Completing the squares, the correct statements regarding the equation of the circle are given by:
- The radius of the circle is 3 units
- The center of the circle lies on the x-axis.
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
<h3>What is the equation of a circle?</h3>
The equation of a circle of center and radius r is given by:
In this problem, the equation is given by:
x² + y² - 2x - 8 = 0.
Completing the squares:
(x - 1)² + y² = 8 + 1²
(x - 1)² + y² = 9.
Hence the center is (1,0), the radius is 3, and the correct statements are:
- The radius of the circle is 3 units
- The center of the circle lies on the x-axis.
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
More can be learned about the equation of a circle at brainly.com/question/24307696
#SPJ1
Area of the canvas: 96 = 2 · W² + 2 · W L,
where W is the width and L is the length of a back and a top side. Two square sides have area W².
2 W L = 96 - 2 W² /:2
W L = 48 - W²
L = ( 48 - W² ) / W.
The inside volume of the shelter:
V = L · W · W = L · W²
V = W² · ( 48 - W² ) / W ;
V = 48 W - W³
We have to find the derivative:
V ` = 48 - 3 W²
48 - 3 W² = 0 ( for V max. )
3 W² = 48
W² = 48 : 3
W² = 16; W = √16; W = 4 ft.
L = ( 48 - 16 ) / 4 = 32 / 4 = 8 ft.
Answer: The length of the shelter for which the volume inside is maximized is 8 ft.
3 or 2.70. it may also be a fraction which in that case it would be 11/4
<h3>
Answers: x = 30 and y = 150</h3>
============================================================
Explanation:
For any cyclic quadrilateral (aka inscribed quadrilateral), the opposite angles are always supplementary.
One pair of such angles is A and C
A+C = 180
x+y = 180 is one equation to form
The other pair of supplementary angles is B and D
B+D = 180
y-45+2x+15 = 180
2x+y-30 = 180
2x+y = 180+30
2x+y = 210 is the other equation to form
--------------
So the system of equations we have is
Both equations involve 'y', with the same coefficient, so we can subtract straight down to eliminate this variable.
- The x terms subtract to x-2x = -x
- The y terms subtract to y-y = 0y = 0, so the y terms go away
- The right hand sides subtract to 180-210 = -30
We end up with -x = -30 which solves to x = 30
--------------
Once we know x, we can determine y by plugging it into any equation involving x,y and solving for y
Let's say we picked on the first equation
x+y = 180
30+y = 180
y = 180-30
y = 150
Or we could pick on the second equation
2x+y = 210
2(30) + y = 210
60+y = 210
y = 210-60
y = 150
Only one equation is needed. However, doing both like this shows that we get the same y value, and it helps confirm the answers.