A rain drop hitting a lake makes a circular ripple.. if the radius, in inches,, grows as a function of time in minutes according to R(t)=20sqrt(t+2), find the area of the ripple as a function of time. What is the area of the circular ripple at t=2?

Answers

Answer 1

Answer:

Step-by-step explanation:

Area A(t) = πR² = π x 400 (t + 2) = 400π (t + 2)

A(2) = 400π (2 + 2) = 1600π = 5026.5 in²


Related Questions

What is the median of 3,4,5,5,7,8

Answers

the median of the set of numbers is 5.

Find the value of x.
x
x = [?]

Answers

Answer:

Step-by-step explanation:

x + x + x = xxx

=> 3x = x³

=> x³ - 3x = 0

=> x(x² - 3)  = 0

=> x(x² - (√3)²) = 0

using a² - b² = (a + b)(a - b)

= x(x + √3)(x - √3) = 0

=> x = 0 , -√3 , √3

x = 0 , ±√3

100 Points and I will mark you brainiest if right.
What is 2 x 4 x 8 x 16 x 32 x 64 divided by 2^4

Answers

Answer:

131072

Step-by-step explanation:

Let's put it into expression form and simplify as much as possible :

[tex]\frac{(2)(4)(8)(16)(32)(64)}{2^{4} }[/tex] =

[tex]\frac{2097152}{16}[/tex] =

131072

Hope this helped and have a good day

Answer: 131,072

Step-by-step explanation:

2 x 4=8

8 x 8=64

64 x 16=1024

1024 x 32=32768

32768 x 64=2097152

[tex]2^{4}[/tex]=16

2097152/16= 131072

Drag each tile to the correct box. a с C b A David proved the Law of Cosines with reference to AABC using a different method. Arrange the steps of his proof in the correct sequence. k² = c² - (b − x)² In AABD, (Pythagorean Theorem) In ABCD, k² = a² - 1² (Pythagorean Theorem) c² (6²-26x + x²) = a² — 1² (on simplification) Similarly, prove that a2b² + c² - 2bccos A and 82 6² = a² + c²2accos B B​

Answers

Big question:
where is the question here

Can someone pls help quickly?

Answers

From the question given above, the ratio of L : W in simplified form is given as: 6 : 5. See the explanation below.

What is a ratio?

A ratio, simply, can be defined as the quantitative relationship that exists between two values which is indicative of the number of times one value can be obtained from the other.

What is the explanation for the solution above?

Step 1  - Indicate your assumptions

Let X be the width of one of the rectangles and let its height be Y.

It is clear from the image that:

4X = 3Y

Hence

(4/3)X  = Y

Therefore,

Lenght (L) = 3Y

= 3 (4/3)X

= 4X

Width (W) = Y + 2X

= (4/3)X + 2X

= (10/3)X

Therefore,

L : W =  4X: 10/3X

= 4:10/3

To remove the fraction, multiply both sides of the ratio by 3

= 12 : 10, furhter simplify by halving each value, and we have

= 6:5

Hence, the ratio L: W in simplified form is 6 : 5.

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8. Find the area of the shaded region.

Answers

Answer:

7

Step-by-step explanation:

did the math

Answer:

Answer:4π

Step-by-step explanation:

As we know,

Area of circle=πr^2

=π(2)^2

=4π=12.57m^2

Ashley has 100 books that she wants to give away at the rate of n books per week. Write a recursive function that represents the number of books Ashley has at any time.
The recursive function that gives the number of books Ashley has at any time is
=
, starting at
.

Answers

The recursive function that gives the number of books Ashley has at any time is f(t) = f(t-1) - n where f(0) =100

How to determine the recursive function?

The given parameters are:

Initial = 100

Rate per week, r = n

The initial number of books means that:

f(0) = 100

The rate of n means that Ashley has n less books each week.

So, we have:

f(t) = f(t-1) - n

Where t represents the number of weeks

Hence, the recursive function that gives the number of books Ashley has at any time is f(t) = f(t-1) - n where f(0) =100

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why is the answer to this integral's denominator have 1+pi^2

Answers

It comes from integrating by parts twice. Let

[tex]I = \displaystyle \int e^n \sin(\pi n) \, dn[/tex]

Recall the IBP formula,

[tex]\displaystyle \int u \, dv = uv - \int v \, du[/tex]

Let

[tex]u = \sin(\pi n) \implies du = \pi \cos(\pi n) \, dn[/tex]

[tex]dv = e^n \, dn \implies v = e^n[/tex]

Then

[tex]\displaystyle I = e^n \sin(\pi n) - \pi \int e^n \cos(\pi n) \, dn[/tex]

Apply IBP once more, with

[tex]u = \cos(\pi n) \implies du = -\pi \sin(\pi n) \, dn[/tex]

[tex]dv = e^n \, dn \implies v = e^n[/tex]

