t₂

t₁ = 1.387, t₂ = 1.612

From  V²+29.32·V +625= 291²/t₁², we have

V²+29.32·V +625= 291²/1.387²

Which gives

V²+29.32·V -43336.5 = 0

(V + 233.35)(V-194.03) = 0

V = -233.35 mph or V = 194.03 mph

Given that V is a natural number, we have, V = 194.03 mph.

The direction is given by the relation;

V×(sin(9.1) + cos(9.1)) + 25×(-sin(45) + cos(45))  × t₁ = 291 miles

V×(sin(9.1) + cos(9.1)) + 25×(-sin(45) + cos(45))  × t₁ = 291 miles

194.03×sin(9.1 degrees)-25×sin(45 degrees)j + 194.03×cos(9.1 degrees) + 25×cos(45 degrees)i = 291/1.387

13j + 209.27i = 208.81 mph

The angle tan θ = 13/209 = 0.00622

θ = tan⁻¹(13/209.27) = 3.6°.

What is the slope of the graph shown below?
A. -2
B. 1
C. 2
D. 1/2

Answers

Answer:

i think its the answe d but not sure

Mr.Brown is creating examples of systems of equations. He completes the steps to find the solution of the equation below. Based on this week, what solution to the system?
•(-4,-4)
•(0,0)
•no solution
•infinitely many solutions

Answers

Answer:

infinitely many solutions

Step-by-step explanation:

0 = 0 ← is a true statement.

Indicates that the 2 lines are the same line, that is one lying on top of the other.

Thus the system has an infinite number of solutions

Because Mr. Brown arrived to an identity, we conclude that there are infinitely many solutions.

How many solutions does the system have?

First, the solutions of a system of equations are the points (x, y) where the graphs of both equations intercept.

Particularly, if we have two times the same equation, then the graphs intercept in infinite points, which means that we will have infinite solutions.

So, always that we have an identity in our solution (something like 0 = 0) we have infinite solutions (that happens because we do not have restrictions for x or y, which means that for every value of x, we will find a point (x, y) that is a solution of the system).

Then we conclude that the system has infinitely many solutions.

If you want to learn more about systems of equations:

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A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an inequality as x + 2x + 6 < 50, where x represents the smaller number. From the set {13, 14, 15, 16, 17}, the values of x for which the inequality holds true are choise 13,14 13,14,15 15,16,17 16,17

Answers

Answer:

5

Step-by-step explanation:

To which set or sets below does the number -7/8 belongs to ?

Answers

Answer:

-7/8

Step-by-step explanation:

The volume inside of a sphere is V=4πr33 where r is the radius of the sphere. Your group has been asked to rearrange the formula so that it is rewritten to solve for r. Below are various solutions that your group-mates have arrived at. Select the correct one A) r=3V4π−−−√ B) r=3V4π−−−√3 C) r=3V√34π D) r=4V3π−−−√3

Answers

Answer:

Step-by-step explanation:5

Run A Regression Analysis Job Evaluation Weighted Points Avg. $ X Y Dealer 120 19944.44 Shark 145 29458.33 Laborer 175 34000 Banker 215 56875 Consultant 245 62900 Completion of:
Task A: Conduct a simple regression in Excel to create a market pay line by entering the job evaluation points (on the X axis) and the respective weighted average market base pay (on the Y axis) for each benchmark job. Completion of
Task B: What is your R squared (variance explained)? Is it sufficient to proceed? Completion of
Task C: Calculate the predicted base pay for each benchmark job. Completion of
Task D: Because your company wants to lead in base pay by 3 percent, adjust the predicted pay rates to determine the base pay rate you will offer for each benchmark job. Completion of
Task E:
Task H: Create pay grades by combining any benchmark jobs that are substantially comparable for pay purposes. Clearly label your pay grades and explain why you combined any benchmark jobs to form a grade Completion of
Task F: Use your answer to Task H to determine the pay range (i.e., minimum and maximum) for each pay grade. Completion of
Task G: Given the pay structure you have generated, consider the following: Does this pay structure make good business sense?
Do you think it is consistent with the organization’s business strategy? What are the implications of this pay structure for other HR systems, such as retention and recruiting

Answers

Answer:

task b

Step-by-step explanation:

If f(x) is the total cost, in dollars, of x candles, which of the following statements best describes the meaning of f(2)=6

Answers

Answer: A) The total cost of 2 candies is $6.00.

