(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA dt in terms of dr dt . dA dt

Answers

Answer 1

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt. dA dt = dr dt (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 25 m?

Area of the circle A = πr²

dA/dr = 2πr where r is the radius of the circle

dA/dt = dA/dr * dr/dt

dr/dt is the rate of increase in radius of the oil spill.

Given

dr/dt = 1m/s

radius r = 25m

Substitute into the formula above;

dA/dt = dA/dr * dr/dt

dA/dt = 2πr * 1

dA/dt = 2π(25) * 1

dA/dt = 50πm²/s

dA/dt = 157.1m²/s

Hence the area of the spill is increasing at the rate of 157.1m²/s


Related Questions

Use synthetic division to find f(2)

f(x) = 2x3 –3x²+7X-12​

Answers

Step by Step Solution:

More Icon

STEP

1

:

Equation at the end of step 1

 

STEP

2

:

           x3 + 3x2 - 7x - 12

Simplify   ——————————————————

                 x + 4        

Checking for a perfect cube :

2.1    x3 + 3x2 - 7x - 12  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  x3 + 3x2 - 7x - 12  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -7x - 12  

Group 2:  x3 + 3x2  

Pull out from each group separately :

Group 1:   (7x + 12) • (-1)

Group 2:   (x + 3) • (x2)

1 result(s) found

x  

2

−x−3

Three workers arrive at work 15 minutes late, at a cost of $11 hour.

Answers

Answer:

They earned 8.25

Step-by-step explanation:

If they arrived late 15 minutes, then they lose a 1/4 of the pay. So they'd be making $8.25, and not the full $11 for that first hour.

Find the remainder when f(x) is divided by g(x) given that f(x) = 4x3 − 5x2 − 3x + 2 and g(x) = x − 3.

Answers

Given:

[tex]f(x)=4x^3-5x^2-3x+2[/tex]

[tex]g(x)=x-3[/tex]

To find:

The remainder when f(x) is divided by g(x).

Solution:

According to remainder theorem, if f(x) is divides by (x-c), then remainder is f(c).

Using remainder theorem, if [tex]f(x)=4x^3-5x^2-3x+2[/tex] is divides by [tex]g(x)=x-3[/tex], then remainder is f(3).

Substitute x=3 in f(x).

[tex]f(3)=4(3)^3-5(3)^2-3(3)+2[/tex]

[tex]f(3)=4(27)-5(9)-9+2[/tex]

[tex]f(3)=108-45-7[/tex]

[tex]f(3)=56[/tex]

Therefore, the required remainder is 56.

Louis deposited $300 into his bank account. She now has $4501. Enter and solve an equation to find how much was in his account before the deposit. Let it represent the variable.

Answers

Answer: $4,201

Step-by-step explanation: 4,501 - 300 = 4,201

Answer:

d+300=4501

Step-by-step explanation:

Take the total: 4501 and subtract it by the amount of money he deposited the second time: 300 and that will show you the missing amount he had in his account before the deposit.

4501-300=4201

A grocery store sells cheese for $0.48 a pound. What would be the price for 6 pounds of cheese?

Answers

Answer:

$2.88

Step-by-step explanation:

0.48×6=2.88

os the right answer

$0.48 x 6 pounds = $2.88

Calculate the area of the trapezoid.
12 mm
5 mm
9 mm
________square millimeters

Answers

Answer:

52.5 square millimeters.

Step-by-step explanation:

Area of a Trapezoid = (a+b/2)h

= (9+12/2)•5

=(21/2) • 5

= 10.5 • 5

= 52.5 square millimeters

hope this helps!

Answer:

52.5 mm^2 (square millimeters)

Step-by-step explanation:

Just split the figure into two sections to make a rectangle, and a right triangle (This whole figure can be thought of as a composite figure)

Once that is done, you will notice that the length and width of the rectangle is 9mm by 5mm, and the triangle is 3mm by 5mm (because 12mm - 9mm is 3 mm, and the height of the triangle is shared with the width of the rectangle).

