The area, A of 2 semi-circles separated by a fixed length can be expressed as a quadratic equation provided the perimeter of the shape, P is known: A = -ar² + Pr (1) Consider an application of this equation where a pool is to be constructed as shown below with the following dimensions: Figure 1: Top view of a pool design. a) Derive an equation for the perimeter of the pool, P in terms of 1 and r. b) Express the area of the pool, A in terms of 1 and r.

The area, A of 2 semi-circles separated by a fixed length can be expressed as a quadratic equation provided the perimeter of the shape, P is known: A = -ar² + Pr (1) Consider an application of this equation where a pool is to be constructed as shown below with the following dimensions: Figure 1: Top view of a pool design. a) Derive an equation for the perimeter of the pool, P in terms of 1 and r. b) Express the area of the pool, A in terms of 1 and r.

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: Rey's father is four times as old as Rey. Five years ago he was seven times as old. How old is each…

Q: 2. Solve each equation. Identify any extraneous roots: a) (x+3)2 – 1=X -1= x b) V3x +13 = X +5 c)…

Q: Consider the function y = x2 + 0.1x + 0.03 a) write in completed square form, b) hence write down…

Q: Given the equation (z - 13)+y? = 64, identify the center and radius. Do not enter any spaces when…

A: In this we have to tell the center and radius of circle.

Q: Consider the parabola given by the equation: f(x) : -x² + 12x – 8 %D Find the following for this…

Q: Q4) Find the y-intercept, x-intercept(s) and the vertex point for the parabola y = x2 + 6x + 5 then…

A: Given: Parabola: y=x2+6x+5 To Find: The y-intercept, x-intercepts and the vertex point for the…

Q: Sx dx 3 x2 ४

Q: a. x² +8x-3 = 0 Find the equation with following roots: -4+2i6

Q: Find the values that satisify the given equations: a) 16x2-9 0. x2 +4x-12

A: Solution of Equation: An equation is a mathematical statement formed by placing an equal sign…

Q: 02u at2 = ә2u аг 0x2

Q: Convert r= 3 sec e to its equivalent Cartesian equation.

Q: find the value of x

A: DE bisects BC BC = 5x – 3 CE = 2x + 25 From above given facts, it is seen that point E is on BC.…

Q: A seagull sits atop a cliff and spies a fish under the water. To catch the fish, the seagull dives…

A: The given equation of path is y=2x2-28x+90.…

Q: EXC :- solve By Gauss -Jordar NO (1) :- 2X1+2 X2 – 2X4 = 4 4X2 +2 Хз -4X4 — 6 -X2 + X4 = -4 -3X3 +…

A: Given equations are 2x1+2x2-2x4=4 .........(1) 4x2+2x3-4x4=6 ..........(2) -x2+x4=-4…

Q: User = }= * 3 – 5 2t to parameterize the equation: y t+ TI t²³ + +²2² +

Q: An historic, parabolic arch which provides a walkway under a building can be modeled by the 36…

Q: A ball is thrown directly upward from the top of a 25-foot-tall building. Its height is represented…

A: Given equation of s(t) = 25+20t-5t^2

Q: A chicken coop has been built 30 yards south of a farmhouse and is enclosed by a circular fence.…

A: We have to find the equation of the circular fence.

Q: could you please show the steps of how you obtained that rectangular equation? thank you!

A: As per the question we are given the equation of an ellipse in parametric form, and we have to find…

Q: Identify all three (distinct) solutions to the equation z3 = 27i. Write your answer in x + iy form.

A: Given equation is z3=27i we have to find the solution in x+iy form

Q: Write an equation (any form) for the quadratic graphed below: y = -4 -3 -2 -2 4 3 2 1 -1 -2 -3 -4…

Question

The area, A of 2 semi-circles separated by a fixed length can be expressed
as a quadratic equation provided the perimeter of the shape, P is known:
A = -лr² + Pr
(1)
Consider an application of this equation where a pool is to be constructed
as shown below with the following dimensions:
1
1
r
Figure 1: Top view of a pool design.
a) Derive an equation for the perimeter of the pool, P in terms of 1
and r.
b) Express the area of the pool, A in terms of I and r.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Worked out the expression for "P"

VIEW

Step 2: Solved second Part

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

e) If the pool shape is restricted such that the dimension, 1 is 1.5 m,
what will be the radius, r if the pool is to maintain its perimeter,
P of 8 m?

Solution

by Bartleby Expert

SEE SOLUTION

Follow-up Question

c) Hence, or otherwise show that A = -r² + Pr.
d) Find the radius, r and the dimension, I that maximises the pool
area for a pool perimeter, P of 8 m.

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

Find the foci for (x-6)² 9 + (y-7)² 25 = 1
b) Determine the type of the given equation: xxx +(x-2)²xy +XZyy=0
Q4) Solve two of the following: C) f tan³x dx
Could you help me with the following questions please? 1.Solve this parabola y = -2(x - 4)2 + 7 Vertex: Direction of opening: Max/Min value:  Equation of axis of symmetry: 2.Expand and simplify the following. a) (4x + 3)(7x – 1) b) 8(x – 1)2 + 4 3.Factor the following. b) y = x2 – 19x + 60 b) y= 4x2 − 24x − 28 c) y=x2 −81 4. Tasha invested $5000 for 30 weeks at 5%/a simple interest. a) How much interest was earned? 5.The height, h meters, of a basketball, t seconds after it is thrown is given by the equation: h=-5(t-1.7)2 +6 a) What is the maximum height of the ball? b) How long does it take for the ball to reach its maximum height? b) Find the area of the shaded region if x = 6 mm. 6.In a national park, a wolf population increased by a growth factor of 1.078 per year over a ten-year period, beginning in 1997. The formula P =124(1.078)n models the wolf population P after n years. a) What was the wolf population in 1997? b) What was the wolf…
6) Determine the constants A and B that make this equation an identity: 8. B (1- 4)(x + 4) x-4x+4
By completing the square, find the standard form of the equation of the parabola: y = x^2 + 6x + 7 B) Sketch the graph of the parabola:
A parabolic stream of water is spraying out of a hole in the floor two feet behind Veronica. The water is passing over her at a height of six feet. It then lands on the floor 18 feet in front of her. Write an equation for the stream of water.
Solve for r: 9x +237 4x + 172°