A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 70 cm/s. Find the rate at which the area within the circle is increasing after each of the following. A. After 1 second B. After 5 seconds C. After 6 seconds

Answers

Answer 1

Answer:

(A) 30772cm^2/s

(B) 153860cm^2/s

(C) 184632 cm^2/s

Step-by-step explanation:

We are given

speed of the ripple = 70cm/s

this speed is increasing the radius which means speed = radius /time

radius = speed*time

r= 70t

Now we know the area of the circle

A = π[tex]r^2[/tex]

this area will be increasing as ripples in water will spread out

upon differentiating

dA/dt = 2πr * [tex]\frac{dr}{dt}[/tex]

dA/dt = 2π*70t*70       ( r= 70t , dr/dt = speed = 70)

dA/dt = 9800π*t

(A) after 1 second

dA/dt = 9800π*1=9800π = 30772cm^2/s

(B) after 5 seconds

    dA/dt = 9800π*5 = 153860cm^2/s

(C) after 6 seconds

 dA/dt = 9800π*6 = 184632 cm^2/s


Related Questions

what is the equation of aline that passes through the point (4,-8) and has a slope of -1/2?

Answers

Answer:

The equation of the line will be:

[tex]y=-\frac{1}{2}x-6[/tex]

Step-by-step explanation:

Given

slope = m = -1/2point (4, -8)

Point slope form:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

substituting the values m = -1/2 and the point (4,-8)

[tex]y-\left(-8\right)=\frac{-1}{2}\left(x-4\right)[/tex]

[tex]y+8=\frac{-1}{2}\left(x-4\right)[/tex]

subtract 8 from both sides

[tex]y+8-8=\frac{-1}{2}\left(x-4\right)-8[/tex]

[tex]y=-\frac{1}{2}x-6[/tex]

Therefore, the equation of the line will be:

[tex]y=-\frac{1}{2}x-6[/tex]

Each week, Mrs.Mack buys exactly 3 5/8 pounds of cheese for her mac-and-cheese recipe. She chooses from these kinds of cheese. Mrs.Mack buys as many packages as she needs— up to three packages of any kind. What packages of cheese (and how many of each kind) does Mrs.Mack buy? 7/8pounds of american cheese. 0.5 pounds of cheddar cheese. 0.2 pounds of swiss cheese. HELP PLEASE

Answers

9514 1404 393

Answer:

3 packages of American (7/8 lb)2 packages of cheddar (1/2 lb)

Step-by-step explanation:

The amount of cheese Mrs Mack needs is an odd number of eighths of a pound. So, she must buy an odd number of the 7/8 pound packages.

If she were to buy any 1/5 pound packages, she would have to buy a multiple of 5 of them so as to have an integral number of eighths. The only suitable multiple is 0.

If Mrs Mack buys 1 of the 7/8 pound packages, she cannot make up the difference with half-pound packages. She must buy 3 of the 7/8 pound packages, for a total of 2 5/8 pounds of American cheese. The remaining pound can be bought as 2 of the 1/2 pound packages.

To buy 3 5/8 pounds, Mrs Mack must purchase ...

  3 packages of American cheese (7/8 lb each)

  2 packages of Cheddar cheese (1/2 lb each)

Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.

Answers

Answer:

m= 1

Step-by-step explanation:

find to ordered pair on the graph and [tex]y^{1} - y^{2} \\ x^{1} - x^{2}[/tex]

About 1/5 of all adults in the United States have type O blood. If four randomly selected adults donate blood, find the probability of each of the following events.

a. All four are type O.
b. None of them is type O.
c. Two out of the four are type O .

Answers

Answer:

We know that:

1/5 = 0.2 of all adults in US have type O blood.

Then: 4/5 = 0.8 of all adults in US do not have type O blood.

a)  All four are type O.

Let's think this, as four events with two possible outcomes, having type O blood, with a probability of 0.2, and not having type O blood with a probability of 0.8

Now if we want the four people to have type O blood, then we have the outcome with probability 0.2 four times, and as we know, the joint probability is equal to the product of the individual probabilities:

P  =0.2^4 = 0.0016

b) None of them is type O.

