Step-by-step explanation:
The equation of a circle can be the expanded form of
\large \text{$(x-a)^2+(y-b)^2=r^2$}(x−a)
2
+(y−b)
2
=r
2
where rr is the radius of the circle, (a,\ b)(a, b) is the center of the circle, and (x,\ y)(x, y) is a point on the circle.
Here, the equation of the circle is,
\begin{gathered}\begin{aligned}&x^2+y^2+10x-4y-20&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4-49&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &x^2+10x+25+y^2-4y+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &(x+5)^2+(y-2)^2&=&\ \ 7^2\end{aligned}\end{gathered}
⟹
⟹
⟹
⟹
x
2
+y
2
+10x−4y−20
x
2
+y
2
+10x−4y+25+4−49
x
2
+y
2
+10x−4y+25+4
x
2
+10x+25+y
2
−4y+4
(x+5)
2
+(y−2)
2
=
=
=
=
=
0
0
49
49
7
2
From this, we get two things:
\begin{gathered}\begin{aligned}1.&\ \ \textsf{Center of the circle is $(-5,\ 2)$.}\\ \\ 2.&\ \ \textsf{Radius of the circle is $\bold{7}$ units. }\end{aligned}\end{gathered}
1.
2.
Center of the circle is (−5, 2).
Radius of the circle is 7 units.
Hence the radius is 7 units.
Answer:
The measure of one interior angle of a regular pentagon is 108 degrees.
Step-by-step explanation:
Use a digital ruler.
Answer:
The curvature is 
The tangential component of acceleration is 
The normal component of acceleration is 
Step-by-step explanation:
To find the curvature of the path we are going to use this formula:
where
is the unit tangent vector.
is the speed of the object
We need to find 
, we know that 
so
Next , we find the magnitude of derivative of the position vector
The unit tangent vector is defined by
We need to find the derivative of unit tangent vector
And the magnitude of the derivative of unit tangent vector is
The curvature is
The tangential component of acceleration is given by the formula
We know that and 
so
The normal component of acceleration is given by the formula
We know that and 
so
The equation of the profit function is 300x - 3600
Total cost function C(x) = 74x + 3600
Total revenue function R(x) = 374x
The profit function is the difference between the total revenue and the total cost and this will be:
= R(x) - C(x)
= 374x - (74x + 3600)
= 374x - 74x - 3600
= 300x - 3600
In conclusion, the equation of the profit function is 300x - 3600
Read related link on:
brainly.com/question/24495359
9 1/2 = 19/2
(29/5) / (19/2)
When changing division to multiplication, flip the number (right hand side).
(29/5) * (2/19)
58/95