Notice that the ∫ v du term contains the original integral, so that

[tex]\displaystyle I = e^n \sin(\pi n) - \pi \left(e^n \cos(\pi n) + \pi \int e^n \sin(\pi n) \, dn\right)[/tex]

[tex]\displaystyle I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n - \pi^2 I[/tex]

[tex]\displaystyle (1 + \pi^2) I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n[/tex]

[tex]\implies \displaystyle I = \frac{\left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n}{1+\pi^2} + C[/tex]

Of the equations listed below, which represent functions that are linear?
1.y = 3x
II. y = 3x²
III. y
A. Equations I and III
B. Equation I only
C. Equations II and III
D. Equation II only ​

Answers

Answer:

c i think

Step-by-step explanation:

c because jesus told it was c

An investor earns 12.49 percent before tax and is subject to a 32 percent tax on such earnings. Calculate the investor's after-tax rate of return.

Answers

Answer:

How do you calculate after tax rate of return?

After-tax return on investment is the net return to the investor after ordinary income and capital gains taxes are subtracted. This is calculated as: After-tax return on investment = ((P1 - Po) (1 - Tc) / Po) + C1(1 - To) / Po.

How do you calculate before tax return?

The pre-tax rate of return is calculated as the after-tax rate of return divided by one, minus the tax rate. For example, suppose a person obtains a 4.25% reporting rate for ABC shares and is subject to a 15% income tax. Therefore, the pre-tax rate of return is 5% or 4.25%/(1 - 15%).

How do you calculate real rate of return after tax and inflation?

To calculate the real rate of return after tax, divide 1 plus the after-tax return by 1 plus the inflation rate. Dividing by inflation reflects the fact a dollar in hand today is worth more than a dollar in hand tomorrow. In other words, future dollars have less purchasing power than today's dollars.      

Hope this help's :)

Mr. Simmons figures he can paint his house in 5 days. If his son helps, together they can paint it in 2 days. How long will it take his son to paint the house if he works alone?

Answers

Answer:

3 hrs 20 min

Step-by-step explanation:

1/5 + 1/x = 1/2

x = 10/3

The length of a rectangle is 6 inches longer than it is wide. If the area is 160 square inches, what are the dimensions of the rectangle?

Answers

Answer:

L = 16

w = 10

Step-by-step explanation:

Givens

Area = 160 sqr inches

width = x

length = x + 6

Equation

Area = L * w

Solution

Substitute in the equation all of the givens.

160 = x(x + 6)                     Remove the brackets

160 = x^2 + 6x                   Subtract 160 from both sides.

160-160 = x^2 + 6x - 160

0 = x^2 + 6x - 160

This equation factors. Turn it around first

x^2 + 6x - 160 =  0

(x - 10)(x + 16) = 0

Answer

x (width) = 10

x + 16 = 16

Answer:

The length is 16 inches and the width is 10 inches.

Step-by-step explanation:

See attached. Thank you for your help.

Answers

Answer:

76

Step-by-step explanation:

when i text my boy he is ute

A bank pays interest rate of 15% per annum on the savings in a customers account. calculate the total amount in a customers saving account at the end of the year​

Answers

Answer:

Matty is the most precious ma ma ta the best I don't think so I can see good

what is the volume of the solid

Answers

Answer: 12 cubic yards

Step-by-step explanation:

Volume = (1/2)(3)(4)(2)=12

calculate the sum of the following series 17+51+153+…334611

Answers

Answer:

Ans=...334832 can be your questions answer

Erica earned a total of $67,250 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than three times the amount she earned from her job at the college. How much did she earn (in dollars) from her job at the college?

Answers

Step-by-step explanation:

x = earnings from the store

y = earnings from the college

x + y = 67,250

x = 3y + 1,250

now we use the identity of the second equation in the first equation :

(3y + 1,250) + y = 67,250

4y = 66,000

y = $16,500

x = 3y + 1,250 = 3×16,500 + 1,250 = 49,500 + 1,250 =

= $50,750

Convert from a fraction to a decimal 1/4

Answers

Answer:

Convert from a fraction to a decimal 1/4. 0.25

Answer:

0.25 is the correct answer of the question

Houa bought 11 chicken wings for $23.10 . How much does each wing cost

Answers

Answer:

Answer = $2.10

Step-by-step explanation:

To solve this we take the total cost divided by the total number of chicken wings to get $2.10.