Similar to the above case, but this time we work with four times the probability 0.8

P = 0.8^4 = 04096

c) Two of the four are type O.

Here we will have two times the probability 0.2, and two times the probability 0.8.

p = 0.2^2*0.8^2

But, if the people is ordered, the two persons with type O blood can be:

first and second

first and third

first and fourth.

second and third

second and fourth

third and fourth.

6 different combinations, then the actual probability for this case will be:

P = 6*p = 6*(0.2^2*0.8^2) = 0.1536

The probability of All four are type O, None of them is type O, and Two out of the four are type O is 0.0016, 0.4096, and 0.0256 respectively.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

About 1/5 of all adults in the United States have type O blood.

p = 0.2

q = 1 - p = 1 - 0.2 = 0.8

a. All four are type O. The probability will be

P = p⁴  

P = 0.2⁴

P = 0.0016

b. None of them is type O. The probability will be

P = q⁴  

P = 0.8⁴

P = 0.4096

c. Two out of the four are type O. The probability will be

P = p² × q²  

P = 0.2² × 0.8²

P = 0.04 × 0.64

P = 0.0256

More about the probability link is given below.

https://brainly.com/question/795909

20+20 omg.please help :( ​

Answers

Answer:

40

Step-by-step explanation:

The length of the rectangle is 3ft less than twice the width,and the area of the rectangle is 27ft^2,find the diameter

Answers

Answer:

The dimensions of rectangle are:

width = w = 4.5 ftlength = l = 6 ft

Step-by-step explanation:

Let 'l' be the length and 'w' be the width of the rectangle

The length 'l' of the rectangle is 3ft less than twice the width 'w'.

so

[tex]l=2w-3[/tex]

Also, the area of the rectangle is 27ft^2.

[tex]A=27\:ft^2[/tex]

As the area of the rectangle has the formula:

[tex]\:A\:=\:l\times w[/tex]

so

[tex]27=\:l\times w[/tex]

so the equation becomes

[tex]27=\left(2w-3\right)\times \:w[/tex]

[tex]27=2w^2-3w[/tex]

[tex]2w^2-3w-27=0[/tex]

[tex]\left(w+3\right)\left(2w-9\right)=0[/tex]

if   [tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

[tex]w+3=0\quad \mathrm{or}\quad \:2w-9=0[/tex]

[tex]w=-3,\:w=\frac{9}{2}[/tex]

as the width can not be negative, so

[tex]w=\frac{9}{2}=4.5[/tex] ft

As

[tex]l=2w-3[/tex]

[tex]l=2\left(4.5\right)-3[/tex]

[tex]l=9-3[/tex]

[tex]l=6[/tex]

So the dimensions of rectangle are:

width = w = 4.5 ftlength = l = 6 ft

Find the solution to the equations.
3x - y = -4
x + y = 0
(0,0)
(-1, 1)
(1,-1)

Answers

Answer:

(-1,1)

Step-by-step explanation:

also use elimination steps by using simultaneous

Determine the check digit for the UPCs that have these initial 11 digits. a) 73232184434 b) 63623991346 c) 04587320720 d) 93764323341

Answers

Answer:

The check digits

a) x₁₂ ≡ 5( mod 10 )

b) x₁₂ ≡ 2( mod 10 )

c)  x₁₂ ≡ 0( mod 10 )

d)  x₁₂ ≡ 3( mod 10 )

Step-by-step explanation:

Given the data in the question;

We know that the formula for determining the UPCs check is;

3x₁ + x₂ + 3x₃ + x₄ + 3x₅ + x₆ + 3x₇ + x₈ + 3x₉ + x₁₀ + 3x₁₁ + x₁₂ ≡ 0( mod 10 )

now we will substitute the given values to determine the value of the last bit

a)

73232184434

we substitute into the formula

3×7 + 3 + 3×2 + 3 + 3×2 + 1 + 3×8 + 4 + 3×4 + 3 + 3×4 + x₁₂ ≡ 0( mod 10 )

                                                                                          x₁₂ ≡ 5( mod 10 )

b)

63623991346

we substitute into the formula

3×6 + 3 + 3×6 + 2 + 3×3 + 9 + 3×9 + 1 + 3×3 + 4 + 3×6 + x₁₂ ≡ 0( mod 10 )

