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:
2) 77°
3) 85°
4) 103°
Step-by-step explanation:
2) 77
3) 85
4) 103
Step-by-step explanation:
R = 6.5cm and r = 2.3 cm
area of the shaded region = area of the outer circle - area of the inner circle
= πR²-πr²
=π(R²-r²)
=π{(6.5)²-(2.3)²}
=π (42.25-5.29)
= 3.14× 36.96
= 115.866
= 116 cm²
The answer to this would be 6
Answer:
10% probability that the part has at least one flaw
Step-by-step explanation:
We have these following probabilities:
90% probability of the part being flawless.
8% probability of the part having a minor flaw
2% probability of the part having major flaws.
What is the probability that the part has at least one flaw
Minor or major flaws. So 8% + 2% = 10%
10% probability that the part has at least one flaw