The area of a triangle is 1/2(base×height) [just as a triangle is half of a rectangle], so the area of the rectangle is (length × width).

Therefore the 9mm by 5mm rectangle has an area of 9×5 mm = 45 mm^2, and the 3mm by 5mm triangle has an area of 1/2(5×3) = 15/2 = 7.5 mm^2.

Add both areas to find the total area:

45mm^2 + 7.5mm^2 = 52.5 mm^2.

____________________________

Or using the formula for the area of a trapezoid: A = h (b1 + b2) / 2

Where A is the area, b1 is the first base, b2 is the second base, and h is the height of the figure.

Given that our first base is 9, second base is 12, and our height is 5.

A = h ( b1 + b2 ) / 2 → A = 5 ( 9 + 12 ) / 2 → 5 ( 21 ) / 2 → 105 / 2 → 52.5

Then just put this quantity in mm^2 because it is the area of the figure in that unit.

→ 52.5 mm^2

_____________________________

Use the figure to decide the type of angle pair that describes 4 and 5

Answers

Answer:

Alternate interior angles

Step-by-step explanation:

Angles 4 and 5 are alternate interior angles

These are the weekly wages paid to staff in a hotel.

£245
£140
£525
£163
£195
£174
£140

What is the range of these wages?

What is the mean wage?

Answers

Answer:

range is 525-140=385

The mean of a set of numbers is the sum divided by the number of terms. Mean= 226

Step-by-step explanation:

hope that helper, have a good one

Range = 525 - 140 = 385

Mean =

[tex](140 + 140 + 163 + 174 + 195 + 254 + 525) \div 7 = 226[/tex]

someone pls help, find the length of the segment

Answers

the segment is 4 units long

hope this helps

The segment is 4 units long

Find the value of x. 4^3 = x

Answers

Answer:

x=64

Step-by-step explanation:

What is the sum of (2x2 + 5x -3) and (-3x2 -10 + x2)​

Answers

Answer:5x-13

Step-by-step explanation:

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[tex](2 {x}^{2} + 5x - 3) + ( - 3 {x}^{2} + {x}^{2} - 10) = \\ [/tex]

[tex]2 {x}^{2} - 2 {x}^{2} + 5x - 3 - 10 = [/tex]

[tex]5x - 13[/tex]

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What is the value to the expression -2.1(4.7+(-7.4))

Answers

The correct answer is 5.67
Someone said 5.67 so

HELP ASAP PLEASE

Given x^2=81, select all possible values of x.

A. -9
B. -3
C. 0
D. 3
E. 9

Answers

Answer:

A and E

Step-by-step explanation:

x² = 81

~Take the square root of both sides

x = ±9

Best of Luck!

Answer:

The answer is a and e

Step-by-step explanation:

Water flows through a pipe at a rate of 8 pints per hour. Express this rate of flow in cups per week.

Answers

Answer:

2,688 cups per week

Step-by-step explanation:

Lets begin by figuring out the pints per week/pints per day. Multiplying 8 times 24, we get our daily total of 192 pints per day. Multiply this by 7 and we get a total of 1344 pints per week. We now must convert these pints into cups, which can be done by multiplying the total amount of pints by 2. 1344 times 2 = 2,688 cups

2. If Mrs. Esposito drove 585 miles to North Carolina in 9 hours, what speed was she driving? (miles per hour) a. 55 mph b. 60 mph c. 58.5mph d. 65mph

Answers

Your answer is 65

Step-by-step explanation:

You need to divide 585 by 9 the answer is 65

Find f(5). f(x) = x2 + 2x
Help please

Answers

Answer:

Your answer is: 15

Your equation would have f(5) = x^2 + 2x

Substitute the given value into the function and evaluate.

