Answer:
The standard form of the equation of the circle is
.
Step-by-step explanation:
A circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center.
The equation of a circle in standard form is
where <em>r</em> is the radius of the circle, and <em>h</em>, <em>k</em> are the coordinates of its center.
When the center of the circle coincides with the origin
, so

We are also told that the circle contains the point (0, 1), so we will use that information to find the radius <em>r</em>.

Therefore, the standard form of the equation of the circle is
.
Answer:
See explanations for step by step procedure to answer
Step-by-step explanation:
Given that;
.f (x comma y )equals 8 x squared y minus 3 Confirm that the function f meets the conditions of the Second Derivative Test by finding f Subscript x Baseline (0 comma 0 ), f Subscript y Baseline (0 comma 0 ), and the second partial derivatives of f.
See attached documents for clearity, further explanations and answer
<u>Given</u>:
The equation of the circle is 
We need to determine the center and radius of the circle.
<u>Center</u>:
The general form of the equation of the circle is 
where (h,k) is the center of the circle and r is the radius.
Let us compare the general form of the equation of the circle with the given equation
to determine the center.
The given equation can be written as,

Comparing the two equations, we get;
(h,k) = (0,-4)
Therefore, the center of the circle is (0,-4)
<u>Radius:</u>
Let us compare the general form of the equation of the circle with the given equation
to determine the radius.
Hence, the given equation can be written as,

Comparing the two equation, we get;


Thus, the radius of the circle is 8
Answer:
All are 63
Step-by-step explanation:
m∠1 = 180 - 117 = 63 (linear pair)
m∠2 = 63 (alternate interior angle with ∠1)
m∠3 = m∠1 = 63 (isosceles triangle property)
Hope it helps :)
Please mark my answer as the brainliest
<h3>
Answer: 24 yards, choice D</h3>
There are 4 sides to this figure (trapezoid). The left slanted side and the right most vertical side, combined with the top and bottom horizontal sides, will get us the perimeter.
left slanted side = 5 yards
right most vertical side = 4 yards (see note below)
bottom side = 9 yards
top side = 6 yards
Add up the four sides mentioned: 5+4+9+6 = 9+15 = 24
note: the rectangle has opposite sides that are the same length. While the right most side isn't labeled, it is the same length as the left side of the rectangle, so both are 4 yards long.
Another thing I should probably mention is that we do not add in the interior 4 yard side. The perimeter is only the outer or exterior sides we care about. Think of it like we're trying to fence around some property lot and we don't want to subdivide the property up. Finding the perimeter will help us find the amount of fencing needed to surround the property.