                                                                                           x₁₂ ≡ 2( mod 10 )

c)

04587320720

we substitute into the formula

3×0 + 4 + 3×5 + 8 + 3×7 + 3 + 3×2 + 0 + 3×7 + 2 + 3×0 + x₁₂ ≡ 0( mod 10 )

                                                                                           x₁₂  ≡ 0( mod 10 )

d)

93764323341

we substitute into the formula

3×9 + 3 + 3×7 + 6 + 3×4 + 3 + 3×2 + 3 + 3×3 + 4 + 3×1 + x₁₂ ≡ 0( mod 10 )

                                                                                         x₁₂ ≡ 3( mod 10 )


Cathy's food usually costs $212.90 a week. One week, it cost $198.98. How
much less money did she spend that week?

Answers

Answer:

$13.92

Step-by-step explanation:

$212.90-198.98

equivalent fraction of 6/126

Answers

Answer:

1/21

Step-by-step explanation:

Answer:

1/21

Step-by-step explanation:

6/126 = 1/21 because 6 divided by 6 equals 1 and 126 divided by 6 equals 21.

Hiiii I really need helppppp pls pls

Answers

Step-by-step explanation:

sas

side angle side

mark me as brainliest

7. Jenny is saving to buy a laptop worth $960. Her parents promise to match every $3 saved
by her with $5 of their own.
a. How much will Jenny contribute?
b. How much will Jenny's parents have to pay?

Answers

First off, if you divide $960/$8, you will get 120 “sets” of payment. Multiply this value by the amount of money Jenny is responsible for paying and the amount her parents are responsible for paying to find their total contributions.

a. Jenny will have to pay $600

b. Jenny’s parents will contribute $360 to her new laptop.

Solve five and three sixths minus two and one third.

(GIVING EXTRA POINTS ON THIS ONE! IM ALSO GIVING BRAINLIEST!) (Btw three and two ninths is incorrect :) )

A) Two and three eighteenths

B) two and two ninths

C) three and two ninths

D) three and three eighteenths

(Here is an image if needed) :

Answers

Answer:

3 3/18

Step-by-step explanation:

I did this on paper, but im typing on computer, sorry I cant send a photo

Answer:

D is the answer 3 3/18 i am sure it is correct

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. The probability that the average pregnancy length for nine randomly chosen women exceeds 268 days is about a) 0.35 b) 0.40 c) 0.65 d) 0.27

Answers

Answer:

The probability is    [tex]P( \= X > 268 ) =0.35376[/tex]

Step-by-step explanation:

From the question we are told that

   The mean is  [tex]\mu = 266[/tex]

    The standard deviation is  [tex]\sigma = 16[/tex]

Generally the standard error of mean is mathematically represented as

        [tex]\sigma_{\= x} = \frac{\sigma}{\sqrt{n} }[/tex]

=>     [tex]\sigma_{\= x} = \frac{16}{\sqrt{9} }[/tex]

=>     [tex]\sigma_{\= x} = 5.33[/tex]

Generally the probability that the average pregnancy length for nine randomly chosen women exceeds 268 days is mathematically represented as

        [tex]P( \= X > 268 ) = P (\frac{ \= x - \mu }{ \sigma_{\= x}} > \frac{268 - 266}{5.33 } )[/tex]

[tex]\frac{\= X -\mu}{\sigma_{\= x} }  =  Z (The  \ standardized \  value\  of  \ \=  X )[/tex]  

          [tex]P( \= X > 268 ) = P (Z > 0.3752 )[/tex]

From the z table  the area under the normal curve to the right  corresponding to  0.3752  is

P (Z  >  0.3752)   =    0.35376

So  

       [tex]P( \= X > 268 ) =0.35376[/tex]

The table shows the weekly profits of a fruit
vendor. What is the mean profit for these weeks?
Week
1
2
3
4
Profit -$125 -$86
$54
- $35
The mean profit is $

Answers

Answer:

-48

Step-by-step explanation:=-48

The mean profit of the fruits will be $75.

What is mean?

Mean is defined as the ratio of the sum of the number of data sets to the total number of data. The mean is just like an average it is calculated by taking the ratio of the sum of all the numbers to the total count of the numbers.

