The area of the square is greater than the circle: the area of the circle is pi(r)^2 while the area of the square is length times width. The area of the circle is about 12.5 while the area of the square is 16.

4 0

3 years ago

The center of a circle lies on the line y = 4x + 1 and is tangent to the x-axis at (−3,0) . What is the equation of the circle i

Hunter-Best [27]

Answer:

$(x+3)^2+(y+11)^2=121$

Step-by-step explanation:

Consider a sketch of the problem as shown in the picture, where:

Blue line is given by y = 4x + 1.
Point B is the center of the circle.
Point A is (-3, 0).

Since the center of the circle lies on the line y = 4x +1 and is tangent to the x-axis at point A, then its radius BA is perpendicular to the x-axis. To find the coordinates of point B, we must replace x = -3 into the blue line equation: y = 4x(-3) + 1 = -11.

So, we know that the center of the circle is at B=(-3, -11). And furthermore, the radius BA is of length r=11.

Since the <em>general equation of the circle</em> of radius lenght r centered at (h, k) is given by

$(x-h)^2+(y-k)^2=r^2$

then with h = -3, k = -11 and r= 11, the equation of our circle is

$(x+3)^2+(y+11)^2=121$

5 0

2 years ago

3x+4y+z=-2<br> 2y+3z=-8<br> z=-3

masya89 [10]

Answer:

z=-3 so 2y+3(-3)=-8, 2y-9=-8, add 9 to both sides 2y=1 divide both sides by 2, y=1/2, so 3x+4(1/2)+-3=-2, 3x+2-3=-2, 3x-1=-2, add 1 to both sides, 3x=-1, divide both sides by 3, x=-1/3

3 0

2 years ago

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