Hope that helps! :)

Answer:

1 wing = $2.10

Step-by-step explanation:

11 wings = $23.10

Let 1 wing = x

11x = 23.10

To solve for x, we divide both sides by 11 :

11x÷ 11 = 23.10 ÷11

x = 2.1

So 1 wing = $2.10

Hope this helped and brainliest please

BRAINLIEST AND 50 POINTS IF U ANSWER ALL PLSSS SOLVING REQUIRED PLSSS

Answers

#1

LSA

4(1/2BH)4(1/2×9×12)2(9)(12)216cm²

TSA

LSA+9²216+81297cm²

#2

LSA

3(1/2(13)(15))1.5(195)292.5cm²

TSA

292.5+1/2(195)1.5(195)+0.5(195)2(195)390cm²

#3

LSA

4(1/2(6)(16))2(96)192cm²

TSA

LSA+6²36+192228cm²

#4

LSA

2(1/2(8)(6))+2(1/2(6)(6.5))8(6)+6(6.5)48+3987cm²

TSA

87+8(6)87+48135cm²

#5

We know

TSA=LSA+Area of base

So

LSA=TSA-Area of base

She can use this formula

8 19. Marcus claims that fractions with denominators 1 through 10 follow a pattern
when they are converted to decimal form. If any one fraction can be converted
to a terminating decimal, then all of the fractions with that same denominator
will also convert to terminating decimals. On the other hand, if one fraction
converts to a repeating decimal, then all fractions with that same denominator
will convert to a repeating decimal. Is Marcus correct? Explain.

Answers

Answer:

No

Step-by-step explanation:

Marcus is not correct because 1/12 converts to the repeating decimal 0.8333... but 3/12 converts to 0.25 which is not a repeating decimal.

Assume a normal distribution and that the average phone call in a certain town lasted ​12 min, with a standard deviation of 2 min. What percentage of the calls lasted less than 6 ​min?

Answers

Answer:

I think it's 23 but I might be wrong

Find f(3) if
f(x)=x^3+2x^2-x-1

Answers

Answer:

41

Step-by-step explanation:

[tex]f(x) =x^3 +2x^2 -x -1\\\\f(3) =3^3 +2(3^2) -3 -1\\\\~~~~~~~=27+18-4\\\\~~~~~~~=27+14\\\\~~~~~~~=41[/tex]

A manufacturer of kitchen utensils and gadgets is considering changing the design of the salt and pepper shakers. Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder. the figure shows both designs.

Which set of additional details are the minimum required to ensure the new design will have the same volume as the original design?

Answers

For the current cylinder to have the same volume as the oblique cylinder, the height of both design must be the same and the base area of both designs must be the same.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Volume of cylinder = area of base * height

For the current cylinder to have the same volume as the oblique cylinder, the height of both design must be the same and the base area of both designs must be the same.

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Answer:

C

Step-by-step explanation:

happened to do the test

Buying rental property is an investment option that carries a higher risk than some other options. However, the returns can be good. Assume you have purchased a single-
family home that you intend to rent for $850 per month. You will have the following expenses:
Monthly mortgage $390
Monthly insurance $60
Semiannual property taxes $340
Repairs (yearly estimate) $500
Monthly lawn care or snow removal $100
The return on investment for the property is
% (Round to one decimal place.)

Answers

Based on the expenses involved in running the property, and the rental amount, the return on the investment would be 31.1%.

What is the return on investment?

First find the amount earned per year:

= 850 x 12

= $10,200

The yearly expenses would be:

= (390 x 12) + (60 x 12) + (340 x 2) + 500 + (100 x 12)

= 4,680 + 720 + 680 + 500 + 1,200

= $7,780

The annual ROI is:

= (10,200 - 7,780) / 10,200 x 100%

= 31.1%

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Solve for x
5x= -9
Give your answer as an improper
fraction in its simplest form.

Answers

We proceed to solve the equation:

[tex]5x \: = \: 9[/tex]

We divide by 5 the two members that make up the equation.

[tex]5x \: \div \: 5 \: = \: - 9 \: \div \: 5[/tex]

Since it is divided by itself, it is equal to 1.

[tex]x \: = \: - 9 \: \div \: 5[/tex]

We transform it into an improper fraction:

[tex]x \: = \: \boxed{ \bold{ - \frac{9}{5} }}[/tex]

MissSpanish

A shirt and a tie together cost $58 the shirt cost $30 more than the type what is the cost of the shirt and dollars

Answers

Answer:

Shirt + tie = $ 58

shirth = 30 more than that of tie

let the price of tie be X

therefore the price of shirt = 30 + X

30 + X + X = 58

30 + 2x = 58

2x = 58 - 30

2x= 28

x = 14

x + 30

= 14 + 30

Cost of tie = $14 Cost of shirt = $44

Mario invested a certain amount of money in selling a fish balls. After 3 weeks, he counted his money and found out that he had 900 which was 2255 of what he originally had. How much did he invest?

Answers

Answer:

[tex]5.3 \times 105 - 2.4 \times 104[/tex]

A square is inscribed in a quarter of a circle,calculate the quarter circle.​

Answers

Answer:

Step-by-step explanation:

Evaluate this exponential expression 7 • (6+2)^2 - 3^2=

Answers

Answer: 441

Step-by-step explanation:

[tex]7*(6+2)^2-3^2[/tex]

[tex]7*8^2-3^2[/tex]

[tex]7*64-9[/tex]

[tex]448-9[/tex]

441

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