Given that the weekly profit of the fruits is $125, $86, $54, and $35. The mean will be calculated as:-

Mean = ( 125 + 86 + 54 + 35 ) / 4

Mean = 300 / 4

Mean = $75

Therefore, the mean profit of the fruits will be $75.

To know more about mean follow

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Which lines from Natalie Merchant's song "Wonder" most likely inspired R. J. Palacio to give August's mother's great determination in the novel Wonder? O Doctors have come from distant cities just to see me O stand over my bed disbelieving what they're seeing with love, with patience and with faith she'll make her way I'm over your heads how I confound you and astound you​

Answers

Answer:

C)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The guy above me is correct

A statement of an employee's biweekly earnings is given below.




Earnings


Deductions




Week Ended


Regular


FED. SOC. MED STATE


WITH. WITH. CARE. WITH.


NET PAY


8/18


$_____


$72.00 $35.05 $15.54 $14.40


$793.01



What is the employee's gross pay?


A.

$900.50


B.

$1000


C.

$930


D.

$975.10

Answers

Answer:

kjj ,mStep-by-step explanation:

Cooper wrote checks on his checking account for $20 and $35. He also deposited $63 in the account. Which number describes the change in the balance of his account? A.$12 B.$8 C.$15​

Answers

Answer:

the change is b 8. 63-55=8 35+20=55

Given: △ABC, m∠A=60°
m∠C=45°, AB = 9
Find: Perimeter of △ABC
Area of △ABC
ABC is scalene

Answers

Answer:

Perimeter = 32.3

Area = 95.24

Step-by-step explanation:

Given:

△ABC, m∠A=60°

m∠C=45°, AB = 9

To find:

Perimeter of △ABC

Area of △ABC

Solution:

Using angle sum property in a triangle:

m∠A + m∠B + m∠C = 180°

m∠B = 180° - 45° - 60° = 75°

As per Sine Rule:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]

Where  

[tex]a[/tex] is the side opposite to [tex]\angle A[/tex]

[tex]b[/tex] is the side opposite to [tex]\angle B[/tex]

[tex]c[/tex] is the side opposite to [tex]\angle C[/tex]

[tex]\dfrac{BC}{sin60^\circ} = \dfrac{AC}{sin 75^\circ} = \dfrac{AB}{sin 45^\circ} \\\Rightarrow \dfrac{BC}{\frac{\sqrt3}{2}} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow BC = 12.73\times 0.87 \\\Rightarrow BC = 11.08[/tex]

[tex]\Rightarrow \dfrac{AC}{0.96} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow AC = 12.73\times 0.96 \\\Rightarrow AC = 12.22[/tex]

Perimeter of △ABC = AB + BC + AC = 9 + 11.08 + 12.22 = 32.3

Area of a triangle is given as:

[tex]\dfrac{1}2\times ab sin(angle\ between\ a\ and\ b)[/tex]

[tex]\Rightarrow \dfrac{1}{2}\times AB\times AC\times sinA\\\Rightarrow 9\times 12.22\times sin 60\\\Rightarrow \bold{95.24}[/tex]

A surgical procedure requires choosing among four alternative methodologies. The first can result in five possible outcomes, the second can result in two possible outcomes, and the remaining methodologies can each result in four possible outcomes. What is the total number of outcomes possible?

Answers

Answer:

15 possible outcomes

Step-by-step explanation:

Since each one of these methodologies are not related to one another and they do not need to be chosen in any order or consecutively then the possible outcomes would only need to be added all together to calculate the total possible outcomes. Since each outcome is independent. Therefore,

m1 = 5 outcomes

m2 = 2 outcomes

m3 = 4 outcomes

m4 = 4 outcomes

5 + 2 + 4 + 4 = 15

we can see that there are a total of 15 possible outcomes

BRAINLIEST FOR CORRECT ANSWER!
At a sale, dresses were sold for $24 each. This price was 12% of a dress's original price. How much did a dress originally cost?

Answers

Answer:

$200

Step-by-step explanation:

To find the original price, divide the price by 0.12:

24/0.12

= 200

So, the dress originally cost $200

Answer:

$200.