Step-by-step explanation:

Hope this helped ; )

What is the z-score for Paula If she got 1400 on the SAT, the mean was 1100 and the
standard deviation was 275?

Answers

Yea it is 275 with standard subtract
1400-deviation=275

A bug starts at the origin of the coordinate plane. The bug moves One-fourth units right and One-fourth units down to point A. Which graph shows the location of point A?

Answers

Answer:

the answer would be d

Step-by-step explanation:

i took the test on edge2020

Answer:

D

Step-by-step explanation:

Edg 2020

The quadratic function modeling the height of a ball over time is symmetric about the line , where t is time in seconds. Which statement is true about this situation?


A.

The height of the ball is the same after 1 second and 3 seconds.

B.

The height of the ball is the same after 0 seconds and 4 seconds.

C.

The height of the ball is the same after 0.5 second and 5.5 seconds.

D.

The height of the ball is the same after 1.5 seconds and 3.5 seconds.

Answers

Answer:

A. The height of the ball is the same after 1 second and 3 seconds.

Step-by-step explanation:

The quadratic equation function modeling is used to analyze the relationship between variables in the equation. If the ball is at height and t is time then the ball is on symmetric line which will move for initial 1 second then stabilizes at 3 seconds.

grrrrrr please help i’ll give u a cookie :)

Answers

im only in 6th grade

Step-by-step explanation:

Which postulate or theorem proves that A CFE and ADFE are congruent? o OSSS Congruence Postulate O SAS Congruence Postulate O AAS Congruence Theorem O ASA Congruence Postulate 1 2​

Answers

Answer:

Option (1)

Step-by-step explanation:

Given:

CF ≅ DF

CE ≅ DE

To prove:

ΔCFE ≅ ΔDFE

Solution:

From ΔCFE and ΔDFE,

               Statements                             Reasons

1). CF ≅ DF                                  1). Given

2). CE ≅ DE                                2). Given

3). FE ≅ FE                                 3). Reflexive property

4). ΔCFE ≅ ΔDFE                       4). By SSS property of congruence

Therefore, SSS postulate of congruence will be the answer.

Option (1) will be the answer.

Answer:

the correct answer is sas

Step-by-step explanation:

took the test

What are the domain and range of the function?

f(x)=35x5

Answers

Answer:

Assuming that the question is  

[tex]f(x)=\frac{3}{5x^5}[/tex]

The asnwer would be

Domain: (- ∞,0) U (0, ∞)

Range: ( - ∞,0) U (0, ∞)

Step-by-step explanation:

The domain and range of the function are:

Domain: (- ∞,0) U (0, ∞)

Range: ( - ∞,0) U (0, ∞)

Domain and  Range of function

The domain are the input values for which a function exist while the range are output value for which the function exist.

Given the function:

g(x) = 35x^5

The function can exist on all real values since we will have a correspoding value of y for every value of x.

Hence the domain and range of the function are:

Domain: (- ∞,0) U (0, ∞)

Range: ( - ∞,0) U (0, ∞)

Learn more on domain and range here: https://brainly.com/question/2264373

i cant figure this out

Answers

Answer:

(xy) ^ (-1)

Step-by-step explanation:

Good luck!!

The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO2 to fuel photosynthesis, more CO2 may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO2 to a 30-meter circle of forest. They selected two nearby circles in each of three parts of a pine forest and randomly chose one of each pair to receive extra CO2. The response variable is the mean increase in base area for 30 to 40 trees in a circle during a growing season. We measure this in percent increase per year. Here are one year's data.

Pair Control plot Treated plot
1 9.728 10.748
2 7.276 8.332
3 5.612 6.632

Required:
a. State the null and alternative hypotheses.
b. Explain clearly why the investigators used a one-sided alternative.

1. The researchers have no preconceived idea what extra CO2 will do to the growth rate.
2. The researchers have reason to believe that CO2 will decrease growth rate.
3. The researchers have reason to believe that CO2 will increase growth rate.

c. Carry out a test and report your conclusion in simple language.