Step-by-step explanation:

Hi, the question is incomplete,  options are :

A) The total cost of 2 candies is $6.00. B) The total cost of 6 candies is $2.00. C) The total cost of 2 candies is $3.00. D) The total cost of 3 candies is $2.00.  

So, to answer this question we have to analyze the function given:

f(2)=6

Since the input value x (number of candles) is 2, and the output (cost in dollars ) is $6, the correct option is :

A) The total cost of 2 candies is $6.00.  

The exchange rate for US dollars is £1=$1.62.How many dollars will I get for

a) £3. b)50p. c) £2.60 d) £5.63
Round your answer to 2 decimal places.​

Answers

A-4.86
B-
C-3.31
D-8.92

The length and width of a rectangular yard are 11 meters and 5 meters respectively. If each dimension were reduced by x meters to make the ratio of length to width 8 to 3, what would be the value of x

Answers

Answer:

x=7/5

Step-by-step explanation:

Original dimensions

Length=11 meters

Width=5 meters

Each dimension reduced by x meters

L=11-x

W=5-x

Length/width=ratio of length/ratio of width

11-x/5-x = 8/3

Cross product

(11-x)3 =( 5-x)8

33-3x=40-8x

-3x+8x=40-33

5x=7

x=7/5

Check:

11-7/5=55-7/5

=48/5

5-7/5=25-7/5

=18/5

48/5÷18/5

=48/5*5/18

=240/90

=24/9

=8/3

Length: width=8:3

Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.

(–2, 0)
(–2, 0) and (2, 0)
(–2, 0) and (3, 5)
no solutions

Answers

Answer:

c

Step-by-step explanation:

c

Answer:

the answer is C ;D

Step-by-step explanation:

I WILL GIVE BRAINLIEST!!!! A teacher is grading the final exam. He notices that the mean test score is 61, and the standard deviation is 10. The test scores were normally distributed. if there were 450 students in the data sample, how many would have a test score between 61 and 71 *Round your answer to the nearest full value.

Answers

Answer:

153.586 close to 154 students

Step-by-step explanation:

mean=61

standard deviation =10

sample 450 students , x between 61 and 71

(x-mean)/deviation for score 61 and 71

61-61/10=0

71-61/10=1

the z-scores is between 0 and 1 ( use calculator)

the percentage is 0.3413 close to 34%

number of students that score between 61 and 71=

450*0.3413= 153.586 close to 154 students

Need help quick quick quico

Answers

Answer:

7 batches

Step-by-step explanation:

3t+1/16-2t-3/7=t+3/8+3t-1/14​

Answers

Answer:

t = -(25/112)

In the xy-coordinate plane, a line has a slope of −5/3. If the line crosses the y-axis at (0, b), at what point does it cross the x-axis?

Answers

Answer:

([tex]\frac{3}{5}[/tex] b, 0 )

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

Here m = - [tex]\frac{5}{3}[/tex] and b = b , thus

y= - [tex]\frac{5}{3}[/tex] x + b ← equation of line

The line crosses the x- axis when y = 0, substitute y = 0 into equation and solve for x, that is

- [tex]\frac{5}{3}[/tex] x + b = 0 ( multiply through by 3 to clear the fraction )

- 5x + 3b = 0 ( subtract 3b from both sides )

- 5x = - 3b ( divide both sides by - 5 )

x = [tex]\frac{3}{5}[/tex] b , thus

x- intercept = ( [tex]\frac{3}{5}[/tex] b, 0 )

Answer:

( b, 0 )

Step-by-step explanation:

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