Step-by-step explanation:

To find the original price, divide the discounted price by 0.12.

$24 ÷ 0.12% = $200

The dress originally cost $200.

Question 2 (1 point)
For problem 2 - 26, what is the slope of line C?
A
B
2-26.
D
+
E
8
10
2
a
m = 2
Ob
m = -2/3
c
m = 0

Answers

Answer:

Option e: 2/3 is the correct answer.

Step-by-step explanation:

The slope of a line is given by:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Two-points on line are needed to calculate slope of a line. In the attached diagram, two points are highlighted which are located on line C.

The two points are:

(x1,y1) = (9,4)

(x2,y2) = (3,0)

Putting the values in the formula

[tex]m = \frac{0-4}{3-9}\\=\frac{-4}{-6}\\=\frac{2}{3}[/tex]

The slope of line C is: 2/3

Hence,

Option e: 2/3 is the correct answer.

(c) What is the value of p if 4x² + 20x + p is a
perfect square​

Answers

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[tex]( {a + b})^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]

_________________________________

[tex]4 {x}^{2} + 20x + p = [/tex]

[tex]( {2x})^{2} + 2(2x)(5) + p = [/tex]

Thus ;

[tex]p = {5}^{2} [/tex]

So

[tex]p = 25[/tex]

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Solve for h: h + 4.18 = 19.74​

Answers

H= 15.56. Because 19.74 - 4.18 will equal 15.56

Morning can someone help me please and can you please let me know how you got the answer

Answers

Answer:

The customary system states that one pound is equivalent to sixteen ounces(oz).

Step-by-step explanation:

Since the package is one pound, it contains sixteen ounces(oz).

The length of a rectangle is 3 more than 3 times its width. The perimeter of the rectangle is 174 inches. What is the length of the rectangle?

Answers

Answer:

l = w + 3cm

l = w + 3cmp = 2l + 2w = 58cm

l = w + 3cmp = 2l + 2w = 58cm

l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:

l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58

l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58

l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13

l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13

l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:

l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:l = (13cm) + 3cm = 16cm

l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:l = (13cm) + 3cm = 16cmStep-by-step explanation:

I hope this helps you.

If the measure of the width is 21 inches. Then the measure of the length of the rectangle will be 66 inches.

What is a rectangle?

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

The length of a rectangle is 3 more than 3 times its width. The perimeter of the rectangle is 174 inches.

Then the length of the rectangle will be

We have

L = 3W + 3

Then the perimeter will be

   P = 2(L + W)

174 = 2 (3W + 3 + W)

87 = 4W + 3

84 = 4W

 W = 21 inches

Then the length will be

L = 3W + 3

L = 3 x 21 + 3

L = 63 + 3

L = 66 inches

More about the rectangle link is given below.

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I don’t understand this at all pls help I will mark brainliest

Answers

Answer:

D

Step-by-step explanation:

-2/3 is -.666

-3/5 is -.60

1/2 is .5

and 5/8 is a little more than half since 4/8 is half. so -2/3, -3/5, 1/2, 5/8, or D

I need help with this! 20 points pls dont take advantage.

the average adult drinks 1095 cups of coffee annually, About how many cups does the average adult drink per week? 1 year=52 weeks

15
91
21
3​

Answers

Answer:

the answer is 21

Step-by-step explanation:

If they drink 1,095 cups per year, and there are 52 weeks in a year, you would divide 52 from 1,095(1,095/52) to get your answer which is 21.05769231. If you round it to the nearest whole number, than it is 21. I hope this helps have a great day.

Simplify 6(x + 2)- x(x - 1)

Answers

-x^2+7x+12


Let’s use distributive property
6(x+2)-x(x-1)

6x+12

Now the other part of the expression
-x(x-1)
-x^2+x

Put both parts of the expression together

6x+12 -x^2+x

-x^2+7x+12

Hope this helps

What is the sum of the interior angles of a quadrilateral?
90°
180°
270°
360°

Answers

Answer:

360º

Step-by-step explanation:

too easy

Answer:

360

Step-by-step explanation:

I had it on a quiz also plz mark brainliest im trying to level up

Other Questions
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