### Problem DescriptionSuppose you take a straight piece of wire measuring 20 cm and cut it to make two pieces. You then take one piece and make it into a square, and the other piece and make it into a circle, like in the following picture:![Diagram showing a wire of length 20 cm divided into two pieces, 'x' and '20 - x', with one piece forming a circle and the other forming a square.](image_url_here)### Questionsa. Write a function, $ A(x) $, that gives the total area of the circle and the square you make in this scenario.b. What is the domain of $ A(x) $?### Detailed ExplanationTo solve this problem, we first need to use the lengths of the wire pieces for both the circle and the square.1. **Dividing the Wire**: - Let $ x $ cm be the length of the wire used to form the circle. - Then, $ 20 - x $ cm will be the length of the wire used to form the square.2. **Forming the Circle**: - The circumference of the circle is $ x $ cm. - Using the formula for the circumference of a circle, we have: \[ 2\pi r = x \] - Solving for the radius $ r $, we get: \[ r = \frac{x}{2\pi} \] - The area of the circle, $ A_{\text{circle}} $, is given by: \[ A_{\text{circle}} = \pi r^2 = \pi \left( \frac{x}{2\pi} \right)^2 = \frac{x^2}{4\pi} \]3. **Forming the Square**: - The perimeter of the square is $ 20 - x $ cm. - Each side of the square, $ s $, is: \[ s = \frac{20 - x}{4} \] - The area of the square, $ A_{\text{square}} $, is given by: \[ A_{\text{square}} = s^2 = \left( \frac{20 - x}{4} \right)^2 = \frac{(20 - x)^2}{16}

Answered: Image /qna-images/answer/c46b3bd7-5d70-4695-b9ba-8acb3a92ee87.jpg

Suppose you take a straight piece of wire measuring 20 cm and cut it to make two pieces. You then take one piece and make it into a square, and the other piece and make it into a circle, like in the following picture: 20 cm 20-x а. Write a function, 4), that gives the total area of the circle and the square you make in this scenario. b. What is the domain of A(.x)?

Suppose you take a straight piece of wire measuring 20 cm and cut it to make two pieces. You then take one piece and make it into a square, and the other piece and make it into a circle, like in the following picture: 20 cm 20-x а. Write a function, 4), that gives the total area of the circle and the square you make in this scenario. b. What is the domain of A(.x)?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Rewrite the following quadratic function y = ‒3x2 + 12x in vertex form by completing the square.…

A: The question has asked about some basic concepts of quadratic equation.

Q: D.FFerenticate the function. y = ( 7 x-6) ³ 10d to у

Q: Ravi is exploring the formula for the circumference of a circle. He computed the circumferences of…

Q: While in Paris France, part of the group goes to the observation deck of the Eiffel Tower (a height…

Q: We are to take a piece of paper and fold it in half and record the number of regions it shows. So, I…

A: To find an equation to determine the number of regions, R, as a function of a number of folds.

Q: The fixed costs of a company is $3200. The variable cost to produce a widget is $25. CRP1. Set up…

A: Given that the fixed costs of a company is $3200 and the variable cost to produce a widget is $25.…

Q: Graph the function. y=(-3x)2/3 +3 O C. **** O A. Q O B.

Q: V5. 1 Determine the value of x using the diagram provided.

Q: Consider the quadratic function y=-x² +6x-2 (a) Graph the function on the grid to the right

A: The given quadratic function is y=-x2+6x-2

Q: х + 40, where 4 b. The temperature (in degrees Fahrenheit) can be approximated by the function c(x)…

A: For a function, y=f(x) , x is the independent variable and y is the dependent variable . Consider…

Q: Falling with a Parachute If an average- sized man with parachute jumps an airplane, he will fall…

Question

### Problem Description

Suppose you take a straight piece of wire measuring 20 cm and cut it to make two pieces. You then take one piece and make it into a square, and the other piece and make it into a circle, like in the following picture:

![Diagram showing a wire of length 20 cm divided into two pieces, 'x' and '20 - x', with one piece forming a circle and the other forming a square.](image_url_here)

### Questions

a. Write a function, $ A(x) $, that gives the total area of the circle and the square you make in this scenario.

b. What is the domain of $ A(x) $?

### Detailed Explanation

To solve this problem, we first need to use the lengths of the wire pieces for both the circle and the square.

1. **Dividing the Wire**:
- Let $ x $ cm be the length of the wire used to form the circle.
- Then, $ 20 - x $ cm will be the length of the wire used to form the square.

2. **Forming the Circle**:
- The circumference of the circle is $ x $ cm.
- Using the formula for the circumference of a circle, we have:
\[
2\pi r = x
\]
- Solving for the radius $ r $, we get:
\[
r = \frac{x}{2\pi}
\]
- The area of the circle, $ A_{\text{circle}} $, is given by:
\[
A_{\text{circle}} = \pi r^2 = \pi \left( \frac{x}{2\pi} \right)^2 = \frac{x^2}{4\pi}
\]

3. **Forming the Square**:
- The perimeter of the square is $ 20 - x $ cm.
- Each side of the square, $ s $, is:
\[
s = \frac{20 - x}{4}
\]
- The area of the square, $ A_{\text{square}} $, is given by:
\[
A_{\text{square}} = s^2 = \left( \frac{20 - x}{4} \right)^2 = \frac{(20 - x)^2}{16}

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Transcendental Expression$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

3. Determine the domain and range of the function y = 2c0sx
1. A swimming pool is being drained. The table below shows the volume of water, y, in cubic feet, after x minutes of draining. y 8850 8200 7550 6990 6340 Which equation can be used to model the function shown in the table? A. y= 650x +8850 B y= 650x +9500 C y = - 65Qx + 8850 D y= -650x +9500 ere to search SAMSUNG F7 F8 F10 F11 F12 @ क 000 00
2. State the domain of the function. x² -3x +2 a. y=- X-4
The path of a soccer ball can be modelled by the function h(d) = ‒0.1d2 + 0.5d + 0.6 where h = the height of the ball and d is the horizontal distance from the kicker, both in meters. How far from the kicker did the ball land? Answer step-by-steps.
MA.912.F.1.5 Date: Period: Callie and her friend Elena are reading through different novels they checked out from their school library last Tuesday. Callie's progress through her novel can be modeled by the function p(d) = -25d +318, where p(d) represents the number of pages remaining to be read and d is the number of days since receiving the book. Elena's progress through her novel is modeled by the graph below. АУ # Pages Left 400 350 300 250 200 * 150 100 50 (3275) (8,75) 2 3 4 5 6 7 # Days Part A. Which student's novel has more pages to read? 8 9 10 11 Part B. Assuming they both continue to read at a constant rate, which student will complete their novel first?
. Town MHF determines the amount of property tax (P) in hundreds of dollars as a function of thebuilding size (s) in 10 square meters.?(ℎ) = 5 √? − ³√3 + 5a. What property tax would you need to pay on an empty lot (no building)?b. Determine the average rate of property tax increase (per 10 square meters) for s = 2 to s = 5. c. What is the instantaneous rate of change of property tax for a building that is 100m²(s = 10)?