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dsp73
2 years ago
8

The circumference of a circle is 23pi m. What is the area, in square meters? Express

Mathematics
1 answer:
trasher [3.6K]2 years ago
8 0

Answer:

Step-by-step explanation:

d and r are the diameter and radius, respectively.

circumference = πd = 23π

d = 23 meters

r = 23/2 meters

Area = πr² = 133.25π square meters

You might be interested in
The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day.
puteri [66]

Answer:

\displaystyle \frac{dA}{dt} = 102 \ m^2/day

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Geometry</u>

Area of a Rectangle: A = lw

  • l is length
  • w is width

<u>Calculus</u>

Derivatives

Derivative Notation

Implicit Differentiation

Differentiation with respect to time

Derivative Rule [Product Rule]:                                                                              \displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)

Step-by-step explanation:

<u>Step 1: Define</u>

<u />\displaystyle l = 10 \ meters<u />

<u />\displaystyle \frac{dl}{dt} = 4 \ m/day<u />

<u />\displaystyle w = 23 \ meters<u />

<u />\displaystyle \frac{dw}{dt} = 1 \ m/day<u />

<u />

<u>Step 2: Differentiate</u>

  1. [Area of Rectangle] Product Rule:                                                                 \displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}

<u>Step 3: Solve</u>

  1. [Rate] Substitute in variables [Derivative]:                                                    \displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)
  2. [Rate] Multiply:                                                                                                \displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day
  3. [Rate] Add:                                                                                                      \displaystyle \frac{dA}{dt} = 102 \ m^2/day

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

8 0
3 years ago
Rico paid $180 sales tax on his new $2,400 motorcycle. What was the sales tax percentage rate where he bought his motorcycle?
liraira [26]

Answer:

The answer is 7.5 tax rate

Step-by-step explanation:

I used a calculator to get the answer and it is correct.

3 0
3 years ago
8) Find the endpoint Cif M is the midpoint of segment CD and M (2, 4) and D (5,7)
Elenna [48]

Answer:

8. c. (-1, -1)

9. a. (-6, -1)

b. True

Step-by-step Explanation:

8. Given the midpoint M(2, 4), and one endpoint D(5, 7) of segment CD, the coordinate pair of the other endpoint C, can be calculated as follows:

let D(5, 7) = (x_2, y_2)

C(?, ?) = (x_1, y_1)

M(2, 4) = (\frac{x_1 + 5}{2}, \frac{y_1 + 7}{2})

Rewrite the equation to find the coordinates of C

2 = \frac{x_1 + 5}{2} and 4 = \frac{y_1 + 7}{2}

Solve for each:

2 = \frac{x_1 + 5}{2}

2*2 = \frac{x_1 + 5}{2}*2

4 = x_1 + 5

4 - 5 = x_1 + 5 - 5

-1 = x_1

x_1 = -1

4 = \frac{y_1 + 7}{2}

4*2 = \frac{y_1 + 7}{2}*2

8 = y_1 + 7

8 - 7 = y_1 + 7 - 7

1 = y_1

y_1 = 1

Coordinates of endpoint C is (-1, 1)

9. a.Given segment AB, with midpoint M(-4, -5), and endpoint A(-2, -9), find endpoint B as follows:

let A(-2, -9) = (x_2, y_2)

B(?, ?) = (x_1, y_1)

M(-4, -5) = (\frac{x_1 + (-2)}{2}, \frac{y_1 + (-9)}{2})

-4 = \frac{x_1 - 2}{2} and -5 = \frac{y_1 - 9}{2}

Solve for each:

-4 = \frac{x_1 - 2}{2}

-4*2 = \frac{x_1 - 2}{2}*2

-8 = x_1 - 2

-8 + 2 = x_1 - 2 + 2

-6 = x_1

x_1 = -6

-5 = \frac{y_1 - 9}{2}

-5*2 = \frac{y_1 - 9}{2}*2

-10 = y_1 - 9

-10 + 9 = y_1 - 9 + 9

-1 = y_1

y_1 = -1

Coordinates of endpoint B is (-6, -1)

b. The midpoint of a segment, is the middle of the segment. It divides the segment into two equal parts. The answer is TRUE.

4 0
3 years ago
Standard form of -2x^2+8x+5
Ksivusya [100]
-2x^2+8x+5 is the standard form
5 0
3 years ago
Which side lengths form a right triangle?<br> Choose all answers that apply:
kkurt [141]

Answer:

All 3 are right triangles.

Step-by-step explanation:

In a right triangle c^2 = a^2 + b^2   where c is the longest side.  ( by Pythagoras).

a) 3^2 = 9, 6^2 = 36 and √27 ^ 2 = 27

36 = 9 + 27

So this is a right triangle.

b)

17^2 = 289, 15^2 = 225 and 8^2 = 64

289 = 225 + 64

Also right triangle.

c) √50 ^ 2 = 50, 5^2 = 25 and 5^2 = 25

So also right triangle.

3 0
2 years ago
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