Answers

Answer:

this is math go to siecne noob

Step-by-step explanation:

Solve the formula d = rt for t.
A. t=d/r
B. t= rd
c. t= r/d
D. t= d-r

Answers

It’s A t=d/r

Steps
Dr=t swap the sides
T=dr

Answer:

A,t=d/r

Step-by-step explanation:

if d=rt t=?

d/r=rt/r (to get alone t we devided by r on both sides)

d/r=t

i think it is clear

&i hope it helps you

2) Jamie studies her Social Studies vocabulary for 30 minutes and studies 15
her Math problems for 15 minutes. After several days, she has studied her
Math problems for 60 minutes. How many minutes did Jamie study her
Social Studies vocabulary in the same time period?"
Your answer
This is a required question​

Answers

Answer:

2 hours or 120 minutes

Step-by-step explanation:

So, let's assume that she studies the same amount each day. If she has studied math for a total of 60 minutes, she should have studied for 4 days because 60 (total) divided by 15(time each day) would equal to 4 (period of time). So we have to multiply 30 minutes by 4 (period) to get 120 minutes, which is 2 hours.

Use technology to solve the following problem: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean μ = 38 and standard deviation σ = 7. What proportion of tires have lifetimes between 36 and 46 thousand miles?

Answers

Answer:

0.4859

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score,

μ is the population mean, and

σ is the population standard deviation.

From the question:

mean μ = 38,000

standard deviation σ = 7,000

For.

36 ( thousand miles) = 36,000

z = (x-μ)/σ

z = 36,000 - 38,000/7000

z = -0.28571

Probability value from Z-Table:

P(x = 36000) = 0.38755

For 46 thousand miles = 46,000

z = (x-μ)/σ

z = 46,000 - 38,000/7000

z =1.14286

Probability value from Z-Table:

P(x = 46000) = 0.87345

The proportion of tires that have lifetimes between 36 and 46 thousand miles is calculated as:

P(x = 46000) - P(x = 36000)

0.87345 - 0.38755

= 0.4859

Determine whether the following probabilities are best categorized as subjective, empirical, or classical probabilities.

a. Before flipping a fair coin, Sunil assesses that he has a 50% chance of obtaining tails. Subjective probability Empirical probability Classical probability
b. At the beginning of the semester, John believes he has a 90% chance of receiving straight A’s. Subjective probability Empirical probability Classical probability
c. A political reporter announces that there is a 46% chance that the next person to come out of the conference room will be a Republican, since there are 80 Republicans and 93 Democrats in the room. Subjective probability Empirical probability Classical probability

Answers

a) Classical. This is because there are 2 sides and 1/2 = 0.50 = 50% is the chance of landing on tails. Classical probability is also known as theoretical probability.

b) Subjective. This is based off John's belief and his gut feeling. There doesn't seem to be any empirical data to back him up, unless he's looking back at previous semesters.

c) Empirical. When you have a finite set of data and you compute the probability based on it like what we're doing here, we're computing empirical probability. Another example would be that if you flipped a coin 30 times and got 17 heads, then the empirical probability of getting heads is 17/30 = 0.5667 approximately. Note how this is slightly different from the theoretical probability 0.50

An experiment consists of determining the speed of automobiles on a highway using a radar equipment. The random variable in this experiment is a:

Answers

Answer:

the speed value that the radar equipment outputs.

Step-by-step explanation:

A random variable in an experiment is also (and most times the case) called a dependent variable. In this scenario, the random variable would be the speed value that the radar equipment outputs. This is because this value depends on the actual velocity of the cars that pass by the equipment. The faster the car is moving when it passes the radar the higher value will be displayed on the equipment. Therefore, depending completely on the vehicles.

6m + 4n + 3m - 6

What is the expression in simplest form

Answers

9m+4n-6 thats the answer
9m+4n-6

you only add the like terms 6+3
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